Welcome to Access to Trader, the number one community for those who are committed to taking control of their trading in order to achieve success, profitability, and longevity. Thank you for joining us. Here's Dan Shapiro to help you find your edge, master your process, and own your future. Hey, guys. Good evening, everybody. Welcome to another edition of the Access to Trader.com weekend update show. Once again, it is five o'clock on Friday. Again, dad life, right? A million basketball games this weekend, only for my daughter. My son kind of tore up his calf a little bit, so he's kind of sidelined for a couple of weeks, but again, still a part of dad life. So let's talk about the markets. So today ended the quarter, right? Today ended the third quarter. And the numbers are pretty ugly, right? Very, very ugly numbers. Let me just kind of run down for you for the quarter, right? For the quarter. Let's see here. Let's see here. Let's see here. Let's see here. Well, how about this? For the month, the S&P 500, right? Down 9.3%. That's a lot. The Nasdaq down about 10.5% and the New York Stock Exchange tumbled about 9% for September. I mean, these are big numbers. And we've been talking about ever since, again, we lost the 50-day moving average on the Nasdaq 100 and pretty much on everything else. We lost it on that CPI, and all we've been doing is just going lower, lowest, lower, lowest, lower, lowest. And we've been talking about the sell bias nature of this market. You start looking at earnings, and you start looking at all these different groups that are coming out with earnings. Like, for example, today, you saw a pretty good display of weakness everywhere. You have Nike, foot and apparel, you have Carnival, right? You have Carnival, cruise ships, and you have Micron, which is the semiconductor space with the whole story of semiconductor shortage. But it really does show you this is not isolated to like tech technology. This is isolated to everything else. So we've been watching these videos. I've been highlighting the most important group in my opinion, right? Not from the trading aspect of it, not even from the investment aspect, but from kind of Main Street. Now, it's the most important thing, and that's the consumer cyclical. Basically, the products that you need, right? You need that you use every single day subconsciously that supposedly is not putting a dent into your wallet. It doesn't make a difference what your level of income is. It's those names that you turn around and you say, well, I really need shampoo. I really need razors. I really need shower gel, whatever the case may be. And those are the names that are getting hit. And those are the names that are being sold very, very aggressively, right? Procter and Gamble, Colgate Palmol. I mean, these are massive moves. Coca-Cola, right? You have Kellogg, which I really like setting up into next week. Names like General Mills that had a really nice move or just another day away from getting hit. So you're seeing all these, again, it goes on and on. You got Estee Lauder, you got Kimberly Clark, right? All these names that are consumer cyclicals, they're just really, really dying out. A name that we talked about on last night's video, Pepsi, right? We talked about Pepsi. Pepsi, if Coke already broke down, guess what? Pepsi is going to break down as well, and it did that today, and it looks like lower prices coming in for its future. But more important of what is happening right now, the question is what happens down the road? Again, this is the most dangerous part of where a new trader is focused on or at least trying to be focused on. I've traded several bear markets that lasted for two, three years, right? If you guys remember, after 2000, right? After the 2000 bubble came 9-11. From 9-11 all the way up to 2003 was a really, really hard trading environment. Again, do I call it a bear market?  You go from 2007 to 2009, 2007, 2008. I don't know if there was math involved in this update, but carry the one, right? That's almost three years as well, right? From 2007, 2008, all the way 2009. That's almost three years worth of selling pressure as well. Again, heavy catalyst, global potential Armageddon. So that was validated. And here we are, right? Here we are. You know what's going on with the Fed. Again, there's no reason to kind of go through what the Fed is doing and inflation. Is it transitory?  We are where we are, right? And that's the bottom line. So always remember, the market doesn't need to do anything, right? There was some periods of time and you could, you know, you could go back on the 100-year chart and you could turn around and go, well, it doesn't make a difference, right? The market will be okay eventually. Yeah, eventually it will be. Now the question is, can you be okay? Can you stay solvent when the market becomes quote-unquote okay again, right? So there's no guarantee ever that the market has to go up when you want it to go up, right? And when you look at what the S&P did this month, right? This is the, we had the worst month, quote-unquote, March 2020. What was March 2020? Remember the pandemic broke out? Well, this month was worse than the pandemic, okay? So the numbers are staggering. They're very aggressive.  And I asked somebody a question a couple of years ago.  I don't short stocks. I like buying breakouts. Cool, right? So my question to them was, well, what do you do when the market goes down? And their answer to me was, well, what do you mean? That's my point. A lot of traders started into what do you mean? Stocks only go up. What do you mean? We're in the mean generation. Stunks, right? GameStop, this one, that one, right? We've never seen. We've never seen a down market. Stop talking about this, Dan.  We don't want to talk about no down market. The market's going higher. And we love a bull market. We love a bull market. It feels good. Everybody's more attractive. Everybody's taller.  Everybody's happier. But unfortunately, again, like we've been talking about for a long, long time, gravity's real, right? Technical damage is real. There's other aspects of trading, right? That there are geopolitical, geopolitical. And now we're seeing the financial aspect of it. Taming inflation. That is not going to be a pretty picture for a very long time, but not from the point of the trading aspect from the main street aspect. And again, if little Johnny asks his mom and said, mommy, mommy, mommy, can I get that box of frosted flakes? And mommy says, no, I can't. We can't buy that. We're not asking for a Lamborghini for God's sake. We're asking for a box of, and that's where the problem is. And slowly but surely, stock prices are starting to reflect that and have been reflecting that for quite a while. Again, if you look at any consumer cyclical stock, you could possibly see that. The question is not to figure out when all this bad dream goes away. And again, it all depends on who you talk to.  I love a bull market. Who doesn't? We don't need a bull market. And that's the most important part. Stocks are very, very aggressive to the downside. The same way you look at a chart that's breaking out is the same way you look at a chart that's breaking down. And it's a little bit different, right? It's a little bit different trading, because again, there's less market participants on the way down. There's a little bit less liquidity on the way down because of the less market participants. But the good news is stocks go down a lot faster and a lot more aggressive. And the one thing, and again, I'm going to reiterate this to newer traders, okay? There's no such thing as a breakout during a bear market, right? There might be a stock that's green on the day and it might have its 15 minutes, maybe even two hours of glory. But the end of the day, no matter how strong that stock was or is, what you think it's going to be, the laws of bearishness kicks in and that stock doesn't become strong. All you got to do is look at any stock that was strong today, right? Snow today was very, very strong, right? It was very, very strong. If you look at the 60-minute view, it was strong. It was very, very strong, not so much, right? If you look at any stock, any stock, it doesn't make a difference. Literally any stock today that was green on the day that looked strong didn't end up strong and that's the whole point of a bear market. And again, like I said on every single video, you're not going to see the market go straight down, right? There's definitely up days. There's definitely dead cat bounce days. Those days, like I've been talking about in every video, I have zero interest. Yeah, you'll get your little scallops, the stuff, the other thing, but you want the meat and potatoes on the down days and that's the most important part.  You guys remember that, right? It took like, you know, even today's action, you saw moves to the upside on snow and maybe a name like meta, it took like the whole army, the whole brigade, right? The whole, you know, literally everything for this stock just to move up a dollar before it crashed, you know, two, three hours late and that's the whole point. The value is always to the downside and the one thing that we've been kind of talking about all the time, the event rate, right? When the market is good, okay? And this is something kind of an important lesson especially for new traders. When the market's good, when a stock comes out with earnings, unless they use the word chapter 11, the stock is probably going to perform, right? Because there's so much you for it. Again, case in point, this past quarter, Microsoft, Google, and a whole slew of other tech names, they all guided down. They all missed the top and bottom line and guess what happened? They rallied, right? We remember this whole area here, right? They all rallied within this month, okay? When the market is bad, it doesn't make a difference what kind of good news you have. It doesn't make a difference. It's going to sell everything and ask questions later. It's just kind of the reality. The majority names, no matter what the event, no matter what the catalyst is going to sell. So case in point, right? Let's talk about Tesla. So if you've been watching the video now for the last, just over this week, we've been talking about, we've been talking about this AI event, which I don't know what time it starts. It's right now, it's Friday. It's five o'clock Eastern time. I think at some point it's coming out some sort of news. Maybe they've got some robot or something. Sounds cool, right? It absolutely sounds cool. But again, if you're watching this video for the first time and you haven't watched any prior videos the last few days, there's been a lot of institutional sell bias on the stock. Not just because people hate Tesla. People don't hate Tesla, right? There's a lot of people who don't understand the technology or hate on Elon or hate on the car. We love Tesla, right? We love it. Again, upside, downside. We love the car. We love the boring company. We have the flamethrower, right? In Halloween, I'm going to use the flamethrower on my mother-in-law. Right? So we love all that, okay? But the one thing the market goes based on what we just talked about when an event happens is the market doesn't care. So the AI event starts up at some point this afternoon. There's always, I think there's also some sort of inventory, excuse me, the deliveries this weekend. And let me say this much, right? There's a high probability and also institutional money flow. If you guys have been watching this video, they've been betting nonstop deep out of the money puts this whole week. There's not a lot of, there's not a lot of, there's not a lot of optimism, right? At least from institutional money flow that this AI is going to change something that the world is seeing. Again, I could be wrong. I could be absolutely wrong. But I will say this much, okay? Nothing is a buy into the event, right?  It's closing at the bottom of the range. And all I know is, I don't care about an event. I don't care about anything else. I don't care about the deliveries. I don't care about anything else, right? Anything. Anything in the world. The only thing I care about is this channel right here going into Monday session. So if they release their event and they release their robots and everything else in, you know, in the world, doge shit, doge coin, whatever, anything, any news, right? The point is, if they sell off that news, okay? And they start violating this bottom channel here. The only thing I know is there's 25 points of downside. That's all I know, right? So we don't know about deliveries, mililaries, anything else in between. We know technical analysis. We survive, breathe, eat, fart, everything in between about technical analysis. Not the news. It's not what the market says, right? It's how the market trades off that news. So if there is, right? If there is some sort of good news and they do gap Tesla on Monday, I am not looking for a gap and go.  And if this bottom channel, right? If this bottom channel starts getting violated, yeah, you can see how much room you have downside. Here's the crazy part, right? There are so many kids in the gallery. If this stock actually goes higher, guess what? The worst case scenario, we buy stock. So scary, right? That's exactly what happens, guys. Have an opinion.  That's how every thesis is built. And we don't do something unanticipation. Again, we could be having this conversation Monday morning. Hey, can you believe Tesla went up 20 points today? Hell, was I wrong, right? We don't care about being wrong. It's not a popularity contest. It's not about clicks and likes and shares and all that nonsense. Smash the like button, bro, right? It's not about that. It's all about taking data and trading off that data technically. There's no anticipating. There is no positioning overnight ahead of an event. It's all about what happens next. And if you look at the surface, if you look at all the data that's been consumed in the stock over the last week or so, then yes, the institutions are betting against the event. I am looking at the bottom channel here and all I care about, right? I don't care if the stock is here, here, here. All I care about is if the stock continues to get below this channel here and then you have a lot of room to the downside. So it's very, very important to understand. Again, we all love Tesla, right? Beautiful car, great trading stock. We love a good bull market because it's nothing crazy than Tesla. But guess what? There's nothing crazy than Tesla to the downside as well. And that is at least where the value is going to be. So going into this week, again, you've got to start looking at a bigger picture, right? You have a potential move all the way down to the 64 level on the Qs. If you look at the weekly view and this is where you know, this is where you know you start looking at a bigger picture because you can't even see the chart anymore, right? We closed below this trend line that started a long time ago, below the trend line for the first time in a long, long time on the Qs, right? If you look at the spies, spies did, well, they basically stopped right on the trend line. And if you look at the IWM, right? They are below this monthly trend line. So that's not a good thing. So the only way, guys, always remember this, the only way stocks are ever going to go higher, they have to take out the previous channel, okay? We had that opportunity on Wednesday and the bulls failed and that's the most important part. And yesterday, right, yesterday they couldn't get above the previous days high. And today, right? And today, wait, what channel? This is IWM. I know it looked weird. Here we go. Ah, there we go. Much better, right? So two days ago, they had a chance to get above the channel and they didn't confirm. Yesterday, they took out this whole channel's low and today we took out the previous days low as well. And unfortunately, again, if you are a permeable, I wish I had some better news for you. But again, guys, again, this is the greatest opportunity to learn how to trade. There's a big difference between a trader and a person who buys stocks in the bull market. It's very, very important to understand the difference. And until you can call yourself a trader, don't you have to learn from both sides of the market? Again, it doesn't mean and it doesn't dictate that the market's going to collapse. Nobody's talking about Armageddon. The market's going to crash. All this is a normal cycle of buyers and sellers. And unfortunately, at least for the permeable, the sellers are the ones who are in control. So that's it. That's it, guys. So look for value. Pepsi I like for next week to go lower. That looks really good. Amazon is setting up for lower prices. You can see the bottom of the range here. Very, very close. Very, very close to getting hit. So keep an eye on that. Let me see. Let me give you guys a couple more ideas for next week. Let me give you guys a couple more ideas for next week. I like Kellogg, right? Again, the whole consumer cyclical thing. I like Kellogg below this channel here. I like Archer Daniels Midland, right? Weird names, but again, that's consumer cyclical. ADMs and ag stock, food, all that crap, right?  So look how tight the channel is, right? Looks good as well. Abbey got absolutely murdered today. Right? Look at Abbey for next week. Again, look at the weekly chart on Abbey. Right? Look at that weekly chart on Abbey. Oh my goodness. Look at this. It's such a pretty girl. Would be the prettiest girl at the ball, right? Look at this. Gorgeous. That's it, guys. Have a great week, everybody. Stay safe. Continue to work. Keep the faith. It'll click, right? It'll click, but you have to have the ability to trade both sides of the market and make unbiased judgment based on technicals. Guys, God bless, and I will see you all on Monday.


I have yet to see this clip, and I know I'm super late to the party on this, but just the synopsis here from Bad Stats really has me intrigued. So Andy Noe asks Jordan Peterson how psychology can explain why Auntie Fa is so evil and bad. Jordan Peterson says it's revenge against God for the crime of being then he starts crying. I'm genuinely confused by this. I don't even know how to process this paragraph here. There's a lot going on. This is only a one minute and ten second clip, but I feel like this is going to be a bit of a beast to unpack. So without further ado, I will let them talk. And yeah, and for those of you who are unaware of who Andy Noe is, Andy Noe is a fascist journalist.  So he doesn't like Auntie Fa because he is very explicitly pro-fa. So I love how he's going to try to get Jordan Peterson to explain what's going on in someone's head when they're against fascism. I don't know, Andy, they're normal. I would assume that most good people are against fascism. If that's even the context of the way that they discussed this, but based on the wording here. Anyways, I'll shut up and we'll watch it. I'm really excited about this. I wanted to ask you about your knowledge, your background, your clinical experience. What is the psychology of this mob violence? When I see it, I don't even recognize some of these. They seem animalistic is what I mean. No, they're worse than animals. They're worse than animals because animals, they just kill to eat. You know, human beings, they have a twist in them that makes them far worse than animals when they really get going. Well, I think you really want to know what I think? I think it's revenge against God for the crime of being. What does that even mean? Okay, so we're talking about the mob mentality when it comes to political groups. In this instance, Auntie Fa, because Auntie No has made it his mission to condemn people who don't like fascism. In other words, people who are normal. And Jordan Peterson's response is, it's a crime against God for being... I don't even know where to begin to break that down. To get going. Well, I think it's... I think you really want to know what I think? I think it's... It's like he's like, you really want to know what I think? I'm going to have a really hot take right now, so here we go.  Against God for the crime of being. I don't even know what that means.   How do people take him seriously? I genuinely don't understand why this person is popular. I get the whole self-help thing, but I feel like he needs help himself, right? I can help him. I'll give you some advice. I've got 12 steps. Clean your room. That's number one. Stop being so overly emotional. Chill out. Smoke some pot. Don't do the whole all meat diet thing, because that's not good.  Stop surrounding yourself with reactionaries. I don't know.  That's really what I think. Wow, so profound. Cain and Abel. It's like, oh, Abel's your guy, God. How about I take him out in the field and beat him to death?  Yeah, God. Well, God, how do you like that, God?  I'm an Abel person, God. I genuinely am confused. I remember the story of Cain and Abel when I was indoctrinated into Christianity when I was young, and I don't remember the specifics. I know that one of them killed the other one. I actually don't even remember more than that, but one of them killed the other. But, you know, you can be like, you're okay.  How about that, God? How do you like that? I just, I feel like all of this is extremely incoherent, and I'm trying to be a little bit more deeper, go below the surface here and try to extract some value out of what he's saying.  Like, what's the point? What's the main takeaway from this? At this point, I don't know. We'll watch it again, right?  But we'll watch it again, but I just... So, Cain killed Abel after Abel was said to be the better brother. Okay, thank you for the refresher. It's been a while since I've read the story of Cain and Abel, but okay. You feel about that? The sacrifices went unrewarded. Yeah, it's like... Yeah, that's what it is at the bottom of the hell of things. Why did that make you cry? My dude, that didn't make sense. Why are you crying? The way he transitioned to crying, and like you could see he was trying to fight back tears.  Okay, we'll watch the whole thing again, right? Because I keep pausing it. But we'll watch that part again.  How about I take him out in the field and beat him to death? How do you feel about that? All my sacrifices went unrewarded. Yeah, it's like... Yeah, that's what it is at the bottom of the hell of things. Crying? Why are you crying?  Why is he... I don't know why, but I feel like it's kind of mean that I find that funny, but... It's just so weird.  So I'm gonna make myself cry because of this point. You know, when I think about God and Cain and Abel...  We should watch that, by the way, is what the hell we're gonna do without men. Let me pull that up. I'm gonna... Listen, I promise you, we're gonna watch it one more time. I'm not gonna pause it once, okay? I will chop off my fingers if I press that pause button. But as I'm finding that, I will queue up the clip where he infamously says...  Because I think that's honestly a banger as well. That's like his greatest hit. But oh my God, the laughter is killing me. Based on your knowledge, your background, your clinical experience, what is the psychology of this mob violence? When I see it, I don't even recognize some of these... They seem animalistic is what I mean. No, they're worse than animals. They're worse than animals.  Human beings, they have a twist in them that makes them far worse than animals when they really get going. Well, I think it's... I think, you really want to know what I think? I think it's revenge against God for the crime of being. That's really what they think. It's Cain and Cain and Abel. It's like, oh Abel's your guy, hey God. How about I take him out in the field and beat him to death? How do you feel about that? All my sacrifices went unrewarded. Yeah, it's like... Yeah, that's what it is at the bottom of the hell of things. Does that make me a bad person but I find it funny that he's crying?  It is objectively funny that he's crying at that because what he's saying doesn't make sense. And speaking of him crying, so I don't know what the context was for this but he talks about toxic masculinity and he starts breaking down into tears for some reason.  I don't get why he cries so much. I feel like I'm a good enough person to where I should in theory feel bad at anyone crying but when he cries it makes me laugh because it's so absurd. He cries over the weirdest things. We've met some of your fans and we got the impression they were all meal fans, the ones that we talked to and that they were struggling with their manhood and that you give them this message that it's okay to be a man. It's not okay, it's necessary. He's alright like just from the jump. He's about to burst out in the tears.   You look around the city here you see all these buildings go up, these men they're doing impossible things, they're under the streets working on the sewers, they're up. What are we gonna do without men? Who's gonna fix the sewers?    I just, I, why are you crying? Why are you crying? That's so weird. I don't understand why you're crying at this already.  Power lines in the storms and the rain. When I see them working with their bulging biceps and their hot uniforms with their cutoffs and their booty shots I genuinely I want to interview him.  This impossible infrastructure functioning this thing that works in a miraculous manner they work themselves to death and often literally and the the gratitude for that is sorely lacking, especially among the people who should be most grateful. You see university professors especially of the social justice bent who are among the most protected and privileged people that the world has ever produced they take everything they have for granted failing to understand entirely that there's a massive infrastructure of unbelievably hard working solidly laboring working class men breaking themselves in half on a regular basis making sure that everything that always breaks works and so a little gratitude for that is in order and it's very useful to tell everyone not just men that they have I just have to point out that he's trying so hard to keep it together and really the second this camera cuts like that the tears are streaming down his face I just don't know that I've ever seen an adult who talks about like masculinity and stuff cry this much and I feel like it's almost toxic masculinity for me to make fun of him for crying but I'm sorry I don't care this dude is I just I don't get the tears what's what the water works and I think that he's not faking it I don't think that he's being insincere I think he's actually thinking that in his brain he's saying something so profound that it's moving him to tears I just don't think that it's warranted right men crying is perfectly normal we're human beings we all cry we eat shit and sleep nothing to be ashamed about but like I don't know why you're crying here it seems like not the appropriate situation to cry in I just I'm so confused by Jordan Peterson an important role to play a necessary role and that if they act properly and honestly and forthrightly that they can put their lives together and they can help their families and they can make their communities better and that that's not toxic masculinity that appalling phrase it's what keeps the world going round if we had any sense we'd understand that instead of doing everything at every possible moment to label what we have in the west as oppressive and patriarchal and fundamentally predicated on power I don't think I've ever realized there's an ambulance in the background it just adds to the ambiance it just makes it so much better insane propositions holy shit what a psycho dude it's like yeah that's what it is


Hello, in this lecture, we're going to work a problem dealing with treasury stock. We're going to have the information over here on the left-hand side. We'll post that information to a table on this section. Then we'll record the general journal entries in this blue area here. And then we'll see what happens by posting those general journal entries to a trial balance format so that we can see a quick outline of what the journal entries would do in context with a set of accounts on the trial balance. So let's take a look at the trial balance at this time and see what we have and then go back to the problem. We've got a simplified trial balance, we've got cash as our only asset right now. We have the liabilities on the payables and the common stock payable. And then we have the equity accounts for this world where we will be spending some time working with the treasury stock, which is a part of this equity section for a company. Then we've got the revenue and expenses. We don't have any revenue and expenses at this time for this problem. We know that we are in balance by the fact that the debit's positive numbers minus the credit's negative numbers adds up to this zero down here so that zero indicates that we are in balance. No net income at this time. Then we have the assets lined up here, the liabilities and the equity on this side so we can see that we are in equation in balance on the accounting equation as well. Alright so let's take a look at the problem and see what we have. So first off it says we're going to purchase treasury stock, number of shares we're going to purchase $5,000 and the cost will be $25. So we're going to purchase our own treasury stock. So if we think of the calculation on that what's going to happen here is that we will be purchasing 5,000 shares so I'm going to do this calculation right here, 5,000 shares is what we will purchase of our own treasury stock that is outstanding. We're going to purchase those for $25. Now how did we get that $25 number? That's basically going to be the market price that we're going to pay for our stocks to purchase them back. So we're going to multiply that out. That means that this equals the 5,000 times the $25 which means that we are going to purchase them for $125,000. So then let's take a look at what the journal entry would look like for that transaction. I'm going to scroll over here and take a look at our chart of accounts. First question generally is cash affected and yeah cash is affected. We are purchasing our own treasury stock. So our own treasury stock is outstanding trading and we are purchasing it back for cash. Cash has a debit balance. We need to make it go down. Therefore we're going to do the opposite thing to it which in this case would be a credit. So we're going to credit cash. So I'm going to copy cash and right click and copy cash going to put that on the bottom. What we could put the date here as well. The date should be 1-1 and we're going to put it on the bottom from the date because the credits traditionally go on the bottom. Right click. I lost it. I'm going to copy cash again. Copy cash. Put our cursor in the bottom H-3. Right click and paste 1-2-3. So just the values only in there. We could type that in there as well. I'm going to put this number. This is how much we're going to pay. I'm going to put it in there with a negative for this worksheet to represent the negatives with negative numbers. The credits with negative numbers in this worksheet. So we say negative 125,000. That's how much we will pay. Then we're going to have a debit for 25,000 as well, 125,000. So we have 125,000. What will that debit be? It will be treasury stock. So note that this is very similar to purchasing any stock where we would debit the stock and credit the cash if we purchased stock. The treasury stock note where it's located on the trial balance. It's over here in the equity section. It's not an asset. We're not buying someone else's stock. We're buying back our own stock. However, the transaction looks an awful lot like a normal transaction when we would buy stock, but the difference being that the treasury stock will be down here in the equity section. So keep that in mind. We're going to copy the treasury stock. That's what the debit will be. I'm going to put that in H2, right click and paste 123. All right, we're going to post this out now and see what happens in context to our trial balance over here. So we're going to post the treasury stock to the treasury stock in the blue area on the trial balance. So we are in N12. N12 equals going to post this 125 and see what happens should go up in the debit direction to 125. Note that it's in the equity section and it has a debit balance. That means it's kind of like a contra equity account then. Why? Because most equity accounts have credit balances, as you can see, and this one has a debit balance. So it's the opposite contra to the norm. And therefore it's going to bring down the equity section and be a contra equity account. We're going to post the other one to N7 in the cash area. So we're in N7 equals we're going to point to that 125. That's a credit. This is a debit. Those are opposites. That's going to make the cash go down. So that puts us back in balance here and we were posted that first transaction. Now of course we have treasury stock on the book at 125. We could sell that and we are including there the 500, the 5,000 shares. Next transaction we have on N12, declared dividend per stock holder of $2. So $2 per share dividend is what we will be declared outstanding as of this point in time. So let's think about the journal entry when we declare the dividend. So the first question we have is generally is cash affected? And in this case it is not because we haven't yet paid the dividend. We've declared the dividend but we haven't yet paid it. When we do pay the dividend of course it will be coming out of cash. So therefore what we have then is a form of payable at the time of declaration and that is going to be a liability account. It's going to be something that we owe. So we have a common dividend payable being the liability for the dividends that we have declared as of the time we have declared them. We have an obligation to pay them and therefore we need to record the liability as of that point in time. So the date here will be, I'm going to skip a line and put our date on N12 and we're going to record a liability. Note that liabilities have credit balances. We need to make it go up. We owe more money to people because of the declaration that we have made the company owes money. Therefore we're going to do the same thing to it as what it is. They have a credit. We're going to make it go up by crediting the dividends payable liability account. So I'm going to click on L9, right click and copy that. Put our cursor in H6 which is under the date. We're going to put it on the bottom again. Right click and paste it 123. Then we'll be over here in J6 and we're going to say this is going to be, now we're going to have to do the calculation for the dividends that will be outstanding. Now note that what we have, we have the $50,000 at 10, $500,000 worth of shares. We can see that in here, the $500,000. If we divide that by the par value, we know that there's $50,000 shares included in that number. However, we also have the Treasury stock here that we purchased back and it's not on the books at the par value. It's on the books at what we purchased it for. So what we need to do then is note how much is issues and outstanding. We got the $50,000 that are originally issued but we bought $5,000 of Treasury stock back. Therefore, what we have is the $50,000 minus the $5,000 because we're not going to pay dividends to ourselves. The company doesn't pay itself dividends, $45,000 shares that we're going to pay dividends on and then we're going to multiply that times the $2 and that'll give us the $90,000. So let's do that calculation again. I'm going to do it here. I'm going to put a negative here to make it a negative number. It's going to be the $50,000 originally outstanding minus the $5,000. I'm going to put brackets around that because of the order of operations and then multiply that times 2. So all we did, all we're doing there here's the formula is saying the $50,000 minus the $5,000 gives us $45,000 times 2. We're going to put brackets around it because I want us to do the subtraction before we do the multiplication and we made it a negative in this case to flip the sign so that it would be a credit on our worksheet. Then we're going to debit something for $90,000 and that debit will be for the retained earnings in this case. What is a dividend? A dividend is the payment of the retained earnings, the accumulation of income in the company to the owners. So the retained earnings is going to be down here. That represents the amount of money that has accumulated, which we are now going to pay out to the owners in the form of dividends. Note that it has a credit in it and we're going to make it go down. So we're going to make it go down by doing the opposite thing to it, which in this case is a debit. So we're going to copy that. I'm going to put my cursor on the retained earnings, right click and copy. Put that up here in H5, right click and paste 1, 2, 3. So here we got our transaction. We're going to post this out. We got the retained earnings at 90. There's the debit. Here's the retained earnings down here. We're going to post it here. We're going to post it into column N. So in column N, we're going to say equals 0.2 to the 90,000 and this is a debit. This is a credit.  Then we're going to do this for the second account being the common dividends payable here, which is going to be represented by this account here and we're going to post that to the sale of N9. So in N9, we're going to say this equals 0.2 to the 90,000. That's going to make the liability go up in the debit direction and put it back in balance down here. So we'll say enter goes up. We're back in balance down here and we can take a look at the next transaction. So next transaction is going to be on 228. And then in this case, we're going to, in this transaction, we're going to pay the dividend declared. So we're going to go over here and say on 228, we're going to pay the dividend. So if I take a look at the trial balance, then we could ask our basic question on this one, is cash affected? Yeah. So we paid with cash. So cash has a debit balance. We're going to make it go down. So we're going to do the opposite thing to it, which in this case would be a credit. So we're going to copycash them in L7, right click and copycash, put our cursor under the date. So it's in H9, right click and paste it 1, 2, 3. And we're going to pay the dividend. So we're going to pay this 90,000 that we just put up here. So I'm going to make that a credit in J9, negative 90,000. Then we're going to debit something for 90,000, 90,000. And what are we going to debit? We're going to debit that declaration that we had just made in the liability here. So that 90,000 that we said we obligated ourselves to pay, we are now paying. That 90,000 is a liability with a credit balance. We need to make it go down to zero. Therefore we're going to do the opposite thing to it, which in this case would be a debit. So I'm going to copy that. Put that on H8, right click and paste 1, 2, 3. All right, let's post this out now. So we have the common stock dividend payable debit. And then we have where we're going to post it here. Note that there's something in it already. And so there's something in it. Of course, J6 is what is in it. So we're going to double click on it, go to the end of it and add plus the 90,000 here. This is a debit. A credit is currently in there. Those are opposites making it go back down to zero. We're going to do the same thing for cash. So we're going to post the cash. Here's cash. Here's cash in the trial balance. Here's where we're going to post it. It's NN7. We're going to double click on that. Go to the end of it and say plus and then point to this 90,000. And of course, this is a credit. This is a debit. Those are opposites making this go down, putting this back in balance down here. All right.  We're going to look at the next transaction. So the next transaction is going to be on 75 sold treasury stock for the amount in the amounts of 1005 shares at a sales price of 30. So now we're going to sell treasury stock back the treasury stock that we purchased. We will now sell back and we're selling it for the sales price. We're going to do the calculation. We're going to have a gain or loss again, very similar to if we had actually purchased someone else's stock. We're going to do a similar calculation. But we are, of course, selling our own stock back to the market. Note that this is going to be different than when we originally issued the stock. We're selling treasury stock, which is stock that we purchased back in our selling, not stock that we are originally issuing out to the public. So we're going to post this out. It's going to be 1500. And the cost or sales price, in this case, the sales price is going to be 30. The amount in dollars is going to equal the 1005 shares times 30. So that's going to be the sales price. Now let's calculate the cost. And the cost is going to be the same, 1005 shares. And the cost, remember, was back in this transaction, we bought 5000 shares at 25. So the cost is 25 per share, because we're selling part of this 5000 shares. And therefore we're going to multiply that out. This equals the 5000 shares times the 25. That gives us the 37.5. If we subtract that out, that will give us the gain or loss. We're going to say this equals the 45,000 sales price minus the 37.5 and enter. We should also be able to come up with this 7.5 by doing this. We can say the 1.5 and we can take the difference in the sales price versus the cost per share, which is $30 minus $25. And so if we take the 1,005, 1.5 times 5, we will get the same 7.5 here. Let's think about that in terms of a journal entry. So we're going to be over here and we are now on 7.5 and we're going to post this journal entry. First question we'll have, let's scroll back over here. We can see our chart of accounts on this first question. Is cash affected? And we're going to say, yeah, cash is affected. We sold our treasury stock for cash. And therefore cash has a debit balance. We're going to make it go up.


Item number, SCP-446, Object Class, SAFE. Special Containment Procedures, SCP-446 is to be kept locked in its case and only removed for testing. Any clothing and accessories must be removed from SCP-446 when not in use. SCP-446 in its normal state appears to be a Caucasian female, early 20s, brown hair, 17.78 centimeters at its longest point, unusually bright blue eyes, light skin with a tattoo of the Marshall, Carter and Dark logo on its lower back, 1.75 meters tall and weighing 52.16 kilograms. SCP-446 is anatomically correct, at least on the outside. All physical characteristics are consistent with the living human, including skin tone and texture, eye color, and clarity of the sclera, even body heat. SCP-446 does not respond to any communication, however, and also does not breathe or exhibit a pulse. SCP-446 is normally stored lying on its back, inside a long aluminum box with a hinged lid. SCP-446 in its storage box were discovered in by Foundation agents. The storage box itself is unremarkable, aside from a plain white label listing SCP-446's clothing sizes. When the agents attempted to lift SCP-446 by the shoulders into a sitting position, SCP-446 responded to their touch by sitting upright on its own. A gentle push on its shoulders from the front encouraged it to lie back down. Further coaxing can compel SCP-446 to stand up on its own, and it will remain standing until downward pressure is applied to the top of its head, encouraging SCP-446 to sit again. SCP-446 generally does not move without prompting of some kind, although its eyes will follow the nearest person, and it will make eye contact if possible. Moving and posing of SCP-446's limbs is also possible. Once moved into position, they will hold the established pose indefinitely. This works even in cases where delicate balancing would be required for a person, such as standing on one foot, or even one hand. Attempts to push SCP-446 over have exactly the expected effect. It makes no attempt to preserve its balance, and simply falls over. A medical examination of SCP-446 revealed additional information. See Document 4461A for details. Incident 4461, SCP-INVOLVED, SCP-446, Personnel-INVOLVED, Guard- Dr. Sunderland, Date, 9-2-2010, Location, Storage Room 6, Site, Description. In the spirit of modesty, SCP-446 was initially stored clothed in a standard Class D personnel uniform. A guard later investigated reports of a thumping noise in Storage Room 6 where SCP-446 is kept. SCP-446's case was found to have moved several inches from its normal resting place, as the result of rhythmic blows to the lid from the inside. Dr. Sunderland was called in, and upon opening the case, found that SCP-446 was attempting to rise to a sitting pose. It would bang its head against the lid, lie back down, and attempt to sit up again. Once the lid was opened, SCP-446 stood on its own without coaxing. SCP-446 then put its hands together at the wrists, lowered its head, and hunched its shoulders. SCP-446 also changed its expression for the first time since entering Foundation Control. Its face took on a subtle mixture of sadness and fear. It held this pose until Dr. Sunderland touched its shoulder, which prompted SCP-446 to return to a normal standing position, expressionless. However, SCP-446 could not be induced to lie down until the Class D uniform was removed. Document 4461A Medical Examination of SCP-446 Conducted by Dr. W... Subject is female. Physical characteristics noted as being consistent with the description in the primary SCP documentation. The subject is nude and reclined on the table. Also as noted in the documentation, the subject sighs follow me as I move about the examination room. Although it is unclear whether or not this subject is alive, given the lack of respiratory and cardiopulmonary functions, this examination will be conducted in the manner of an autopsy in order to gain as much insight as possible. Insofar as the subject is not significantly damaged. The body is warm to the touch. There is no sign of rigor mortis or liver mortis. The neck, torso, and extremities show no signs of injury or trauma. The skin is smooth and undamaged. Of particular note is the clarity of the facial skin. There are no blemishes, nor any sign of past injury. The scalp hair is brown, and the hair color is natural and uniform throughout. Moving on to the eyes. The irises are blue, and the pupils are equal, measuring 0.5 centimeters in diameter. It should be noted that the pupil's size is constant, regardless of light intensity, and the subject does not blink, even when the surface of the eye is touched. The cornea are clear, and there are no signs of patechiae in the sclera or conjunctive eye. Examination of the mouth by pen light reveals a blockage at the top of the throat. The opening is completely covered by a metal plate that appears to be bonded to the sides all the way around. It shifts slightly when pushed, but does not dislodge. Similar blockages are observed in the ear canals, nostrils, genitalia, and anus. Now on to the internal examination. X-rays previously taken of the subject show a number of irregularly shaped masses throughout the body. Among these are the orifice blockages noted above. The brain, heart, liver, and kidneys are also obscured by additional masses. Before attempting the Y incision, I elected to excise a 1 centimeter square of skin from the subject's left flank. Examination of the tissue under a microscope shows nothing out of the ordinary. However, observation of the wound shows that scab tissue is visibly forming already, less than a minute after the excision. Within five minutes, the wound is healed, and there is no scarring whatsoever. Given the rapid healing of tissue damage, the internal examination had to be quick by necessity. I hesitate to repeat the Y incision in order to examine the subject more thoroughly, at least for now. As I completed the incision, I saw the subject's lips moving silently as she continued to stare at me. We should avoid the possibility of irreparable damage until we know more about its behavior, or until we have located a second specimen. During the brief internal examination, I observed that the masses on the X-ray appear to be boxes, made of the same metal as the blockages. They are connected to each other, and to other unobstructed organs by an assortment of wires and hoses. The boxes themselves appear to be seamless, and were not noticeably damaged by my scalpel or bone saw. The wire and hose connections are flushed to the boxes, and have no obvious means of removal. At this point, the Y incision was slowly closing as it healed. I removed the clamps and watched as the incision healed fully in just over 11 minutes, with no visible scarring. The subject's lips stopped moving shortly before the wound closed completely. Unfortunately, it seems that this examination has produced more questions than answers. The movement of the eyes and mouth during the examination suggests that a degree of sapience may be retained by the subject. However, there is no concrete evidence. I can speculate that the organ boxes may be preserving the body and governing its limited and peculiar functions, but there is also little evidence to confirm this. These questions will likely remain unanswered, until I can conduct a more thorough internal examination. Lesson complete. If you missed the previous orientation, go watch SCP-445, Dr. Wondertainment's super paper, right now. Or for the complete course, watch this playlist.


Coming to you from our GIS studios, I'm Nisha Charles and this is your Midday News Brief. Government is in the process of implementing affordable housing for St. Lucian's. During the 2019-2020 budget debate, the Honourable Prime Minister announced that government would be implementing several of those projects to give more St. Lucian's the opportunity to own their peace of the country. Currently, the foundation for one of these developments is being laid down in Boshamiku. Set preparation is also underway in Shok and Wajuli, Denri with several other housing projects to commence later this year. All of the projects are being developed by local contractors. The St. Lucian's is association and the Government Negotiating Team recently signed the Collective Bargaining Agreement which covers the period April 1, 2016 to March 31, 2022. According to Chairman of the Government Negotiating Team, Vern Gill, the agreement reflects outcomes that are beneficial to both parties, including increases in salaries and benefits. The agreement entails a lump sum payment of $1,500 which is aimed at addressing the period 2016 to 2019, 1% for the period 2018 to 2019, 1% for 2019-2020, 1% for 2020-2021 and 2% for 2021-2022. The agreement was signed on June 4, 2019. Prime Minister Hon. Alan Sharsney continues to lead the charge for the Caribbean when it comes to sustainable development and the impact of climate change. The Prime Minister is participating in a high-level panel discussion under the theme Vulnerability to Resilience. You choose at the Caribbean Development Bank's 49th Annual Meeting of the Board of Governors. The event seeks to highlight the current and planned initiatives in regional economies to reduce their vulnerability and strengthen resilience to exogenous shocks, natural hazards and climate change. The event will also identify opportunities or initiatives for improved regional cooperation to foster strength and resilience. The June 5-June 6 meeting is being held at the Hyde Regency in Port of Spain, Trinidad and Tobago. And that's all for your midday news brief. Thanks for tuning in.


Uh, hi guys. So yeah, uh, I'm Andrew and I am just a senior at Amherst College undergraduate institution. Um, so yeah, and I'm here to tell you about enumeration of formative classes on discrete Morse functions. So the contents of the talk will be just kind of a background of where discrete Morse theory came from. It started off as well. It's still Morse theory, it's still a thing. It didn't start off as with Morse theory. But, um, so these are the origins and then we're going to talk about discrete Morse theory. So just some of the basics and how it came to be discrete Morse functions, what they are and how they differ slightly from Morse functions and, um, what the equivalent classes are precisely and the approach to the problem, which I'll introduce at one point, which is counting the equivalent classes. So smooth Morse theory was developed back in 1925 and it was popularized by John Milner. They studied smooth real valued non degenerate functions on manifolds. Um, so these Morse functions alone encoded valuable topological information, so it told you it's diphyomorphism type. Um, it told you it's, yeah, diphyomorphism type, homology, um, a lot of valuable stuff, buddy numbers and so on and so forth. Um, and one, for instance, of a nice, what is it, statement from smooth Morse theory that we're going to see an analog of it and discrete Morse theory is this right here. And what is it? So smooth Morse theory having, what is it, having a Morse function on a manifold, uh, gives you the ability to get a cell decomposition of that manifold, uh, quite easily. Um, so yeah, so just kind of remember this for now because it's going to pop up in a different form and discrete Morse theory. And this is precisely why discrete Morse theory came to be, uh, because we had all these really nice results in the smooth case, but we wanted, uh, to get similar, uh, things when we're talking about messier structures like CW complexes. So what is it? So discrete Morse theory came quite a bit afterwards. It came in 1998 and it was developed largely by Richard Gorman. So again, it was kind of mostly to bring all these nice results about smooth manifolds into talking about regular CW complex, uh, regular CW complexes. And all, uh, regular means is that what is it? Um, is that for each cell, uh, the complex, uh, each cell in the complex, the attaching map is a homeomorphism onto its image. So, but for simplicity and just to make the statements a bit cleaner, uh, we'll stop talking about general CW complexes and we'll just talk about some partial complexes, which are an instance of a regular CW complex. So let's see. So a discrete Morse function. Um, so recall that smooth Morse functions were just, uh, what is it? Morse functions in the smooth case were just smooth functions on a compact manifold that were non, had non degenerate critical points, meaning the, the Hessian matrix had a non zero determinant. Um, in this case, it's a bit uglier. Um, so for each K dimensional face, um, in the complex, uh, there is at most one, the higher dimensional face that contains it, uh, that has a smaller value at that point. So, uh, right here, the function is the, uh, associates to every cell in the complex, a real number. And the second condition, which is kind of just the backwards of the first one for every lower dimensional face that is a boundary of it. Um, the value there is larger, uh, and there can be at most one of these cells. So this is a very messy way to think about them. And it's a bit clunky working with, but soon kind of like how in the smooth case, so smooth Morse theory also allows you to talk about gradient like vector fields for, uh, on a manifold, a discrete Morse theory gives you a similar thing to talk about, uh, a discrete vector field on a simplicity complex. So we'll get there soon. And we won't really have to think about this clunky definition of assigning a real number on every cell. But for now, this is what the actual definition of a discrete Morse, uh, discrete Morse function is. Um, furthermore, kind of like how in smooth Morse theory, we care about critical points. So the, the, what is it? The minimums, maximum saddles, and so on. Um, discrete Morse theory has a similar analog. Uh, we say a cell is critical, uh, in the complex. If essentially around that complex, uh, the values of the values the function takes, um, corresponds with the dimension basically locally. So locally at a single cell, uh, the function corresponds with the, uh, with the dimension. Um, and here is, for instance, a really simple function to keep in mind, just knowing that like discrete Morse functions do exist on any complex, uh, just assigned to every single cell, its dimension at that point, in which case you would get that actually every single cell in your complex is critical. So to see what a discrete Morse function looks like, well, here's an instance. It's not necessarily pretty. It is just like great with numbers, but this is actually a Torus and this is a discrete Morse function on the Torus. And if you were to check on any one of these cells, you'd find that those conditions that were listed, uh, were indeed satisfied. Um, and if you look really closely for a really long time, and I won't put you through that, but you might find that for instance, like, uh, what is it? So if we're looking at vertices in this, um, that it seems like this vertex here is critical because, um, because it satisfied that condition. And it's also a sync of the underlying, uh, skeleton, the underlying graph. And we'll see that pop again soon when we're talking about gradients. So here's a discrete Morse function, but again, we won't have to think too much about these numbers for too long. So what is it? So just to, again, uh, show how, like, how, uh, Forman was able to bring all these analogs, all these nice theorems into the discrete Morse theory case. Um, what is it? So here's one thing that we saw earlier, uh, popping up again in this case in the case of CW complexes. Um, what is it? So if the, if these are the critical faces, uh, after we put a function on a complex, and these are the dimensions associated with them, then it's homotopic to a complex that could be decomposed, uh, with those respective cells. Um, and so here's now the equivalence relation we care about. So in a lot of Forman's work, he re, he keeps using this one equivalence relation and that's, what is it? He says that two cells in a complex are Forman equivalent, uh, sorry, not two cells, two complexes, sorry, my mistake, two discrete Morse functions on a complex are Forman equivalent. If for every pair of simplices, essentially the inequalities match up between the two simplices. So if you put them next to each other, if one is less than the other on one side, the same thing happens on the other side. Um, and this is used for cleaning his proofs, and he seems to care a lot about this equivalence. Well, then that leads us to the question. Well, um, if we fixed a complex or he fixed in this case of graph, just so things are a bit more straightforward, how many classes are there in this equivalence relation? Um, and it was fairly messy, but in the end, the answer was actually a bit interesting. So what is it? So now let's try and trip away from looking at these numbers and, um, we'll find a different way to think about these gradients as well. Uh, not gradient, sorry, we'll think find a different way to think about, um, these Forman classes that doesn't rely on the numbers so much. So notice that for any discrete Morse function app, so this is, this just comes out of the the definition of the function. Um, exactly one of these are true at all times, and that's because, um, the condition that was given for the function is actually said, well, there can only be, there can be only at most one of this and at most one of this. So kind of, phrasing that a different way, you get the statement here that says that, well, there is a unique one for this and unique one for this. And what this says in other terms is that non-critical faces with respect to the function can be partitioned into pairs, uh, where the, what is it, where one is a face of another one, and that matters a lot because that allows us to start talking about orientations on the simple show complex. So going back, um, so this is going to get something a lot easier. So going back to this giant tourists, uh, with the discrete Morse function on it, um, essentially says, uh, you can take an arrow and have it point towards, uh, the cell with a lesser number associated to it. So it's a really, really straightforward way of assigning orientation. And this is how we're going to think about Forman equivalence classes because it turns out that, uh, what is it, two functions, uh, sorry, this is a type right here, but two functions on a fixed graph or form an equivalent if and only if they induce the same gradient. So that means we don't need to think about numbers anymore. We just can have to think about these orientations on simple show complex. And when are they giving rise to the same gradient? So in the case of graphs, uh, we now started looking closely at gradients on graphs and wondering, um, what is it and wondering what is essentially the pattern here. So in the case of gradients on graph, there are something does, uh, there are some things that were immediately straightforward. A vertex is critical if and only if it's a sink of the gradient, uh, in edges critical, uh, because we have critical cells, uh, if and only if it is undirected under this gradient. And if the graph contains a cycle, there must be a critical edge on the cycle. And this last one follows just because essentially if we were going around a cycle, that would mean we'd have, uh, the value assigned here is less than the value assigned here, less than the value assigned here. So when you get back, um, that's a contradiction. So what is it? So yeah, so these are very straightforward. And then there was this extra thing we found that if you take an arbitrary directed graph, how do you know it's the gradient of something? Well, it turns out there's just these two simple conditions. There are no directed cycles and no two edges share a tail. So so far it isn't terribly interesting, but it does. What does it get a bit more exciting? Let's see. So if you have a, uh, graph and we wanted to basically figure out how these critical edges were arranged on the graph. So if you consider a set of independent cycles on the graph, it turns out you can prove that, uh, what is it? The psych, uh, sorry, that it turns out you can prove that the critical edges, there needs to be at least one critical edge on every single cycle. And no two cycles can share a critical edge, meaning if you take a set of independent cycles in the graph, um, you'll never be able to find a single cycle where essentially you don't have a critical edge because that's a problem with what we mentioned earlier, because it turns out if you have a gradient on overall graph, you can restrict to a subgraph and, um, and then you still have a gradient on that subgraph. So then we could just keep going down to the cycles. So in this case, uh, the one on the left is indeed, uh, what is it? So if these black edges had arrows on them, so they were a full-on gradient, and these red edges denoted the critical edges, in this case, this is just fine. This could possibly be a gradient of something, uh, where again, these would have, uh, directions. Um, but the red ones are the only critical edges where the one on the right, um, is not, would not represent a gradient because you might notice that this cycle right here does not have any critical edges on it. So in, we would just restrict down to that subgraph and therefore show it's not actually a, um, a gradient of a discrete Morse function. So we need one more thing in order to, um, in order to kind of get closer to this formula. Um, so we have this lemma that tells us how the critical edges are arranged on a graph, and now we want to know how the orientations work on this graph. So there's actually this, um, theorem, which will be very handy, uh, that was proved by Forman back in his original paper that essentially says, um, what is it? Essentially, it says the critical, the number of critical cells of a given dimension bound the Betty numbers and the other characters that can be expressed using the critical cells. So in which case, notice now if we have a tree, so what is it? So the previous, the pairing lemma essentially was telling us that if we put the least amount of critical edges on our graph, uh, and then we in a sense kind of deleted them or ignored them, we'd be left with a tree that we can leave orientations on. So now consider this theorem when we're talking about, um, just a tree graph, in which case the statement on the right would be saying that since the order characteristic of a tree is one, and we now go over to the statement over here, it would say that we have exactly one critical vertex. And if we have one critical vertex, well, if we go back a bit further, that means we have one sink in our graph. So in other words, if we kind of just use some notation to note the set of equivalence classes, we just, um, noticed this, that the number of equivalence classes and number of gradients where you take out the least amount of critical edges, that is B1 many, the number of independent cycles, or of course they satisfy that pairing lemma condition, then we're only looking at what is it? It turns out we're only looking at the rooted spanning trees of the graph. So that's, um, what is it? And that's what the pairing lemma and the weak Morse inequalities are saying together. It's saying essentially take out as many critical edges as you need in order to have no cycles left over, and the next one is saying pick a root. And yeah, and then the order of this, just by Kirchhoff's theorem, is the product of the non-zero eigenvalues of Laplacian matrix. Um, but we can say more than this. Uh, what is it? So it turns out, um, what is it? Given the previous assertion, it's not difficult to see, like, you can just keep doing this. So once you have spanning trees, well, you can keep taking out edges, and now you aren't worried where, uh, where your critical edges have to be, like where the ones that you're taking out are gonna be from. So in which case you're just essentially disconnecting that spanning tree. So what you end up actually counting is, uh, the rooted forest inside your original graph. Um, and now there's, there's actually this theorem from an algebraic graph theory booked by Biggs that says, um, so these are edge subgraphs that we're now counting, and that subgraphs are actually the coefficients of the Laplacian matrix, um, of the graph. So it turns out actually these gradients are precisely the coefficients of the graph Laplacian. Um, yeah. And that's, that's the main result. Uh, so some, I guess, final comments are, what is it? Is there an analog to this lemma for higher order, uh, higher dimensional simplicial complexes, and could the gradients be counted there? And, um, one thing I didn't get to mention, just because it definitely would have taken too long, is it turns out actually the set of, um, so not m sub k, but m gamma. So the set of all, equivalence classes actually forms a simplicial complex in and of itself. It has that kind of structure on it, and that's what's called the Morse complex. Not to be confused with the Morse chain complex is the Morse simplicial complex. Uh, or it's sometimes called the Morse, uh, what is it? The complex of discrete Morse functions. Um, but it turns out that currently that that's really trying to be understood because it also tells you a lot about the topology of not just the graph, but if you were looking at discrete Morse functions on simplicial complexes, it tells you about the topology of that original simplicial complex. So that's currently where discrete Morse theory is, and, um, what is it? And these m sub k gammas that we were counting here, um, turn out to be the f factor of the complex. Um, and currently what's being kind of researched there is the homotopy type of that complex. And uh, and yeah, that's everything. Thanks, Andrew. Um, does anybody have any questions that they would like to ask? Uh, I have a question. Thanks for the nice talk. Um, is there the appearance of the Laplacian, I think is really interesting. Do you think there's some kind of maybe discrete hodge theory type reason that this would come up? I wouldn't know. I didn't look into anything that deep, admittedly, and I don't know hodge theory, which is the second reason why I didn't think about that. But I'm not sure, honestly, I was also quite surprised when I saw the Laplacian show up. I admittedly thought, um, this discrete Morse theory had no connection to the Laplacian. So when it started showing, when it started showing up here with just the product of the eigenvalues, we started suspecting it could show up some more. Um, but yeah, we actually don't know. We didn't look into it. We're very surprised. And yeah, we're just highly curious what the other gradients could look like then. So for the critical points, is there a way of associating an index to them? Um, oh, to the critical points in the discrete Morse theory case. Yeah. Um, so the index that's associated to them is just the dimension of the cell, whereas in smooth Morse theory, it's the whole, like the number of negative signs when you look in local coordinates here. It's just the dimension of the cell that's considered to be the index. Okay. Do you have a reference for the topology of these Morse functions? Uh, what do you mean by the topology of the Morse function? I mean the simplicity complex that you mentioned. Oh, yes. There is, what is it? It's called, so yeah, there is one paper. I guess I can type that in the chat. I can type that in the chat afterwards. It's called, what is it? It's by a paper by someone named Charry and it's just called complexes of discrete Morse functions, I believe.


I've been at this park for like five minutes got way too excited and This is what happened. I just did a kickflip and I caught it wrong and I snapped my board. So I Gotta go buy another board right now We're at a different park right now and My son Barone is going to set up my board.   That's my stick off I have to keep this one short and sweet for you guys.  It's like dipped in black So I don't know if you guys can see but once the paint starts to kind of wear away You can see the different colored veneers underneath here. It's pretty dope. I've never skated like an all blacked out board Graphic is sick. Yeah, just all around really playful copyboard Really enjoy skating these shapes because they're a bit shorter They have like the shovel nose and tail. So the board is a bit shorter So it's easier to throw around in my opinion anyway super stoked on this purchase also copped a package in the mouth today So I'm gonna open it right now Haven't opened it. Obviously. That's why I'm opening it right now. I Think they're shoes. I think they're shoes that we will find out Hi top Chuck pros the skating ones These are the suede ones. So they last a bit longer than the canvas ones. I really want to like draw Something on the side here on both of them actually I reckon that'll be pretty cool. I want to draw like I want to make these customs. What do you guys think? Could draw something on the side here a little bit of space on the inside I could make a cool video. What do you guys think? Let me down in the comment section below If you guys want to see me customize this pair of converse pro Chuck Taylor I think they're called the c-tas pro for sure But they're the converse chuck Taylor high tops The low tops are sick But I just feel so much more Comfier in the high tops because my ankles are kind of protected in a way But yeah, let me know if you guys want to see me drawing on these or painting on them or whatever Let me know in the comment section below just quickly before I let you guys go Shouts out to everyone that copped a hoodie from the last drop. It was a restock and we pretty much sold out We have two small sizes left right now. So if you want to cop on your size small head on over to evening mob.com Grab on while you can we are probably going to do another restock on the black and the gray hopefully And we've got some crewnecks coming in soon too. So stay tuned If you're not following me on instagram as of yet Make sure you head on over to instagram follow me at enuckism Follow the mob as well at evening mob If you guys are new to my channel Make sure you hit that subscribe button and leave a thumbs up. Shouts out if you've made it this far in the video Thank you very much. Shouts out to all the new subs trying to get to 20k here wherever you guys are in the world I'm hoping that you all are staying safe staying happy Skating a lot progressing and just enjoying skateboarding And I thank you so much for all you guys support means the world to me But until next time. Thanks again for watching the video and I will catch you all in the next one


the master of mystery and adventure, William M. Robson. The human mind is an organ of infinite complexity and of infinite potentiality. This delicate and mysterious organ, when it is healthy, can create beauty, work miracles, and envision God. But when it is shocked, disturbed, and unbalanced, its capacity for horror and evil is equally limitless. It is of such a mind our story is concerned. The mind of a woman who lets her imagination run away with terrifying results. Listen, listen then, as Miss Hillary Brooke stars in A Week a Go Wednesday, which begins in exactly one minute. Let's figure out how to become president of the United States without being elected. All it can be done, all right? See, all you have to do is have a special job in Congress or be a member of the cabinet. Now, naturally, you have to meet the other qualifications of age, birth, and residence. The law determining the order of presidential succession specifies that after the vice president comes the speaker of the House, followed by the president pro-ten of the Senate. Then, if for any reason these people are no longer available, the cabinet members are set up in line to take over the White House duties. The first one is the Secretary of State, followed by the secretaries of the Treasury and Defense. Then come the Attorney General, the Postmaster General, and so on down the line through the secretaries of Interior, Agriculture, Commerce, and Labor. Then, if that list is used up, the only thing is to have an election. But so far, the need has never gone beyond the vice presidency. And now, a week ago Wednesday, starring Hillary Brooke, a tale well calculated to keep you in suspense. My husband and I had quarreled that Wednesday morning. I've tried to remember why, but I can't. Anyway, I wasn't in any hurry to get home after work that day, that Wednesday. So I sat for a while on a bench in Central Park.  I watched the evening happen quickly, because it was going to rain. I started to come down, doing my crying for me. And I started to run. I knew suddenly that I wanted to go home. And I wanted Harry to be there, so I could put my arms around him and tell him how much I loved him. And that I was sick because I hadn't kissed him goodbye that morning. I nearly fell running up the narrow stairway to the third floor. Apartment 3B, I was nervous. My hand was clumsy or thumbed, and the key wouldn't fit. It dropped to the floor. I stooped to pick it up. As I did, the door opened. Harry. Oh, Harry. Yes, what is it? It was a stranger in our apartment.  She was wearing a flowered apron, and she was holding a soggy dish towel. Well, well, what do you want? I can't stand out here all night. I'm cooking supper. There must be some mistake. What apartment did you want? 3B. Well, this is 3B. But it can't be. You see, I live here. Whoever you're looking for, I can't help you much. We've only been living here a few days. Living here? Yes. What's the matter with you? You're closed. They're soft and wet. The rain, I got caught in the rain. What are you talking about? It isn't raining. It is raining. I ran. I ran all the way because there was thunder and lightning. I don't know if you're drunk or crazy. Maybe both. We had a thunderstorm last Wednesday. It ain't rained again this past week. Wednesday? A week ago? Oh, no, no, I... You even look so good.  What is the matter with you? I must have got a chill when I got caught in the rain. Only you say it hasn't rained for a week. You sit right down here. I'll get some water. Now, don't move now. Bummer, not ready, the company's coming. I sat on the sofa. Harry and I had talked last night about having the spring in the middle cushion fix. Oh, I did last night. I ran my hand over the top, cautiously afraid, and then stopped as if I'd suddenly taken hold of a live wire. My fingers curved over the lumpy roughness of a pillow with a broken sprain here. Yeah, I'd make this. Over the rim of the glass, she watched me. I sipped the water slowly as I looked around the room. There was a little table near the window where we could see the morning begin on Central Park while we had breakfast. And the buildings freckled with tiny lights in the evening while we had dinner. There was a rug with a worn spot in it in the fireplace. But our wedding picture was missing from the mantel. And in its place was a cheap blue vase. There. There, better? Feel better now? Yes, yes, thank you. You don't look so good to me. You better call a doctor when you get home. Home? You want me to call a cab for you? Where do you live? I don't know. Now? We're looking for someone when you came. Friends of yours? What's their name? I'll see if I can find them for you. Friends? Yes, just friends of mine. Harry and Mort Haskin. Good friends. Haskin? But don't you read the papers? Yes. But you must know. Know what? Well, about the murder, of course. In a moment, we continue with the second act of... Let's take just about a minute to talk about three little words which mean a great deal to people all over the world. Monarchy, oligarchy, and republic. The first of these, monarchy, means rule by a single person such as a king or queen. The second, oligarchy, refers to a form of government in which the power is in the hands of a few such as Russia's Kremlin. But to us here in the United States, the most important of the three little words is the third, republic. A republic is a state in which the balance of power rests with the people as a whole and is exercised by representatives elected by the people and responsible to them. A republic is a free, popular government in which there are no classes having any exclusive political privileges and in which the voters are guided by constitutional authority. The importance of a republic is recognized by the constitution, which in Article 4 says that the United States shall guarantee to every state in this union a republican form of government and shall protect each of them against invasion and domestic violence. That's how your American constitution works. And now, a week ago, Wednesday. We moved in a couple of days after the murder. My husband didn't like the idea. He put an apartment in an apartment these days and I said to him, Charlie, it's a vacancy. So what if there was a murder? A murder? Tell me about it. Where have you been for a week? I'm not so sure myself. He looked like such a nice young man, too. At least in his pictures. Oh, who are you talking about? Harry Haskin, of course. Harry? Yes, it happened right in that kitchen. The murder weapon was an ice pick. Ice pick? Isn't it awful? And everybody says they seem so much in love. Well, you never can tell about those things. She's so young. They say pretty, too. Do they? Do you know them well? Yes, very well. Oh, sure, I'm sorry. It had to be me to break the news to you if they were friends of yours. You said it's in the paper. Can I see it? Sure. The paper's been pulling nothing out for almost a week. She was right. The headline screen doubted me. Ice pick murder awaits conviction. And there was a picture of Harry. Harry, my husband. I tried to read more, but I couldn't. I kept hearing his voice. Don't you know I do anything in the world for you, darling? Don't you know I love you? Love you. I don't remember leaving, running down those stairs and out the door. I just remember finding myself on the street again, half walking, half running. And then I was back in Central Park again. From out of nowhere, a little boy on a scooter came carrying around the bend. He turned sharply to keep him running into me. I watched him lose his balance.  And I ran over to pick him up. I bent over him. My arms outstretched to lift him to his feet again. And then I realized I was dead. I'd been murdered by my husband almost a week ago. I was dead. And I knew I did not touch this chap. I was afraid for him. And so I ran again. Lady King. And I ran faster and faster, so I couldn't hear him anymore. And then it was later, somehow, and really dark. And I was tired, so very tired. I found myself back on that bench again. The same bench I'd been sitting on earlier that evening. No one was around. I stretched out and tried to sleep. And I suppose I must have. The next thing I knew it was morning. I sat up, stiffly, and smoothed out the wrinkles in my skirt. I wondered where I was going to grow, what I was going to do. I tried not to think of Harry, where he was now. Maud? Maud? Oh, Maud, darling. Harry!  Oh, Harry! Oh, my darling, I'm sorry about yesterday. Come on, let's go home now. Home? Look at your clothes. They're still damp from the rain last night. If you get sick, I'll never forgive myself. How do you feel? Are you all right? Yes, yes, I'm all right. Good. Come on, then. His big hands supported my arm. And as we left the park, from the entrance on 72nd Street, a little bar in the scooter came tearing round the bend. In just a moment, we continue with the third act of... How would you like to be a successful farmer? Naturally, all of us would like to be successful in anything, particularly in our chosen field. But say you are a successful farmer and you have one or two successful neighbors. However, there are other neighboring farmers who, for one reason or another, are not successful. Farmer Adams was hit by a flash flood coming out of the hills. And Brown and Fisher, though they're hard workers, just don't have the knowledge to make a farm pay off. What would you and your successful neighbors do? Would you sit back and allow the other farms to go under, no matter what hardship it might cause to the families? Would you say, let them fail. We'll buy them out when they're broke. Perhaps one of your neighbors might say that, but would you? Or would you go over and help Adams rebuild his farm? And would you go over to Brown and Fisher and say, look, neighbor, you're not planting the right thing here. It's not right for your soil. Let me show you what you can plant. Of course, unless you were greedy, that's what you would do. Throughout the world, that is what the food and agriculture organization is doing. It is an agency of the United Nations, which is man's best hope for the world's welfare, peace, and justice. And now, three of a week ago Wednesday. The problem was just the way it should be. The worn spot on the rug, the crack in the base of the lamp, the wedding picture on the lamp, and the woman with eyes like two shiny, brown buttons was gone. There was just Harry and me. Are you hungry? I am a little. Harry? What? It was raining last night, wasn't it, Harry? It was raining, I'll say it was. What a storm. It was raining. It was raining hard. Oh, Harry. Sweet, don't, please, don't, don't. You're home now. Don't cry, this is Harry. This is your home. No, please, don't. We ate breakfast near the window so we could watch morning begin over Central Park, just like other mornings. He smiled at me and I tried to smile back. He leaned across the table, his eyes steady, serious, watching me. Why was he being so kind? Why should he be so good to me? What was the thought behind those eyes? Watching me, watching me. Was he already planning how he would murder me? I love you. Oh, I'm sorry, I didn't mean it, it dropped. Don't worry about it, just a cup. I'll get a broom, I'll sweep it up. No, don't bother about it now. You just come here to me. No. What? I mean, I'd better sweep it up. I went into the kitchen, glad to be alone for a minute, safe for a minute.  You want me to do it for you? No, I can do it, I'll sweep it up. No, Maude, don't go into work today. Stay home and rest, you don't look well. I'm all right, I want to go into work. All right, you're sure? Anything you want. He was being good to me again. Too good to me. Anything I wanted, anything, anything. Why? I didn't trust him, he was too kind. His lips said sweet things, but what was on his mind? I love you. Do you? Well, don't you know I do? Yes, yes, of course I do. I don't remember what happened in the office that moment. I could only think of one thing. One thought kept repeating itself, repeating. I'm afraid of Harry, I'm afraid. My husband is going to kill me. I know because I dreamed it last night. It was a warning. My husband is going to kill me.  Nothing more sinister than that. I was bored, Haskell, and I was married to Harry who loved me. I was just another girl who'd had a bad dream. The afternoon dragged all too slowly. I knew Harry had been concerned when he left me that morning. I wanted to tell him I was all right. I was all right now. I'd let a silly dream play tricks with me. I'd behave like a fool, afraid, afraid of Harry. I almost laughed out loud, but I felt more like crying. And at last the day was over, and I was on my way home to the man I loved. And this time I knew I wasn't dreaming. This time I could run, run fast, all the way from the subway to 69th Street and home. Harry would be there. I climbed one flight, two flights. Out of breath and hurrying, one more, one more. Excuse me, Miss, do you know where I can find the landlady? Was that woman? A small, dark woman with eyes like two shiny, brown buttons. I said, do you know where I can find the landlady? What? What did you say? You live here? Yes, yes. Well, tell me then. Did you happen to know if there are any vacancies? Vacancies? No! No! Hey, where are you going? Harry! There was a woman in my dream. She was the woman who had been living in our apartment. What was she doing here? Maybe it had been more than a dream. Maybe I was thrown ahead into seven tomorrows to next Wednesday. Maybe by then she would have our apartment, just like in my dream. And I'd be dead. Darling, is that you? Yes, yes, Harry. Got a kiss for me? That a girl. You're home early. I hurry. Did you? So did I. I missed you. I've got a surprise. What kind of surprise? We are going to celebrate, you and me. We're going to have a private party, a reunion. Now, you just wait here. I'll only be a minute. I kept thinking, not a dream, not just a dream, but a warning. A warning. Oh, but that was silly. It couldn't be it. Sounded. I heard the sound. And I began to shake all over. I walked into the kitchen. And Harry was bent over a small boat. I could see his muscle under his shirt move up and down. His arm rose and fell again and again. And in his hand, he held an ice-pink. Bod, what is it? What's the matter? Nothing, nothing. What are you doing? Icing the champagne, darling. We're going to celebrate. I wish you hadn't come in, though. You spoiled the surprise. I'm sorry. Oh, it doesn't matter. Nothing matters as long as you are here. He put the ice-pink beside the bowl and took me in his arms. And while he kept telling me he loved me, I was looking at the ice-pink, thin and sharp. The ice-pink, spoiled a surprise. Yes, I'd spoiled it. He thought he was going to kill me. But I wasn't going to let him. I wasn't going to let him. Oh, darling, how I love you. I love you. I'd sputter the lying words in a soap before he could say them again. I'd been warned. And I wasn't going to let him do it. I reached out and felt my fingers creep around the handle of the ice-pink. I was strong and safe now. The dream wasn't going to come true. I'd make sure. I held it tightly, raised it behind it back, poised like a serpent, ready to strike. Ready? Ready. Oh, darling, I love you. I don't know. His arms still around me grew limp. Come on. I felt them slide heavily, big hands dragging at my body. Come on. His fingers clutched my belt and tore a thumb. And then he fell, still holding it in his hand. He lay still at my feet, a red circle of blood on his wife's shirt. And in that circle, the ice-pink. No one saw me leave the house. All I could think of was, not me, not me. It wasn't me lying dead with an ice-pink in my back. I'd been cleverer than he. I had done it first. I stumbled into the park and wandered aimlessly. Every once in a while, I'd hear his voice. And I put my hands over my ears to blot it out, but it was no use to keep coming back. Nothing matters as long as you are here. I ran to get away from it, but the voice followed me. You're going to kiss for me? That a girl. I'd dropped from exhaustion somewhere in the park and slept all night on the grass. In the morning, I remembered, but I was too sick to care. I was sorry I woke up. I didn't ever want to wake up. But I started to walk again. I kept on walking until I couldn't go anymore. With a bench, I sat down. Someone had been there before and left a newspaper. I picked it up and read it. And then I knew, as big and bold as life, for death, it mocked me. The words, ice-pink murder, jumped crazily on the page. And Harry's picture just had been in my dream. Only this time, I read on. Harry Haskin dead. Murder. Police searching for wife Maud Haskin.  Harry loved me. I had tried to run away from a dream, just a dream. And instead, I made it clear. And now Harry was dead. I wanted to tell you how it was for me. Great. The dream has come true. Wednesday again, isn't it, Father? I've confessed. I don't care what happens now, because I must pay for what I've done. Will you pray for me, Father? Oh, we could go Wednesday. I wonder if she's there. The woman with eyes like two shiny brown buttons reading about me in the paper. I wonder if she's in the apartment now, reading about my execution. Man Robeson's production of A Week Ago Wednesday by Winifred Wolfe. Supporting Ms. Brook in A Week Ago Wednesday were DJ Thompson, John Daener, and Dick Beals. Listen. Listen again next week when we return with another tale well calculated to keep you in suspense.