Good day, fellow investors. If you are a long-term investors, there is only one rule you have to follow. There is one metric that will lead you to satisfying high investment returns over the long term and over whatever happens in the economy and low risk. At the current moment everybody is focused on growth, on buybacks, on taking a lot of debt, takeovers, whatever is going on in this environment of low interest rates and economic growth. However, where people lose their focus is on long-term shareholder wealth creation and you want to get your wealth created, your shareholder value created. Now, this might sound funny from a stock investor, but looking at stock prices, a stock price can go up in one month and then in the next year it can be just 10% of what it was. So don't get so much attached to what's going on on the stock market, but look at what's going on in the business. Now I know that this is not funny, this is not interesting, this is not trendy because the trendiest thing now is to invest in index funds and the stock market can go only up. So I'm not going to get a large fund base, but I think that I have to say this to whoever wants to listen because I think there are some like-minded investors. The most important metric for an investor is book value and the change in that book value. The change in book value tells you the addition of intrinsic value that the company has given you the shareholder over the last year. And if we look at Berkshire Hathaway's first page on the annual report, the first column shows in Berkshire book value change of Berkshire Hathaway. That is Warren Buffett's focus and nothing else. Then he compares it just for fun to the market value and he has started doing that only in the last two years, so the previous 50 he didn't do that and then he compares to the SAP 500. What is very interesting is the compounded annual gain in the last 52 years has been 19% in book value. The compounded annual gain in the market price of Berkshire has been 20.8%. This means that long-term investment returns are correlated to book value growth or intrinsic value growth. So if you want a metric that will tell you exactly where your investment returns will be in the next 10, 15, 20, 52 years, then focus on book value and the value that is created for you. Everything else is just a trend of Fed that will probably quickly evaporate. So I have seen, I don't know, Enron taking a lot of debt, acquiring everything, trading everything and then going bust. I have seen in 2000s dot-com companies taking a lot of equity, just growing their revenues, not caring about earnings, not caring about increases in book value and going bust. Similarly we have seen in 2008 companies taking a lot of debt, buying houses, mortgages, piling up debt and piling up the collateral and consequently going bust, because there was no value creation in that maniac debt taking. And now we again see companies taking a lot of debt, doing a lot of buybacks, pushing temporary earnings higher, but the book values are going down. The price to book value of the SAP 500 has been going just up, up and up. This means that your value isn't created. Stock prices are going higher, yes, but in the long term that book value is what gives you the returns. This might sound old-fashioned, but this is what has worked over the last 200 years. So it's up to you if you want to follow it or not. It's not trendy, it's not cool, but it is what makes you wealthy in the long term. What's very interesting, I have plotted here the changes in the book value, the blue line with the changes in the stock market price for Berkshire year over year. And you can see how the book value is mostly positive and relatively stable. Nevertheless, the stock price goes all over the place. It's much, much more volatile than the book value. So as an investor, of course, look at the stock price, but in order to take advantage of the irrational market. When the stock price is high, extremely higher than the book value, and the book value creation is not significant in relation to the stock price, then you sell. When the stock price is extremely low and much lower than the book value, then you buy and you take advantage of this irrational market. So really think again how to position yourself in relation to what's going to happen in the next 10 years. Inflation and with inflation, again, book value will protect you from it. If there is no book value, nothing will protect you from inflation. So Warren Buffett keeps mentioning book value shows the change in intrinsic value, of course, plus minus if there is a dividend. I see no fault in his reasoning, while I see a lot of faults in the reasoning in the current market and the current financial environment. History has been on Buffett's side. That is why he has been so successful over the past half a century. Others and many of them have been successful for a short time and then went into oblivion as the situation in the environment changed. It's up to you to choose where do you want to be in 5, 10, 15, 20 years with strong value or risking to lose everything when the situation in the environment changes. Thank you for watching. Looking forward to your comments and I'll see you in the next video.


Good afternoon, everyone. Buongiorno, cari amici. Thank you for being here today. I'd like to say a few brief words about our guest, Prime Minister Paolo Gentiloni. He's new to his role as Prime Minister, but has been a dedicated public service servant for much of his working life. As a deputy, he has played a great role on several fronts, especially at the level of the supervision of the Italian National Radio-Diffusion Agency. As Minister of Foreign Affairs, he has faced diplomatic crises with calm and assurance. And now, as Prime Minister, he is defending with courage the international trade. He has greatly supported the European Union's free trade agreement. The citizens on both sides of the Atlantic can thank Prime Minister Gentiloni for many opportunities and many well-paid jobs that will bring about the integral contribution of this trade agreement. Thank you once again, Paolo, for your support of CETA. Of course, our meeting this morning and our meal here today are more than just diplomatic and trade relations. It's a chance for us to come together to celebrate a truly unique and special friendship. Canada, as you know, is home to just over 36 million Canadians, one and a half million of which identify as Italian-Canadian. As I joked earlier today, that number seems to double every time the World Cup rolls around. And that's okay with me, because our history shows that when Italians have made the difficult choice to leave their homeland and settle here, we've always been the better for it. I experienced this firsthand just yesterday when I had the chance to visit the Art Gallery of Ontario. I want to share a quick story with you because I think it says much about the connection that Italian-Canadians feel to both countries. Several business leaders, including Tony Galliano and Tony Veroni, who are here today, brought together 26 different families who together raised $13 million to help build a new gallery space. What's unique is that they didn't want their own names on it. Instead, it was called Galleria Italia after the family's beloved country of birth. They wanted to honour the country they loved, a place that reveres art and artists, while at the same time showing their love and respect for their adopted country of Canada. When the Italian government of the day heard about this, they awarded each family the Italian equivalent of the Order of Canada. I am thankful as a father that my own children will be able to visit the Galleria Italia and better understand the connection between two countries that made it possible. I'm also grateful that as Prime Minister, I'll have opportunities to spend more time with Prime Minister Gentiloni. We'll have a chance to do that next month at the G7 Leaders Summit in Tiramina, followed by an official bilateral visit in Rome. After that, I will be making a visit to the Vatican City for an audience with His Holiness, Pope Francis. I'm especially happy that I'll be bringing a number of prominent business leaders with me to Rome. They will be part of a business delegation that will accompany me, organised by the Italian Chambers of Commerce of Canada, and I know they will represent us very well. So with that, I invite you all to join me in a toast to the enduring friendship between Canada and Italy and to the many close ties that unite our people. May we continue to show the world what it truly means to be partners and friends. Cheers! Salute e buon appetito!


Hey, fellow buddies, thanks for watching. Okay, I have 23 Big Money Bolos coming your way. These are items that I bought low and sold high. I'm gonna tell you where I got it, what I paid for it, and what it sold for. All of these items did sell on eBay. I do sell on multiple platforms. Most of my items are on eBay, Poshmark and Mercari. I do a little bit of Grail, a little bit of Etsy, a little bit of Facebook. But I do use an extension. It's called List Perfectly to Cross-Post My Items. I start on eBay and then I cross-post to the other platforms. That's how I do it. There's other ways you can do it. But if you wanna see how that works and you wanna make more money by getting on more platforms because I always say there's different eyes on different platforms. There is a link to a video down in the description that shows you how to do it, how I use it. And you can also, if you watch the video and you're like, this is something that I definitely need to try, you can use coupon referral code BOLOBUDDYS, all one word, to get 30% off your first month. So it's worth every penny, you guys. And I will say that I do sell lots of items on Mercari and Poshmark. So if you wanna see some of those what sold videos, I do have those available on this channel. So it'll say like Mercari what sold or Poshmark what sold. So you can definitely check those out. And right now we're gonna focus on eBay. And if you're not selling on eBay, I highly, highly, highly recommend it. That is my number one platform. Where I sell the most items, I should say, isn't my favorite. I'm gonna say yes because I sell the most. But there are definitely perks to Mercari and Poshmark as well. If you're a new seller, I would say Poshmark and Mercari are easier platforms. But yeah, let's get started with these big bunny BOLOs. All right, let's see, pull that up. Okay, again, those links are down in the description. So check out the links, lots of good info down there. All right, hopefully I'm getting a little thing that I'm having network connection issues. So I apologize if I'm a little fuzzy or anything. All right, let's start with the first item here. The first item, sorry, just second I know some of you hate when I do that. Okay, the first item is this Cabbage Patch Kids Love and Go Nursery play set. You guys believe it or not, I got this for 50 cents at a garage sale. I also picked up Lisa Frank, vintage Lisa Frank at the same garage sale for 50 cents each. It was a really good garage sale. I wish they would have had so much more in that box, but I was very thankful for what I did get. I ended up selling this for $44.39 and the buyer paid shipping, it's from 1995.  The next item is awesome. I actually did a hashtag shorts on this. So some of you of May have already seen this, but I picked this up at a garage sale for 25 cents, you guys, and it's just unbelievable what some of this vintage nostalgia items, people just want them and they will pay for them. I can't remember. I think this one might have went internationally, but it was missing one of the stoppers. If it would have had the other stopper, I could have gotten even more for it. And I had tons of offers come in. I had somebody message me and tell me why I should sell it to them for their price. And I was like, no. And then I got a full price that somebody bought it for full price. So I was glad that I declined because I knew that it was gonna sell for a lot. This ended up selling for $112.50 and the buyer paid shipping. The next item I sold is this vintage stanae. I'm not sure really how to say it, you guys. It's a silk sequin bead cocktail dress. It's retro. It's from the 80s. It is embellished and beautiful. Just beat it all the way down. Amazing. I ended up selling this for $60. I picked it up at a garage sale for five and the buyer was all in for $67.95. All right, this Playmobile set. I ended up getting two of these from the same garage sale. They were new old stocks. Still sealed you guys from 1998. This one I ended up taking a best offer of $65 for it and the buyer was all in for $74.05. I did pay $10 for this. The next item I picked up at a garage sale and actually I went to this garage sale last year and the lady had mentioned that she sold on eBay. So I was kind of like, am I gonna find anything? And I did really good last year. So when I saw that she was having a sale again this year, I was like, I'm gonna go back. And I ended up picking up this item for $1 and I sold it for 35 plus shipping. It's a Jim Henson Muppets Fuzzy Bear ornament from 1979 and it is paper mache. So really cool piece. No clue why she didn't put it on eBay. Maybe she's getting out of eBay and it's just not doing it anymore. Who knows, but I was really excited to find this piece. The next item is this vintage little people. Now I ended up taking a best offer of 50 on these and they're all wood. I don't know if maybe this guy here in the back brought the price up cause he is different. Condition is just really, some of them not that great and it's still sold for $50 plus shipping. So if anybody knows like, is this why it sold for $50? I mean, I did have it priced at 66. I took a best offer, but I don't know. I just thought maybe that guy was special and then somebody in my Facebook group said they thought it was this guy. So I don't know, he must have been special. This Pokemon Pearl version authentic Nintendo DS game. I got this at a garage sale and I bought it with a game system. I think the whole thing was like $5. So I probably had a dollar in this game, sold it for 45. The buyer was all in for 5407. All right, you guys. So I might have messed up on this. I bought 42 games, PlayStation, Nintendo, Wii, DS, just a big lot. I did take one game out and sold it separately because I wanted to make some money back and I wasn't sure how this was gonna go. I forgot to take pictures. I did the video, packed it up and forgot photos. So I just pulled some of these pictures from the actual video that I did. So here's what I did. I did this as my main photo. I'm gonna tell you that some of these games were in horrible shape. So I decided to do a video showing the condition of the CDs. I figured that was the fairest way to do it. The video ended up being longer than I had hoped. I just wanted it to be like a quick video, but it took a while to show really the detail of how bad the CDs were. I didn't want somebody to get these games and be disappointed. Some of them were excellent, some of them were good, some of them were not great at all. I don't even know if they were gonna work. So I just marked them as untested. Maybe if somebody had one of those CD cleaners, that might have worked. But all of these cartridge games, I'm sure were fine, but it ended up selling for $46. I thought that I could ship this media mail and I was told that no, you cannot. So I ended up shipping it priority mail and I just ate the cost. So I kind of took a hit on this one if I'm being completely honest, but I messed up and I do have a video on, I made a mistake. I think it's what it's called. It's over on my sourcing with Bolo Buddies channel. So if you wanna hear more about that and learn a little bit, you can go check out that video. So kind of a want-want. So the next item I sold are these vintage stickers. They are Puffy scratch and sniff stickers, but these are actually called scrape and sniff. I wish I would have put scratch and sniff somewhere because people usually search that not scrape and sniff. I wonder if I would have got more bids. The person that bought this actually sells stickers. So I don't know if they're a sticker collector and then they sell things as they get sick of them or if they're gonna flip this for more money. I'm just not sure. I have checked their store once and I didn't see it. So they may be a collector, but I sold this for $49.99 with one bid. This came out of a vintage sticker haul. I bought a bag of stickers. I think it was $3. It was amazing. I have a video on it over on my sourcing with Bolo Buddies channel if you wanna see what else I got. Just awesome, awesome find. Super excited about that one. But yeah, 50 bucks for that. The next item is this vintage talking Mother Goose. Definitely a Bolo item if it's in good condition and works. This one did not work, but I only paid a dollar for it. So I just listed it accordingly. I sold it super fast for $37.50. The buyer paid shipping. And when I say fast, it was like pretty quick. Less than a month. And for parts of repair item, that's pretty good. This guy came from a garage sale. I paid $1 for it. Unfortunately, the little music button on the hand did not work any longer and there's no spot to put batteries in. So I'm not sure if you can like un-stitch it and stitch it back up to change the batteries, but either way, I knew it was a Bolo. The Rebel reseller had just posted about one that she had sold. So I was super excited to find this after I saw her Instagram post. She is on Instagram and YouTube, the Rebel reseller. She's a Bolo finder. She has amazing items, awesome videos, what sold videos. So definitely go check her out. But I sold this rabbit for $99.99 plus shipping. The next item I got at the thrift store in the free box, you guys. And I ended up selling these for $52 best offer and the buyer paid shipping. So these are old vintage frames. I did show a picture of the back. There's more detail about each one. Like this one has writing, maybe these didn't. But anyway, yeah, nice little free box find there. The next item came out of a mystery box. I was super excited to find this. It is incomplete for parts only. I did Google Lens and I'm like, oh my goodness, I have a vintage masters of the universe item. So super exciting, sold it for $49.99, one bid auction style buyer paid shipping. The next item are these Barbie books. Okay, lesson learned on this one, you guys. Brandy from My Reseller Treasure. If you're not following her, definitely go and sub her up. She has an amazing channel. She is so knowledgeable about Barbies and toys and she's a Bolo Finder. But she's kind of my go-to for Barbie stuff. She helps me out from time to time. And I messaged her about this. I'm like, hey, somebody just offered me like $65 out of the gate for these. I mean, should I take it? Like what's going on? And she ended up doing some research on it and getting back to me. And apparently certain ones have certain outfits in them and are highly collectible. And these bottom three were not in great condition. This one didn't have the cover. This middle one I guess is kind of sought after. But I didn't get back to the person who made the offer for $65 fast enough and somebody placed a bid on it. I think I started it at $24.99. So unfortunately I lost $20 on this because I was not quick enough to accept the offer. That's okay. I still, I picked this up with something else. I was actually buying the other item and these were just in the box. So it was kind of a bonus. I didn't really pay anything for it but I sure would have liked to have had 65. What would have been even better is if I would have done my research, more in-depth research and figured out what made each book special before I listed it as a lot, I probably would have made a lot more money. So lesson learned. I told Brandy over at my reseller treasure that she should do a video on it and teach us all. I don't know if she's gonna do that or not but definitely go give her a follow. The next item I sold is this Fisher Price Think and Learn Codepillar. I picked this up at a garage sale for $6. It's sold in less than 24 hours for 56.25 and the buyer paid shipping. So they were all in for $79.34. The funny thing is, is I found one the same day this sold, I found another one. So I need to get it listed still, but it's smaller but I'm guessing it'll still be a good 30 or 40 bucks. So definitely be on the lookout for these.  Channel, my other YouTube channel. Okay, so I picked these up at a garage sale for $3. I just thought they were kind of interesting. They're Rapallo Leather Thong Flat Sandals, size eight, made in Italy. And I sold these for $37.50 in the buyer paid shipping. This is so cute, it's a vintage promise puppy and it's got a Bible scripture on the belly. I could not find anything like this. I listed it at $65, had a 25% off sale going. I really feel like I could have held out for the full amount just because it's so rare. I don't know, let's see. It says promise puppy. I was like, did somebody just put the patch on it? I think it really came this way. But it's so, so cute and definitely a hard to find item. I picked it up at a garage sale for a dollar and I ended up taking a best offer of 35 plus shipping. The next item is this Playmobile set. I showed you the other one earlier. This one I paid 15 for and it sold for $150 plus shipping. This set is a little bit bigger. It's from 1998 also. I could not believe my eyes when I saw it. I love selling Fisher Price Loving Family items. I say that and I have like a tote and three bags full in my basement to list that I never seem to get to, but I really like to buy it. I like to buy it and hold it. Oh my goodness, but this one was new with tags and like I said, I just couldn't believe it. Paid $5 for it, sold it for $85 and the buyer paid shipping. I don't know why I have 85 and it says 82.50. Hmm, that's weird because I looked, maybe I wrote it down wrong. Okay, so we'll just say 82.50 plus shipping. The next item I sold is this Snowman playing the piano hallmark and again, oh, I didn't put a, I must have forgot to do a video on that one. I usually do videos. Why didn't I do a video? Or did I do the video and forget to attach it? I don't know, but either way it sold for $40 and the buyer paid the shipping and I got that at a garage sale for five bucks. I got that at the same garage sale that I got the vintage hair things. Isn't it funny how sometimes you're like, I know which sale I got that at and what else I bought at it? Next item is this Uno Hearts. It's rare, the cards are still sealed. It's from 1994. I picked this up in a mystery box, a thrift store mystery box and I sold this for $37.50 and the buyer paid shipping. The next item, I love this item. It's an African hand carved wood 12 piece nativity set. It's rare, it's hard to find. I couldn't find one exactly like it. I picked this up at a thrift store for $4 and I just had a feeling about it. I took a best offer of 130, it sold pretty quickly and the buyer was all in for 150.309. All right, you guys, that was 23 Big Money Bolos. Let me know what your favorite Bolo item was. Thank you for being here, thank you for watching. Be sure to like, comment, subscribe and share. Again, highly recommend you check out this perfectly if you're looking to grow your reselling business and get on more platforms because it is super fast and your items will be cross posted quickly. All right, you guys, thanks for being here. Check out the video description for more links to like my Instagram, my Facebook, my other YouTube channels and all of that good stuff. All right, you guys, thanks for watching.


How come the McDonald's Sprite, specifically the Tropical Sprite, how come it hits so f***ing good? Good thing I have white seats, if you know what I'm saying. I'm so sorry.


In this presentation, we will take a look at some of the cost volume profit analysis or CVP analysis assumptions. These are going to be some of the assumptions you've probably seen along the way. Some of the support accounting instruction by clicking the link below giving you a free month membership to all of the content on our website broken out by category further broken out by course. Each course then organized in a logical reasonable fashion making it much more easy to find what you need then can be done on a YouTube page. We also include added resources such as Excel practice problems PDF files and more like QuickBooks backup files when applicable. So once again click the link below for a free month membership to our website and all the content on it. The limitations that we see along the way in other words we see these items and say hey this isn't exactly how things are working we might have made some estimates oftentimes in some areas to simplify the process. Remember that when we consider the cost volume profit analysis we're doing projections oftentimes and oftentimes we're going to be using estimates we're not going to be exact in some areas and there's arguments that in some cases that non-exactness could cause major problems there's people that say that the CVP is not as beneficial as we might think in first glance because at first glance it looks great because we want to be able to put things down into a numerical format if we put things down into a numerical format as much as possible then our analysis is something that we can break down in a very efficient type of way but if we have to make assumptions that don't apply then we need to be mindful of those assumptions and we need to decide whether or not the application of the CVP analysis is going to be appropriate or not and or when it would be appropriate in what areas would it be most appropriate when would the assumptions that are there possibly be large enough for us to have concerns with or at least qualify some of our our information so just remember the idea here is CVP is going to be a tool we're going to go through some of the problems with it which are going to be some of the assumptions that are made that could cause problems and then we'll discuss some arguments for the CVP analysis some arguments as to why the assumptions and making them is may not be as big a deal so some of the assumptions that we have and we've pointed these out along the way that we can classify costs between fixed and variable costs so note what we've done is this is the first primary assumption we do with the managerial accounting with cost volume profit analysis we say hey we're not going to be grouping things by what they do for us in terms of expenses we're going to be grouping them by the behavior of the cost do they act as a variable cost do they act as a fixed cost because that's going to allow us to break out our income statement to a contribution margin income statement which is going to be the variable cost minus which is going to be the sales minus the variable costs and then think about the fixed costs as a separate section that's the whole basis that we're going to have to set up our our process in and we've noted earlier that we have some costs that are mixed this is not a perfect world there's no we're not going to be able to go through the income statement and say there's a perfect linear relationship that as the as our production goes up the costs will go up with some items with the variable costs and that other items are simply fixed and that's just what it is they never change note that's never exactly the case that's never going to happen almost and even the rent in terms of fixed costs will go up after a certain point in time because we're going to possibly need more property as we increase the sales volume so note that the these are huge huge kind of assumptions that we're making and we've talked about some methods that we can do to make these assumptions more clearly but note of course that's going to be a big assumption that we have and there's no simple way to do that if you're thinking about your financial statements and saying hmm how do I it's not as easy for me to break these out into variable costs and fixed costs well it's not because you're gonna have to make assumptions to do that and making those assumptions is one of the one of the steps that need to be taken to apply this tool and living with the problems that that come with that the possible errors that come with that is part of the cost of applying the tool as well next assumption that selling prices per unit variable cost per unit and fixed costs will be constant so again we're assuming that these things are going to be constant over time as well so the selling price note that we're basically if we're projecting out into the future we're not we can't it's we can't use this analysis if we're going to say well the sales price will be this much and then it'll go up in a week and then it'll go down it'll fluctuate all over the place it may fluctuate in real life we might make decisions to increase or decrease the sales price in the middle of the year in the middle of the month constantly and it could happen but we can't really make the analysis with that assumption being the case so one the sales price the variable costs in a similar fashion we're going to assume are going to be constant and and again we'll see some arguments why this is okay but just remember that there are arguments for and against this because of course depending on where we are the sales price could fluctuate quite a lot same with the variable costs and again the fixed costs you would think depending on the types of fixed costs we have like the rents you would think would be pretty fixed for a certain amount of time unless we needed more property but it could be variable at some given point as well and then we have a constant sales mix and we talked about if we had different inventory items and we were we were trying to figure out that the cvp type of analysis that we're considering a constant type of sales mix the ratio at which we sell our inventory so that we can then apply out this systematic numerical method and the sales mix changing it could be a significant factor it might not be a consistent sales mix we might sell a lot more of one product to another product and if we don't know what the sales mix is then it's going to be difficult for us to to assume you know a consistent sales mix in order to figure out the cost volume profit type of analysis so arguments for the cost volume analysis notice what we looked at of these assumptions and these assumptions are usually given as problems to the cost volume profit analysis note that in managerial accounting oftentimes there's a big drive to get things to be numerical because if we get things to be numerical they feel more exact we can use actual numbers as measurements whereas if we can't do things numerically we're kind of in the clouds we're kind of just guessing as to what you know what things work or not there's no there's no we can't really compare one thing to the other the more we can put things down in a miracle fashion the better off it looks to be however of course if the assumptions that we use to put things on paper are not you know applicable then the having them in a numerical form may not be as valuable as we as we would have thought and those assumptions are some arguments to say hey this isn't as valuable as you would have thought because of these assumptions now some arguments for against those assumptions and for the cost volume profit analysis and note as we make these arguments it's you think about this from a business by business perspective because cvp cost volume profit is not like financial account it's not required do we want to use this tool or don't we the question is does it provide us benefit to do so or not does the does the tool give us better decision-making on it so we have deviations from the assumptions are minor this is going to be one of the arguments that we could have we could say hey look there's going to be deviations we from the from the assumptions the the variable cost the fixed cost of breaking them out between variable and fixed but we could say hey the deviations we believe are going to be minor and possibly the deviations could go either way they could deviate one way and if we if we take all the minor deviations in our assumptions and net them together in other words it's quite possible they could net out and have a minor effect be in essence correct now again they could net out and they all could go the same way for some random reason it's just basically uh it could randomly be that way you know so it's but it also could be the fact that these small assumptions would be minor and the small assumptions then could be uh in such a fashion that they cancel themselves themselves out and therefore result in minor variations and therefore the cost volume profit analysis would be good because it's just an estimate and that's going to be one of the the key factors that we want to keep in mind here and that's going to be the last one cvp is an estimate so the fact that it's not going to be perfect the fact that we're making estimates the fact that we're making an estimate between variable cost and fixed cost and we're doing things a certain type of analysis to break out between variable cost and fixed cost well that's part of estimating if we're trying to project into the future we don't have any better way of doing it we've got to use something to project into the future using a numerical fashion making some type of estimates to do so is you know as good as we can do to to make to make those assumptions and you know breaking things out by behavior from that argument would be a reasonable a reasonable way to go the sales variable cost and fixed costs are often uh close to a straight line on a graph when assumptions are within a relevant range and this is this item that remember there was an assumption saying that we're assuming that the variable cost fixed costs and the sales are going to be constant and they could change note and that's true and it depends on industry but usually they're going to be fairly constant within a relevant range so in other words if we're talking about the production of inventory within a relevant range of units producing from this amount to to the NIS amount within a relevant range then you would think the sales would be relevant relatively constant within that relevant range if we go past that range you would you would see deviation and change the costs are probably more volatile we have more control over the sales so we can kind of predict what the sales will be we might make some little deviations depending on the industry we're in increasing and decreasing sales but you would think they would be fairly constant what our sales price is within a relevant range and then the variable costs could change too because we've noted that variable costs could have some some variation to them but the standard type of variations that we look at with most variable costs are usually can be approximated with a straight line fairly well within again a relevant range fixed costs in a similar fashion should are usually if they're a standard type of fixed costs like the rent are pretty solid within a relevant range but nothing is completely solid forever it's not it's not going to be the same forever the rent's not the same if we need to make a lot more units we're going to need more space and therefore more we have to buy more place to rent more so the rent could go up at that point in time but the assumption here being that it should be fairly constant within the relevant range so note in conclusion then when you talk about cost falling profit analysis people that really like it really favorite because they're numerically oriented generally and they want to come up with a numerical systematic approach to something also note however that there are problems with it and just because we have a numerical assumption doesn't mean that we shouldn't take into consideration those those problems with it if we just have just because we have a number that says something doesn't mean that we we have to know what that number means we have to say okay what are the limitations to the calculation that we have here and are they relevant to the number that we that we've come up with could they be a factor that could significantly flaw the numbers that we've come up with


Hello everybody. My name is Brad Langdell. I'm going to talk to you about vertical circular motion and this video is brought to you by uniform circular motion, which is the unit that this topic comes up in. And so we're talking about things that are in motion. Okay, that's good in physics. We like things that move. We're talking about things that have a circular motion, which means they move in a circle, and then it's uniform as well. The uniform part is we're talking about the speed. The speed of these objects is the same throughout their entire motion. So it's uniform circular motion. And here's the problem that I'd like to give you today. A shoelace can hold a force of 135 Newtons before it breaks. If a 2 kilogram brick is tied to the end of the shoelace, and the total length we've got to deal with here is 1.10 meters, how fast can the brick be spun vertically before the string breaks? So here's kind of the situation that we've got here. Here's the person who has got this brick on a string, and there's their arm, and there is the string, and the string is 1.1 meters long. And on the end of the string is a brick. And the brick is being spun in a vertical circle kind of like this. Good thing it missed that guy's growing. And you can see the length of the string is the same as the radius of the circle. Okay, that's our radius. Now, we're actually interested at the point where the string breaks. So we have to start thinking about where is the string going to break? The string is not going to break here where I drew the brick, is not going to break at the top or anywhere else. The string is going to break more than likely down here at the bottom. It's going to break at the bottom because here, something very interesting is happening to the forces acting on the brick. Well, let's talk about those forces. We've got a force of gravity acting downwards on the brick. And then we also have a force of tension acting on this brick from the rope. And these aren't necessarily drawn to scale, okay? So here we've got kind of a tug of war between our forces. And the fact that gravity is acting on the tension at this point, that they're acting in opposite directions, is what leads to the force of tension being overcome and the string eventually breaking. Okay, so we want to find how fast this brick is going when that string breaks. So if we're talking about that, and we're talking about a unit about uniform circular motion, we're probably going to be talking about the centripetal force, the force which dictates how objects move in a circle. And the centripetal force is always equal to some other force. I tell my kids in class it's equal to some other force, or in this case, a pair of forces. In this case, the centripetal force is equal to the force of gravity. So I'll write that in there, force of gravity. But it's also equal to the force of tension. The centripetal force is kind of like the net force acting on this brick. Okay, now it's substitution time. Let's actually get to putting some numbers in. So in place of centripetal force, I'm going to put in the equation for centripetal force, or one of them anyways, mv squared over r. Where m is the mass of the brick, and v is the velocity I'm spinning it at, and r is the radius. For force of gravity, I'm going to put in mg, mass times the acceleration due to gravity. And I actually know what the tension is, it's 135 newtons, so I'll just stick that in. Now I can start to do a few other substitutions here really quickly, so I can put in my mass, that was two kilograms. I'm looking for my velocity, so I'll leave that as a v. Got my radius, that was given in the question. Got my mass, and the acceleration. Now the one thing I got to be careful of here, and that a lot of students make mistakes with, in my experience, is vectors up and down, plus and minus, the force of gravity is going down. So I got to make sure that I make this force of gravity vector negative. When I'm done, the force of gravity, the mg, the force of gravity will be a negative number, which is what my diagram tells me it should be. So now I can go and I can type it all through my calculator. Out comes the fancy graphing calculator, let's type this through. So I'm going to start by going 2 times negative 9.81 plus 135. So there's my whole right hand side of the equation. Now I'm going to times that by 1.1 to move the denominator over to the other side. I'm going to divide it by 2 to get v squared by itself, and then I'm going to square root. And I don't want that negative sign in there now that I think about it, so I guess I'll take that out. So this object, this brick is going to move at 7.97 meters per second. Yes, and we do want three siktics. So there is a great example of a vertical circular motion type problem. Kids, you're going to see these in the future, so practice, practice, practice. If you'd like more information about vertical circular motion, you can check out my package of notes at LDindustries.ca.


What's good Josh the boros back again with another video. So we got to talk about this one big E breaks his next WWE Superstars react Hulk Hogan and finish is finished and other wrestling news man. I Just want to send a prayer and get well wishes to a big E man What he suffered was definitely terrible would not wish that on anybody And it's just one of those things where it's it's part of the part of the sport of wrestling sometimes Accident to happen injuries do happen And this is why you know, this shouldn't be tried at home by anybody This should be only be this should only be done by professionals and even then sometimes being a professional Still things can happen man. So prayers go out to him. We're gonna check this video out, man Appreciate all the love and support and let's get right into this bad boy, man And on guys it is WrestleMania here back with another video I want shocks and surprises can fans expect on the Smackdown as a WWE prepares for WrestleMania 38 Join us now as we look at this week's edition of the blue brand as well as the wildest wrestling news and rumors You need to know including biggie suffers a broken neck Johnny Knoxville Doxed Sami Zayn the wrestling world reacts to biggie's injury Hulk Hogan is finished and much more be sure to subscribe into that notification bell for daily wrestling videos and follow us on Facebook for exclusive list as always won't recap the matches But just look at the good the bad and the downright ugly as always we start off with the good is number one Tank team turmoil building up to the women's division as the WWE's women's division are wreck We all know the answer to that as the WWE has ignored its singles division with the exception of a less than a handful of stars While dismantling its already weak tank division while we feel the WWE is under utilizing its many single stars It is refreshing to see the company take these performers putting them into tank teams So they have something to do other than to jump to Becky Lynch or Charlotte Flair It's by no means the best thing to do with its talent, but if the WWE treats it as more than a stopgap measure It's a good way to work the women into more matches and eventually back into singles bout number two Rousey honors Kurt Engel around the Rousey has a new weapon in her arsenal The ankle lock and it's a great move on both her and the WWE's part It was great to see Rousey honor another WWE legend adding the whole to her repertoire Rousey has plenty of moves at a disposal But it never hurts to incorporate more into a moveset and it's a sign that Rowdy Ronda is resting on the laurels And in fact owning a craft number three new challenges for the use those a Shinsuke Nakamura and Rick Boomiya Get into that. I think it's cool. Yes. He's using the ankle lock or whatnot. Does this really still excite me about her feud with Becky, not Becky. That's what we wanted her feud with Charlotte Flair Um, it doesn't I guess you could say excite me still even with their little brawl they had I'm just I'm kind of once again still indifferent. I don't think the match will be as good as Probably WWE management thinks it will be but you never know if we could be surprised Who knows but I'm just not still that invested Boogs are the new number one contenders for the Smackdown tag team titles with WrestleMania 38 around the corner It's nice to see the Usos get a fresh starter challenges after demolishing every team on the blue brand's roster But I being said Jay and Jimmy have held a Smackdown tag team championship since last July's money in the bank pay-per-view And it may be time for new champions The only question is whether the team of Shinsuke and Rick Boogs is the best team to append him after the Usos have thwarted the efforts of the mysterious at the new day and the Viking Raiders Must be everybody ricochet wins and it's not a fluke win and ricochet is a new intercontinental champion And while fans are still adjusting to the idea of the perennial loser holding a championship His win over former champion Sami Zayn last night suggests his title win last week wasn't a fluke and that ricochet's career Maybe set for a sustained push. It's hard to early to tell but last night's win was definitely a move in the right direction Fans of ricochet know that he can deliver the goods in the ring and the intercontinental championship could be the vehicle That takes ricochet out of the lower card and into the upper card Please please please Please continue to push ricochet. He is one of the best I have ever seen In WWE they just don't book them like that, but I'm glad they are now. Please continue that momentum He needs to hold the intercontinental championship so he can potentially it could catapult him to something bigger Things fresh with Brock. Oh, Brock Lesnar's appearance on SmackDown a bit underwhelming. Oh, yeah But we applaud the WWE for its restraint after all fans are used to Brock Lesnar f5ing everyone in sight The WWE champion has plenty of reasons to want to destroy people after the bloodline left him a bloody mess at MSG It's safe to say that the fans wanted to see Lesnar get his hands on the bloodline or even tribal council Paul Heyman But alas, he didn't and that's the point The WWE doesn't want to give Lesnar a chance to get much if any revenge on the bloodline until WrestleMania It's also important that the WWE paste things out so that it means something when Brock does get his hands on an opponent It may be hard to believe but having Lesnar come out every week and destroy opponents can get a little tiresome But that was a good. What about the baddest number one? They're building up.  They don't have to rush into it, you know He's gonna get his hands on them, but ultimately he's not gonna matter cuz Roman will Become the WWE champion as well retain the Universal Championship, but it's just a good way to build up the story Lazy booking are the Viking Raiders beaten down backstage? Hmm, that sounds eerily familiar and watching the team of happy Corbin bad cat Moss and Jinnah Mahal take out Eric and Ivar How's the saying? It's deja vu all over again The WWE's booking of the Viking Raiders is not only atrocious, but it's more evidence of lazy booking Does the WWE's creative team spin a wheel to determine what angle will play out?  I'm sorry, man I know some of you guys were like, oh, this is part of his new gimmick. Give it a check, bro You could have still had him be that same character Maybe just kept a name he's been known as Pete Dunne people knew him as Pete Dunne He's been Pete Dunne for the last few years That's why it's just doesn't make sense to change it, bro You can switch up the character to keep the name the name is People know recognize the name. That's all I'm saying One of the longest UK champions longest UK title reigns outside of Walter was Pete Dunne Dude was known for manipulating joints. He's known for manipulating joints.  Hey, man WWE for you. The WWE has done worse in renaming superstars. Let's not forget do drop. Why was this name just so random? Was it a tribute to WWE legend butch read Bushwacker butch or Vince McMahon's outdated idea of what a tough name sounds like What you guys think a smackdown last night? Let us know in the comments down below. Now. Let's move on to the news Our first story looks at Biggie suffers a broken neck Atop in the news today is an update on Biggie's condition following the Devastating belly-to-belly he took outside the ring during the New Day's match against Sheamus and Ridge Holland And in case you missed it Holland and Biggie brawl to the outside during their tank team bout with Holland appearing to botch a Belly-to-belly suplex on Biggie causing the big man to land a ride on his head Biggie was then stretched out of the arena leading to concerns over his condition He was taken to a hospital where he tweeted a video updating his many fans on its condition. I Can't thank all of you beautiful people enough for all of your concern and your messages. It's very heartwarming I can move all my digits, which is awesome. That's nice. That's always a good thing Strength feels fine, but unfortunately right now. They tell me my neck is broken. So there's that but once again Thank you everybody. I'm gonna be all right. I'll be good. Don't worry. Go to sleep Don't worry about all me, but for real. Thank you. And I appreciate all of you for real So I got some really good news All things considered the C1 and C6 are indeed fractured not displacement though, which is a very good thing And I don't have any damage to my spinal cord. No ligament damage and no surgery Which I'm very thankful for and a pro tip if you're gonna break your neck do it in Birmingham They've been great. Everyone here at UAB has been great But for real It's meant a ton to me that so many of you have been so kind and reached out stopped in to see me text me I know I feel like I sound like a broken record, but I am very grateful and I'm gonna be all right. That's a blessing man. That is truly a blessing Once again, like I said at the beginning of this video get well biggie was sitting in I know I'm sending My prayers your way. I know you guys will as well. This is one of those things where it's like it's not about the wrestling It's about making sure the individual the person himself You know is they get back to a speedy recovery man and once again, like I said beginning this video wrestling It's no joke You can be a professional. You could be a seasoned vet and something just goes wrong You know and I don't want people to blame rich Holland and Blame him trying to get him fired. I know some people are doing that. Don't do that man. This was an honest mistake I know he didn't mean for this to happen injuries happen. That's just what it is. It's a part of wrestling You feel me and no one should be out there trying to get this man fired It'd be different if he had a history of just doing this But I don't think he has a history of injuring people and I'm pretty sure biggie doesn't you know You know doesn't have that type of energy towards him. You know say I'm pretty sure he knows it was an accident So please refrain from doing that. That's That's not gonna help the situation man. Just you know, I pray for biggie for speedy recovery and hope to see him back soon, man Rest in peace. Seriously, even after breaking his neck. He's still positive That's incredible while it's too early to tell if Holland accidentally injuring biggie will have any backstage ramifications One has to wonder why the WWE would put one of its most popular stars at risk with a move that requires strength and Balance to pull off the WWE also needs to ask if it's necessary to feature spots like this on television Like many fans and wrestlers we send our well wishes to biggie for a fast and full recovery But what about the wrestling world? How did they react to biggie's injury now? His injury led to an outpouring of support for the former WWE champion as it's no secret Biggie is a beloved figure on camera and behind the scenes Here are just some of the messages of support for biggie FTR's Dax Harwood took to Twitter to say I love you, dude Natalia tweeted we love you so much biggie keeping you in my prayers. We all got your back.  This is true. AEW star powerhouse Hobbs tweeted rest and heal up He knows I rock with you bruh while Mira tweeted speedy recovery your tour five-fold Sean Ross Sapp even tweeted that Ridge Holland did check on biggie in the hospital He tweeted Ridge Holland visited biggie in the hospital to check on him last night several members of the roster also joined Biggie is a beloved fellow and this is what I'm saying man. He went to go check on the guy He clearly cares biggie is beloved by many people in the wrestling community and it's cool to see Other people from other promotions send him love and prayer This is how the wrestling community should be outside of the back and forth. We have with AWW WWE to see someone put that aside and Care for someone individual of the opposite company. That's all that's what I love to see man I love to see that type of camaraderie with the wrestling community and I've been seeing it It sucks that it took an injury of this magnitude to bring that out but people you know are Setting in size there their differences for what company prefer they prefer and recognizing this is a real human being Suffering or you know went through a real situation See your situation and just sending their prayers and loves. I you know, it's beautiful As fans know it's considered good form for wrestlers to check on an injured opponent Especially if they accidentally injure them as Holland did next up biggie's WrestleMania plans now in doubt Biggie's broken neck means that the New Day strongman may be out of WrestleMania 38 However, what did the WWE have planned for big yet this year's show of shows while according to fight while select the WWE Wanted to book Kofi Kingston King Woods and biggie against Seamus Ridge Holland and butch Naturally biggie's health is more important than a match and the best thing you can do is take the time He needs to recover from the injury. So when he does return, he's fully healed Next up Sami Zayn gets doxxed and our rest for Sami Zayn is jackass star Johnny Knoxville's current campaign to make a life miserable for his WrestleMania 38 opponent continues this time with Knoxville revealing Zayn's mobile number We saw a plane flying a banner with Sammy's phone number according to TMZ Knoxville revealed So yesterday Sammy Zayn got my personal phone number and was texting and stalking me all day So today for my birthday. I'm flying his phone number over Los Angeles<PHONE_NUMBER> See her WrestleMania schnookums. I don't know one surprise Chance to let Zayn know what they think of him. I tweeted his dismay. Did you guys text Sammy? Let us know in the comments down below. Okay, I was trying to get the reference of that I saw the clip of Sammy Zayn showing people just blowing his phone up. That's funny That is funny how they're introducing real-life situations Right now. That's funny, bro That is so funny, but he doxxed him even though this is technically illegal, but he doxxed him To promote a feud. Do I still care about the feud? No Don't care about this feud.  I don't care But I will say this is actually funny, bro. That's that's mad funny Logan says he's finished and last but not least a bad news for Hulkamaniacs everywhere as Hulk Hogan is announcing He's finally done in the ring. The Hulkster discussed his physical condition during an appearance on the two-man power trip a wrestling podcast saying No, I mean the last 10 years. I've had 23 surgeries Damn ten back surgeries both hips both knees forget it The Hulkster didn't mention who he'd want to wrestle if he was capable of living in ring return The first one I'm trying to pick off would be Roman Roman, you know them I'd like to get to Brock, but good god I'd be in a wheelchair by the time I get done with that and you may recall past Speculation that Hogan might return to the WWE for at least one WrestleMania appearance by competing and winning the Andre the Giant Memorial Battle Royal. Should he risk it? Let us know in the comments down below No, the dude had how many surgeries like 20 some surgeries and ten years both hips multiple backs. No Would it be cool to have a legend like Hulk Hogan go for Roman Reigns and the What Roman Reigns is now?  You know I'm saying everybody know who Hulk Hogan is. No, let it go Let it go, bro This just just let it go, but hey man comment down below. Let me know Did you guys enjoy this week's smackdown? Are you looking forward to WrestleMania? Still has has the hype for WrestleMania increased for you or for is it still kind of lukewarm? Or do you not really care? Let me know man. I want to get your thoughts and opinions on that and Once again before I in this video. I'm sending my thoughts and prayers with you biggie I know everyone as you know rocks with me and subscribe to the channel. They're also gonna send their thoughts and prayers to you, man Sure, you'll probably not see this video, but just know we appreciate all you do for the business We're wishing you speedy recovery and we love you, man. So but I appreciate y'all kicking with me. I see y'all in the next one


Hi, this is Drew Sutherland. We are here at Innova-Wolfach conference, and I thought I'd ask him to explain to us the polymath project. Sure. So what is it? Well, so the very first polymath project, Polymath 1, was started by Tim Gower's, I don't remember exactly when, some years ago now. There was, and it was an experiment in massive open collaboration between mathematicians to solve a problem of common interest. So the first problem was known as the density-hills-Jewitt theorem, which is a celebrated theorem in extremal combinatorics, and it had been proven, but the proof was very long and involved, and they were looking for a more elegant proof. And this project was created initially by Tim Gower's with a blog post and a place where people from all walks of life didn't necessarily have to be a professional mathematician, anyone who wants to participate. And eventually they found a very nice, beautiful, elegant proof of this theorem. It was published, and the results were written up in a paper and published in the Annals of Mathematics. And the publication was under what kind of authorship? So it was under a pseudonym. They chose the initials DHJ polymath. So DHJ stands for density-hills-Jewitt, which was the name of the first problem they worked on. And then, following that, there were a number of other polymath projects on different topics, and not all of them were somewhere more successful than others, but there have been several papers published under the same pseudonym, like DHJ Polymath. If you go into Maths Signet, you can look up papers written by DHJ Polymath. And so you participate in some of them. What do you think? How is it working? How do you see this project? Well, so I can only speak of the project that I participated in directly, which was the eighth polymath project, on polymath 8, on prime gaps. Not long after Yutang Zhang's breakthrough result, where he proved that there were infinitely many pairs of prime separated by a gap of at most 70 million, which came out in May of 2013. In his paper, Zhang's effort was very much focused on the very difficult technical details of his formal theorem. He consciously decided not to put a lot of effort in trying to make the number as small as possible. I mean, the major breakthrough was that you could prove a finite bound of any size. So getting from infinity down to 70 million was already a huge progress, and he left it to others to try and refine, further refine the results. And then there was some discussion on some popular mathematical blogs, including Scott Morrison's blog, where people started talking about some easy ways one could go about improving this bound of 70 million. And as people started to look at it, they found more and more ways that they might be able to make improvements. And then I think it was June 4th, 2013, Terry Tao, Fields Medalist, and someone who has a very large presence on the internet. He has a very popular blog that he runs and posts on many different topics, and a lot of people follow his blog. He suggested that we start an official polymath project with the intention, really with two goals. One was to really try to better understand Zhang's proof, which was quite new at the time. Not everyone really understood all the details. So he hosted sort of an online reading seminar where he went through different parts of Zhang's paper. And then the other part was to try and optimize Zhang's result to the extent possible. And so first of all, as you said already, but just to emphasize, this is something that is completely open to absolutely anybody. Absolutely. And so how do you think, in your opinion, this, in a way, changing the way mathematics is being done? Well, I think it's done two things. One, it's opened it up to a lot of people who might not have otherwise gotten engaged in this particular case. There were, I know, at least three people who were active participants in the project who would not call themselves professional mathematicians. One of them is a biologist, another one works on robotics. But they had some really good ideas, asked a lot of interesting questions, and made strong contributions to the project. And it also served to bring together mathematicians from very different fields who might not otherwise have been likely to talk to each other unless they happen to work at the same university. So I think it really does help to foster a lot of communication between mathematicians both within the field and even outside the field that might not otherwise occur. And the people that are participating, and say particularly the young people that maybe need to prove that their career is in track and so on, is participating in something like this, something that they can get the right recognition, do you think? Yeah, that's a very good question. I think it's something that we think about a lot. I mean, I think as the Polymath projects are becoming more well-known, I think it's more and more likely that being able to talk about the contributions that you made to a project like this would impress people. Certainly, I know it's kind of funny even within my own department. I mean, I'm well-known among the other number theorists now that you raised my group. But working on the Polymath project actually brought me to the attention of other people in the department who perhaps the only thing they know about me is that I happen to have worked on this project. So it has been actually even more positive than the other way around? Absolutely. It's definitely been a positive. I was invited to speak at one of the colloquium on this particular topic just because the Polymath problems tend to be well-known problems that are of interest to large numbers of people. So working on one of these problems can bring you to the attention of a broader community. And does the system kind of self-policies itself? I mean, how does it have issues with people doing inappropriate things or how does that work? It has really at least, again, I can only speak about the project I worked on. It has absolutely not been a problem. I mean, the results of the project are written up on a Wiki page. Everybody who's participating has access to the Wiki and can make changes. Anybody who wants to can comment on any of the blog posts and make suggestions. It really hasn't been a problem. I will say it has certainly helped that in this particular project we had somebody helping to organize and lead the whole effort in Terry Tao who is extremely capable and very highly respected, obviously. So I think that probably helps to keep everybody on their best behavior. But I think in general, you know, mathematicians are nice people. They like to work together. They like to work together on problems and are happy to exchange ideas freely. So no, it really hasn't been a problem. Great. Well, it's great to hear. So thanks very much, Drew, and I hope things keep going well for you. Thank you. Bye.


Okay. Recording in progress. Go ahead. Hi. My name is John Nelson, and today I'll be presenting on how to use the way it's quantum annealing hardware to perform a high quality deep sampling. Um, and this is work with, uh, Mark McFrey, Andre locove, uh, to me all bash and Colton Coffin. See. Okay, so brief introduction. Our hope is to use D wave to find ground states of classical icing models and a reminder of this icing model is basically it's a some of these terms where we have a variable for these spins that can take the value plus one or minus one. And so we have these coupling terms and then we have these bias terms. Um, and so it biases each spin to either up or down. And to find these ground states, what we do is we start in the ground state of Hamiltonian that's easy to prepare. And then we interpolate between this Hamiltonian and the icing Hamiltonian that we want to, to find the ground state of. And if we kneel slow enough, then we hope to stay in this ground state and eventually find the ground state of this ladder Hamiltonian. And so in reality, um, we don't actually find the ground state every time, but because, um, we only have so much time to perform this annealing, uh, there's some thermal excitation. So, um, we, uh, produce some higher energy states and also air. So in general, we end up with a distribution over low energy states of this icing model. And so once type of distribution is this, um, we'd like to say that it's, uh, like Gibbs like or Gibbs distribution. Um, and that would be really nice because, um, there's lots of practical applications for Gibbs sampling in general. It's, uh, has applications for, uh, simulating physics and sampling from the thermal states of systems would find a temperature. And, um, it's also a sub routine in many machine learning algorithms. Um, and so reminder of this Gibbs distribution, basically, uh, the probability mass of each state depends on its energy and the lower energy states are weighted higher. Um, and the mass decays exponentially with a higher energy. Um, there's also this beta term. Um, and the, uh, this is like, uh, the inverse of the temperature. Um, so if you have zero temperature, then, uh, beta is infinite. And basically you sample uniformly from the ground states. Um, but, uh, there are some challenges that have been observed in previous work. So one is that it's been observed that D wave does not actually sample uniformly from states with the same energy. For instance, uh, it doesn't sample uniformly from, uh, the ground states. Um, and at least under certain conditions. Um, and this is often explained by a freeze out argument. Um, which says that, uh, postulates that at some point in the anneal it gets stuck and doesn't actually finish the anneal. And so there's some residual transverse field. Uh, so that's like these, uh, poly X terms. Um, and that remains, uh, after the anneal and this introduces biases of biases to some ground states over others. Um, and so clearly this is not, uh, like very Gibbs like, but, um, there's another source of error and that's if you scale down the interaction strength. So the interaction strength here, I'm referring to the magnitude of these magnitudes. Um, and so we always take the J and H values, the magnitude to be constant throughout the entire Hamiltonian, but, uh, what changes is the, the sign. So it can take a positive or negative sign. But, uh, yeah, we keep the, the, these magnitudes, uh, constant. I'm referring to that as interaction strength. So when that is small, um, it's been shown that actually it does suffer from this issue of, uh, non-uniform sampling from states with same energy and these, these, uh, residual transverse field, but it does suffer from noise. Um, and so this noise can make the distribution, uh, significantly different from the original, uh, distribution that we want to sample from. And, uh, that was observed by my co-authors a couple years ago. Um, and so these two sources of error have inspired our work. And, uh, in our work, we argue that both sources of distortion can be avoided by carefully tuning the interaction strength. Um, and that comes from the intuition that this residual transverse field, it dominates when there's large interaction strength and the flux noise dominates when the interaction strength is low. Um, and there is a sweet spot in between. And so this number is specific to the de-weighted machine, but around point two to point four, whereas the full range is between zero and one. Um, and in this regime, uh, we observed that, uh, both of these, um, sources of distortion are significantly mitigated. Um, and we then, uh, do some like extensive experiments to evaluate, uh, how well we can sample, do dip sampling for randomly generated icing model instances. Um, and then we also show how you can tune the temperature of the Gibbs distribution you want to sample from, um, by tuning parameters in de-wave. Um, so first, um, I want to present some evidence for this intuition of, uh, why we believe, uh, of these two different sources of error and the, their, um, their, uh, how they dominate in either the small interaction strength regime or the large interaction strength regime. Um, and so to do this, uh, I'll present this like, uh, toy model and then, um, the main results for our, uh, will be after. Um, but okay, so for this toy model, we basically have a three spin system where it spins one and two are coupled and spins two and three are coupled. Uh, then we just collected many samples, uh, from this one. Um, and then using the, this quantum annealing process on de-wave and getting the ground state, which is, uh, these, uh, some spins configurations. Um, and then using the spin statistics, uh, we reconstruct each term, each coupling term. And this will be the coupling term between one, two, two, three and also one three, which is not present in the original Hamiltonian. Um, and we, uh, use a Hamiltonian learning algorithm that we can use to, um, and then finally we'll, uh, re-re-reduce this experiment, but instead of sampling from de-wave, we'll sample from, uh, this, uh, a model of the, uh, Hamiltonian and this model includes the transverse field term and a noise term. Um, and then we'll compare how well the model agrees with the actual data. And, um, the things to note is that the transverse field, uh, depends on interaction strength. So it scales with it. So it gets much worse in the interaction strength. It's, uh, betters that that captures this idea that I mentioned earlier. And, uh, the, the flux noise does not scale with interaction strength. It's actually, we take the aided parameter to be quite small. Um, so it's very insignificant when J, uh, when J gets large. And so then we sample from this like noise average thermal Gibbs state and, uh, do the same Hamiltonian, uh, reconstruction. So, um, here is the data and we see like very good agreement. Um, and the things to note is that the main source of distortion or is this, uh, with this coupling between one and three is not actually present in the, um, original Hamiltonian. And so that, that's, uh, what is really, um, making, uh, our output statistics very non, uh, not matched our desire to Gibbs distribution. And you can see this, uh, like spurious, uh, coupling become much, uh, greater with the greater interaction strength. Um, and also it's hard to see, but it's also becomes negative when you go below 0.25, but it's around zero around this, uh, 0.25 regime. Um, and so we kind of designate that as our sweet spot. Um, and also, uh, we like just by experimenting with this model, we can see that the main feature of the noise is this negative, uh, spurious coupling value for low J. And, uh, this distortion here can be attributed to this transverse field term that scales with J. Um, okay. Okay. So now, um, on to the main experience is, uh, we, uh, a bunch of 16 spin icing models with various ground state degeneracies. Um, for each of these, uh, we redo the experiment at various, uh, interaction strengths. So remember we keep J and H the magnitude to be constant for each of the models. And we take it, uh, or I guess not zero, but a slightly above zero and up to one. Um, and then, uh, we also redo the experiment for different annealing times. And, uh, for each of these configurations, we take, uh, about a million samples from D wave. Um, and then we compare the output distribution to Gibbs distribution. And we do this by, uh, classically computing the exact distribution. And we just use this way, or we do this by brute force because we only have 16 spins. So we've tried to take as big of a model as we can that can still be relatively easily, uh, simulated classically, but brute force. Um, and then, uh, we compute the total variation between the exact Gibbs distribution and, uh, the D wave distribution. And so this variation metric is just the absolute, uh, value of the difference between the, uh, probabilities for each, uh, uh, output. It's been configuration. Um, so, um, here is an example of one of, uh, these randomly generated, uh, IC models and we show all the different annealing times. And basically the punchline is that, uh, alpha in is like an interaction strength. And so for low alpha in, uh, we see like a big divergence from the Gibbs distribution of the due of statistics for large alpha in, we see something similar, but as long as, uh, alpha in is between the sweet spot that agrees with our original free spin, uh, toy model experience experiment. Um, then the, the, uh, distribution matches the, uh, Gibbs distribution very well. And so we kind of designate 5% as this accuracy, uh, threshold. And, uh, it's also interesting that varying the annealing time doesn't really affect, uh, where the sweet spot regime is. Um, and so here are some more results. Uh, this is for various, uh, different randomly generated instances. And by random, I just mean we take the, uh, we include every coupling term in the due of architecture. And we just randomly choose positive or negative. Um, and, uh, the left terms don't include this, uh, field bias and the right terms include this like single spin, uh, field bias. Um, and we see that consistently, uh, we're getting, uh, very good agreement with the Gibbs distribution for this regime between, uh, 0.2 and 0.4. Um, and it's also important to be able to tune the temperature of the Gibbs distribution that we're sampling from. And we can do this by, uh, one, we can vary our interaction strength between 0.2 and 0.4. So it is a kind of a narrow regime that we're trying to hit, but it's not, you know, there is some room to vary. Uh, and then we also can vary the annealing time and that affects, uh, the temperature that you're sampling from. And, um, by varying these together, you can get a pretty, uh, consistent, um, uh, range of, um, temperatures. So in conclusion, um, we analyzed major sources of errors, uh, when trying to perform Gibbs sampling on, on annealing hardware. Um, and again, we identified that, uh, there, there's a specific scaling regime, uh, that you can use to, um, really mitigate these errors. So this is, we showed it for Gibbs sampling, but like in general, um, these errors are not desirable noise and, uh, having this residual transverse field. So it kind of serves as a general, uh, piece of advice to what, if you're going to use these quantum annealing hardware, uh, devices, um, to not push your, uh, interaction strength all the way to one or max it out. But really you want it to be in this middle, uh, middle ground area. Um, and then we showed that by, uh, specifically tuning the energy scale for Hamiltonians, we can, um, improve the Gibbs sampling performance. And we also show that, uh, it's possible to, um, tune the specific temperature that you're sampling from. All right. Thank you. And I'll take any questions. Questions.  How did you fix the temperature? Um, as in how did we, uh, sorry, um, like how do we compute the temperature or how do, how do we adjust it? The machine is the exact Gibbs distribution. Okay. Yeah. I can just explain that a little more in depth. I did brush over that part. Um, so one just, uh, we expect the, um, like scaling the, basically the, the energy scale of, um, the, the input problems that is, uh, effectively changing the temperature of the system. But, um, the same goes with the kneeling time. So, uh, longer and kneeling times, uh, basically relates to, um, more often finding the ground state, which is essentially similar to having like lower temperature in the system. Um, but there's also this question that I glossed over of, uh, how do we actually know what is this temperature that we're sampling from? Um, and so that's calculated by, uh, so when I say we classically compute the exact Gibbs distribution using brute force, we actually calculate this Gibbs distribution for many different, uh, temperatures. Um, this classical Gibbs distribution. And then we see which, uh, Gibbs distribution matches best with D wave. So we're basically implicitly inferring what, through this process, we're inferring what the, this effective temperature is D wave. Um, and so we have to do that step as well to actually see what is the temperature we're sampling from. Uh, yeah. Thank you. Yeah. I think there is a question in the chat. Maybe you could read that and answer the question. Uh, so it says, does this tuning effect both energies and uniformity of samples, both the Gibbs distribution of energies and the uniform distribution of samples at, uh, fixed energy. Um, yeah, so, um, I guess, uh, both. Um, so sampling from the Gibbs distribution is actually, uh, a large part of getting it right is being able to sample uniformly from low energy states. Um, because all the probability mass is on the low energy states and it decays exponentially after that. So you really have to get those right. And so if you, especially if you mess up like the ground state and you don't sample uniformly, then that's like going to be the dominant source of, uh, the power between your distribution and the Gibbs distribution. So, um, yeah, I would say that. One of the main, uh, Uh, like tuning this, um, energy scale is, uh, mainly to kind of fix this to, to try to make, make it so that, um, these, these low energy states are being sampled uniformly. So, um, I guess my answer is yes to that. Any other questions? Questions online? Okay. I have a question. Um, do you think your technique is scalable? I mean, I see that, uh, the temperature I can sample from depends on the annealing time. So I guess if I increase the system size, probably need to increase as well the annealing time. So maybe there will be system size where things might break down. Yeah. That's definitely, um, something that, uh, I guess we'd like to experimentally test, um, how it scales. It's definitely a future direction of this work. Um, I think in general, since we, uh, show from these very small systems, like these three spin systems, the presence of these distortions when you increase the interaction strength. So, uh, And we see that it still persists when you get from, go from three spins to 16 spins. I think that in general, um, it's not a good idea to, uh, really blast up the interaction strength, um, because I, it does really seem like there, there is something, uh, going on where, uh, that really, uh, exacerbates the, um, the effect of this, uh, freeze out, or this residual transverse field that, uh, stays there. Um, and I, so I think like, um, in general, yeah, I think it would scale in the sense that I think always, uh, having too low of interaction strength makes you susceptible to noise and too high, um, makes this, uh, residual transverse field issue worse. Um, and so I think that regime is always going to stay consistent. How good of a gift sampler it is for, uh, bigger systems. I think that remains to be known. I think most likely the performance would, uh, degrade as you get, uh, larger system sizes, but the, the general takeaway message I think would stay consistent in terms of this, uh, uh, trying to operate within this sweet spot regime. Thanks. Well, if there's no other question, let's thank the speaker again. Thank you.


You've got your tags down here. So let's pick a tag. Let's pick a couple tags. And and there it is. Now the customer, notice I picked customer two, but if it was a sub-customer or something like that, then this is where you'd pick basically the sub-customer to be breaking out the sub-customer. If you had splits, then you can use your split item in a similar fashion so you can break out multiple sales categories for the deposit side of things. I'm going to close that that out. And then of course, you could create a rule and it will help you to automate the system. So let's see if all these kind of things, classes, projects and whatnot, are in the rules so I can automatically assign all that stuff as we go. So let's say this is going to be for a customer. I'm going to call the rule customer two because that's what's in the description. It's going to be a money in rule in the checking account. And I'm going to say that the I usually choose bank text because I find it to be more useful or precise oftentimes. And I'm going to say it contains customer number two. So when it sees customer number two, that's when it's going to apply the rule. If I test out the rule, there's only one item that currently meets that condition, which makes sense. And then we've got the transaction type as a deposit sale of product income. That's the income account, the payee. I'm putting it to that sub job. So that's going to be our job area. And here's our tags field. So the tags will be automatically applied. The class will be automatically. But notice that if you wanted to split it, then you'd have to you've got some more options up here in the split area. So you have that. And then the location tracking is one location for the entire transaction. And so there we have it. So let's go ahead and add this one. And so now if I go back on over to my reports on the balance sheet, let's run it. And let's just look at it by total over here. So if I run the balance sheet, and I go into my checking account and drill down on the checking account, we added this one customer number two, let's scroll up and let's just take a look at the profit and loss this time. And so if I run my profit and loss and run it, then once again, I can break this out by the the various the various tools we've been working with, which are the classes. So now it's breaking out by class on the income side of things. And then we're going to go to the location. And it broke out by income on the location. And then you've got your customers, which breaks out the jobs and sub customers. And then again, with the tags, normally I would run the report from the tags area might be the best way to do it. And then you can basically do your filtering by your tags over here. And so we can run by the tags. Alright, let's go back to the first tab again. And let's add another another vendor. This would be like an expense or money out and just add a rule with it just so we can see what the rule looks like. So this is going to be vendor one, but it's going to utilities again, let's say this was good, let's say this is going to go to supplies, supplies. And then I'm going to assign it to this time. Let's pick pick a job or sub customer. We're going to make it billable. It's going to go to location Nevada. The class I'm going to assign will be personal, let's say this time tags, let's pick a couple tags that we can assign out and boom. And there we have it. So I'm not going to split it this time, but instead just go to create the rule. I want a rule. There's got to be rules here. There's got to be some rules. Can't have anarchy crying out loud. It's a money out. So we're going to say description. I'll pick the bank text again. Contains vendor one. If I test it, then it's picking up two transactions. It's going to pick up with this rule. Okay. Expenses. It's going to go to the supplies account, the payee, the customer. This is where we're choosing the sub customer this time. That's where you pick the sub customer or job. So I can run the sales report by sub customer or job. It's picking up the tags. It's picking up the class, but it's applying the class to the full transaction. If I wanted more detail, I can go to the splits and then I've got my location Nevada and then that looks good. So let's notice it's auto adding too. So it's going to add them automatically. If I turn that off by the way, and I save this, then it first gives me another little check before it adds it, which is kind of neat or good when you first start out. But then you're going to probably auto add them because it's super fast to do it that way. And then your rules are being created over here. Boom rules. You can adjust your rules if you so choose. If I pull that into my balance sheet, it's just so cool. I don't know how, there's no other word to describe it. Anyways, so those pulled in and then I'm going to go on the expense side and exit this profit and loss, run it. We can see it by all the various stuff locations. For example, poor Hamplow. We had locations for the supplies. And then we had the class tracking class tracking for the supplies. We had then breaking it out by customers. We had by location or or the job. And then of course you can do it by tags again. So if I go back to the tap to the left, one more one more thing is that you can obviously you can think about the rules and then add the splits. So let's do one more money out, which is more likely where you're going to add, you know, the splits to have multiple classes, for example, vendor. Let's say this time vendor three is going to go to do I have any other? I have a miscellaneous expense. Vendor three is very mysterious. We put it been to miscellaneous. This is going to be project project two or one, let's say billable location. Let's just choose this location. Let's say this is business two or whatever tags, boom, tags, boom. And then I'm going to create a rule with it. And this is going to be vendor three rule money out and all I like choosing text vendor three. Does it match up to anything? One transaction, movie B to the end, BN expense miscellaneous vendor. All right tags are being applied location, but I want to split out that location possibly by by line items. So I can hit the split button. And then we've got some options for, for splitting out the transaction. So on a percent or dollar amount basis, if you're going to do a rule for it, then you might need like a percent breakout so it can kind of automatically break it out oftentimes. So let's say it's going to be 40% miscellaneous and it goes to class two or let's just say straight up business. And then let's say it's going to be, this should be 40. And this is going to be 60, 60%. This also goes to miscellaneous. But we're choosing a separate class, which is going to be personal. So you can set up your rules, something like that vendor project. And so that's the general, that's the general setup. So let's save it and close it and check it out. And so there's our split rule that we put into what's the expense account miscellaneous. It's the mysterious miscellaneous profit and loss run it. And we're going to check it out by class boom. And then in the miscellaneous, it broke out the classes there beautifully. So that's how, so the class tracking is pretty, all these tools, class tracking, projects, location tracking, tags, sub customers, which used to be known as jobs are pretty, you can utilize them pretty well. Using the bank feeds to kind of help you to integrate and automate your transactions. It's going to look a little bit different in the bank feeds. But remember that the bank feeds are basically recording for the most part, the same, do you want to leave the same transactions from this window, but it's only the banking transactions, which means deposits are usually the forms for increases and the expense form or check forms usually expense forms because their electronic transfers would be the decrease.