Hey friends, today we are doing one of my favorite things, the monorail crawl. We're going to be taking the monorail to the different resorts at the Magic Kingdom Loop and actually getting a drink and probably a snack at each of our favorite locations or at this moment each location that's actually open. So let's go do this. And our first stop is going to be the wave with Jackie. And look your hair actually matches the wave. Very fancy. The wave is one of my favorite lounges at the Disney World Resorts and we actually had to make a reservation to come here but normally you don't need a reservation to come in and use the lounge that's just open by availability. We just wanted to make sure but as you can see there's nobody in here. We got the wave to ourselves. We got the whole wave to ourselves. One of the reasons we came to the wave is because they are doing a end-of-summer seasonal drink which I am super excited to try. I'm not big on the liquor drinks. I'd like to stick to my beer but when something fancy happens or appears I got to try it. And also they actually have the top-of-the-world lounge cake right here at the wave. They're serving it down here temporarily because the top-of-the-world lounge is an open. So we're gonna try that as well. Here is the end-of-summer drink and take a look at this because the flowers are edible. These look amazing. Here is a look at all of the ingredients that are in the end of summer splash. Pretty fancy stuff and I'm excited to eat the flowers because they are edible. Edible flowers. First sip. We're gonna try this out. Yeah, again cheers to the end of summer. I have a feeling you're gonna like this and I'm probably not gonna like it. Yeah, I tend to like really light summery gin cocktails. Yeah, I like beer. You know what I'm gonna do? I'm gonna eat the other flower and then take a sip with it. That's like I'm gonna see if that actually changes anything or should I try it straight first? Let's try it straight first. Yeah, okay. It's strong. I don't like it. I mean it's not that it's a bad drink but I don't like grapefruit. Yeah, I don't also like grapefruit. Let's see if the flower helps. I don't know what to say about this. And here is the cake. This is the top-of-the-world lounge cake except for they added a little wave signature right there and it's not like the full piece that you would normally get but it's just really good to know that you can still get this while the top-of-the-world lounge is closed. I feel like it's important to maybe cut it this way and then that way when you take your first bite you're gonna get an actual bite of all seven layers. Can you do that? Can you get all seven? Well, I'm gonna fit it in there. This is gonna happen. We're gonna get seven layers in one bite. I'm gonna fold it over. Yeah, just like that and there it goes. That is a good cake. That is a good cake. The cake was fabulous. I love that cake. It's definitely one of the best cakes on property anywhere and the drink is just not my cup of tea. I mean it was okay. It was a great drink. I finished it. I just don't like the grapefruit, you know? It's not one of my favorite things. So now we're gonna move along to our next destination. I'm excited to get there. Let's head to our trusty, reliable form of transportation, the monorail, and go to the next resort which I believe is the Polynesian. It's also very important to point out that every time you actually board the monorail at a different location they are gonna take your temperature. And here is the temperature screenings area. Thank you. And our escort for today is gonna be monorail yellow. Yellow! And whatever you do, don't stand like a cool guy by the door. Look how cool he's standing. Doesn't he look like a cool guy? Way too cool. Since we've only accomplished one stop and one drink, I don't think I'm gonna be practicing any of my monorail grovics just yet. But I feel like maybe that'll change. Fun fact about the Polynesian. They just announced that they're not gonna actually reopen until 2021 because they're gonna take that time and actually do their refurbishment here. The only thing I'm concerned about is I hope I don't have to wait a year to eat at Ohana. One of the things that did reopen though is Tambu Lounge. And I'm excited because it'll be the first time that I've been out here since the reopening. The bad news is I hear they changed their food menu a little bit. And they also socially distanced a lot of the seating that was actually in here. There's no bar stools. All they do have is five tables. Five tables in there. But you can always get drinks out here in the waiting area.  So I think that's really fun because this is very colorful. And since I can't actually eat at Ohana, at least I can kind of sit down and have a drink near it. The only thing that's separating us is the bamboos and the tiki gods. Here's a look at the appetizers that they're serving here now. California roll, some hot wings, some flat breads, and some barbecue pork ribs. But I want the noodles and dumplings. They've taken them off the menu because I think this is all getting prepared actually in Kona Cafe where used to they actually had Ohana prepare their food. So that's the reason why they changed it. I have to say the seating arrangements in here are spectacular.  And since we're at the Polynesian, I think I'm going to get a beer this time, but I'm going to get a Hawaiian inspired beer. I'm a little excited for this. They have one of my favorites, which is the pineapple mana wheat. I had this at Epcot this year. But then they also have a coconut porter. I think I'm going to try the coconut porter. And here is our beers, a coconut and then a pineapple. Very fancy. Cheers. Cheers. Boom. This truly is what it is. A porter. I don't taste much coconut, but it's still a very delicious beer. I really like the pineapple one. I probably should have stuck with that, but you got to explore. You got to try new things. My sushi has arrived. So it's just a basic California roll. That's all they're serving right now. I would have gotten anything if they had anything else, but this is all they've got. They've also got packets instead of like a jar of soy sauce. So it made some more of that, but we'll make do with what we've got. Jackie actually got the California roll. I am not going to partake in this. I mean, I've had sushi before.  I love it.  I don't think I've ever been to that point. Like I said, it was definitely a porter, but it was still very enjoyable. I feel fancy with this glass too. Be careful. Fancy glass. Now I think it's time we actually move along to our next stop, which is the Grand Floridian. But I really like what the Tambu Lounge did with these little chairs and these like tables. Very comfy. Very cozy. I miss the bar stools. Another question that probably is asked a lot. They do still have the back scratcher. The back scratcher is just served on the side instead of in the cup. Just good to know. I also like how they actually have their signs for the monorail. Look at this. In a true Polynesian spirit, monorail transportation starts at 7 a.m. for breakfast reservations, and then it ends at 8 p.m. No Epcot monorail service at this time, though. And then they got their little lays on top. And speaking of lays, I thought that maybe they would still give them out just like hand them to you instead of giving them to you. But that would actually break tradition. So they're just not giving out any lays at all at this moment, even when you check in or anything like that. We got to get our temperature checked. Oh wow, and look at this. We're going to get back on the same monorail. Monorail yellow. Come on, Jackie. They call me mellow yellow. Oh, and look at that. The beautiful Grand Floridian. It is a very beautiful resort, though. Even though it's pretty occupied right now by the NBA, people can still come and enjoy it. The best thing about the Grand Floridian at this moment is just how empty it is. There is not a single person down there right now. Oh, never mind. There's one person over there. You see him just sitting there? He's just enjoying himself.  It's a good spot to take a nap. And with the Grand Floridian, we're going to go to the Enchanted Rose. This is one of the few spots that's actually open over here to dine. They only have the Grand Floridian Cafe and then the Quick Service. And this is the only lounge, which is a good one. And definitely one of the more visually appealing actual lounges. I love it in here. It is so themed. The library area is closed, but the main area is actually open with very limited seating. This is the main bar area. They actually have a little seating area over here. And I love all of these chairs in here. They look like the best comfy chairs. Look at this. And look at those ones. So we're going to sit right here. Inside the lounge itself, they do have some starters like crab macaroni and cheese, truffle fries and some flatbreads and some amazing cocktails. I have had all of these cocktails. I actually made it a point to try all their signature cocktails. So today I'm just sticking with my good old Bud Light because I like the way they serve it. They serve it in these very nice cups or chalices. I like to call them. I got a Tampa Bay Brewing Florida Crocker. Cheers. Nothing like a fancy Bud Light in a fancy chalice in a fancy room. I like it. Hmm. Not only do I just love these little chalices, but I also love the bar stools that they actually have at the bar. Look at those bar stools. Aren't they amazing? This whole entire bar area itself, like I said, and that up there, it's beautiful. And check out Sheila. She's an amazing bartender. But now we're going to have to move along for our next stop, which is going to kind of just go in order. So we went from the contemporary to the poly to the Grand Floridian. Next place, Magic Kingdom. What's she doing? I'm waiting for Jackie to catch up, but what do you think the chances are we're going to get the yellow monorail again? I see the green ones leaving right now. How cool would that be? Magic Kingdom. How are you today? Thank you. I'm good. I'm sorry. Thank you. Yep. We're going the lime green monorail now. Look at that. And just because the Magic Kingdom is our next stop, doesn't mean we're not going to get an adult beverage. Welcome to the more monorail line. Our next stop is Magic Kingdom for your safety and at all times. Thank you. Thank you. For those guests who just joined us, welcome to our next stop is the Magic Kingdom. For those of you standing, please hold onto the handrail throughout our journey and stay clear of the door. Beach Resort and we are... Can you beach club me? Yep. Just because I was just grabbing those rails doing my monorail aerobics. And look the walkway right there. Where? Oh, there it is. Yeah, we missed it. There's like a little bridge. It actually folds. And welcome to the Magic Kingdom. Monorail coming into station. Monorail gold. Look at that. And like I said, even though we are going to the Magic Kingdom, we're still going to be able to get an adult beverage because at most of the sit down restaurants, they do serve alcohol. At Tonestown Square, they have a selection of Italian beers. At the Plaza, they have Bud Light. And even at Skipper Canteen, they got Blue Moon. And we have a reservation. Everybody's actually leaving because the park closes in literally, I think 45 minutes. So we're getting here just in time. And since we have a couple minutes before our reservation, we might as well just enjoy a little bit of Main Street. I love just hanging out on Main Street, looking at all of the people and the buildings. It's one of my favorite places in the world. They have a new message. Yeah. Very interesting. Oh no. A balloon has left the coop. It's gone. It's a goner. I wonder how far they go up in the sky without bursting. But now it's time for Tonies. And we're going to definitely be sitting outside because then you can enjoy a beer and actually Main Street at the same time. Very rare thing. Yeah. This is so awesome though. Look at this. Oh look. Now we can see all the characters are coming out to say goodbye. Oh my gosh. It's Peter Pan. Pooh Bear. Everyone's out there. Aladdin. Wait, I'm going to zoom in, guys. Oh my gosh. I'm going to zoom in. All up on the second floor. That is so cool. I love it. And it looks like we got ourselves a Stella and a Peroni. Very fancy. Jackie got some fried mozzarella and we got some bread. Fakasha. Fakasha bread. That's right. So they give you the Fakasha bread with any order. That's what I'm talking about right there. That's awesome. Main Street, USA. This is literally the only way to do it, you guys. And like I said before, because I actually did a whole entire video actually hanging out in this patio for several hours, just people watching and drinking Italian beers. This is one of my favorite places to get a drink at Disney World. Like it's like such a rare opportunity. The confectionary is right there. Like I love it. I'm not a big fan of the mozzarella, but Jackie says those are fantastic. They're really good. The sauce is really creamy and delicious. The cheese is delicious. Those are good mozzarella balls. But the bread. Oh, that olive oil is good. Yep. I love the Fakasha. And you know what else is great? I just realized having the music for dinner. Like I don't know if you can hear that too much, but that's amazing. And without doubt, this was definitely my most favorite drink of the night. I love it. I love it here. And with that, I think I am done here today. Had so much fun and what a great way to end than to have a couple beers at Tony's and enjoy Magic Kingdom as it actually closes. So hope you guys enjoyed the video. I enjoyed making it. Make sure you check out Jackie's channel, super enthused. I'll put her channel in the description. And we'll see you next time. Bye!


Welcome to another Narc Survival Live video. I'm out here at the Ket in Thailand, got the new BMW just out here by the beach, the waves are pretty wild, so let's talk about it. How does the narcissist feel when you're not around? When you leave the narcissist, or if the narcissist leaves you, they want you to think that they're so much happier without you, and so they're living a better and happier life now that you're gone. They want you to think that you were the problem.  It's not real. It's an act. They want you to think that they've just moved on and suddenly overnight they've developed this happier and healthier life without you, now that you're gone. Yeah, they'd love if you would think that, because then even if they've moved on to another situation with a new supply, they can still get supply from you as long as they know that you're hurting, as long as they know that you're struggling without them, especially if you're struggling emotionally because it's those emotions that really give them the supply. So that's how the narcissist wants you to think that they feel when you're not around. They want you to think that they're doing so much better without you. They want you to think that they're happier as though you were the problem. The thing is, the narcissist does not feel better without you. They actually feel a lot worse, and it's not so easy for them to just move on and find another grade A source of supply. They'd like you to think that it is, but it's not. It's not easy for them to find someone to replace you, but that's not going to stop them from crying because they know now that you see through them. They know that you're not susceptible to them in ablation. So at that point all they can do is move on and try to replace you, but that does not mean that they're doing better without you. They haven't really got a choice, and many people mistake their lack of empathy for them being happier when they just leave you behind. Or when you leave them and they don't try and make things right. Many people think that because they don't care about you, because you can't see any empathy from them, they think that means that they're happier, that they're living a better life. Well that is not true. Many of these narcissists only end up downgrading. Many of them lose their jobs. They have problems with everyone they encounter. So naturally they lose a lot of things in the process. The narcissist does not feel good when you leave, when they leave you. They do not live a better or healthier or happier life.  They're looking for attention, admiration and validation from someone else, which is never going to be true happiness. Because true happiness comes from within. But they abandoned their false self. They abandoned their true self.  And because of that, now they cannot experience true happiness. They cannot generate those emotions from within. So by default, all they can do is be fake. They can't even be real with you or anyone else. All you'll ever get from them is an illusion, manipulation, deception. But it's never going to be real. Just remember when they first targeted you. They love bombed you. They told you whatever they thought you wanted to hear. They showed you whatever they thought you wanted to see. But it was just love bombing. And that's why it only took a matter of time for them to devalue you and then discard you. Just remember that person that you saw in the beginning. Do you think that person never would have devalued you or discarded you? Do you think they ever would have done that? No, of course not. But that was a false character. That's not who they really are. They just displayed that to you to manipulate you, to lure you in while knowing that they weren't even about any of that. And they know that there's no future in something that started out as a game. But just remember that. Remember the love bombing phase. And then you will see that they're just doing the same thing again. They're just manipulating you again. Making you think that something's something that it isn't. The narcissist is not happier or healthier without you. If anything, they're a lot worse. They're just manipulating you again. They're trying to hurt you to get a reaction because that is what makes them feel good. And that gives them the fuel they need to present the illusion to you. So stop fueling their illusions.  Take your attention away. Put your focus back on yourself. Trust me, the narcissist does not feel happy or good without you. Thank you for joining me tonight on this live video. I'm at Phuket in Thailand, just by the beach. Thanks for the donation, Tima Wima. Thank you all for joining me on this live video here in Thailand. And there are many more to come. I'm going to be here for another six weeks. And there are going to be many videos of my travels on my other channel, spiritual secrets. So type that in the search bar up above. Subscribe to the new channel. And then you will get notifications of all my new videos. The first one will be uploaded very soon. Please give the video a thumbs up. Share your thoughts in the comments. Share the video. Click that subscribe button if you haven't yet. And I will talk to you in another video very soon.


Dr. O'Hare, remember we're going through the whole list of epithelial tissue types. I'm going to be completely honest with you. These two are the least important. So we're going to cover simple and stratified cuboidal in this video. So here we see simple cuboidal epithelial. Remember, simple tells us one layer, cuboidal tells us the shapes of the cells. Primary places you're going to see these are going to be lining your kidney tubules, which we'll cover way later, and the ducts of some of your glands. So they're responsible for absorption, secretion, and those two key places. Here you see another picture. So you see a single layer of these cuboid or square cubed shaped cells. And then the duct or the tube itself would be there on the inside moving some sort of material.  So remember stratified, think protection. So a little bit more protection here. These are pretty rare. Some of your sweat glands are going to have stratified cuboidal epithelium, and then your mammary glands as well. So those are the key examples. And again, not much else to say there, but I do want you to know what simple and stratified cuboidal, at least what they look like. I hope this helps. Have a wonderful day. Be blessed.


Hi there everyone! Today we are looking at the Tendennova MW6 Mesh Wi-Fi system which aims to enhance the wireless internet signal at home or in your office. It covers up to 500 square meters and it comes in an elegant black box. As you can see there is the product image and some information and on the inside there is yet another cardboard box which is again very high quality cardboard we must mention that and it carries the three cubes. They are quite lightweight made of plastic of course and they are really cute to be honest with you along with them you will see some product information some setup guides instructions and all that also there are three power cables which are needed to power the products and also a single ethernet cable you will need this to connect one of the cubes to your router or your modem. On the bottom of each cube you have two ethernet ports and a DC jack as well as a hardware reset button. We begin the installation by connecting one of the cubes to the power supply via the supplied power cable and the next thing you do is take the ethernet cable and plug it into your cable modem or router once you've done that you'll see that the LED above the nova logo starts blinking in blue. After that you'll need to download the Tendo Wi-Fi app and go through a couple of steps to configure your product. After you download this software product you'll need to use the default username and password and of course later you can just change them to whatever you like them to be and all you're left with is to set up the other two cubes the app will guide you through this process and that's basically it thanks for watching be sure to subscribe give us a thumbs up or tell us what you think in the comments below bye bye


f the known facts about the friendship paradox is that it's present in social networks most nodes in social networks have friendship index larger than 1 or this means they have friendship paradox it holds true at both individual network levels and last but not least the presence of friendship paradox was confirmed in some random networks generated by the Barabasi-Albert model and the final theorem for today from my presentation here we'll estimate the share of nodes for which friendship index is larger than 1 actually so if random Barabasi again follows the power low with parameter gamma and its failures begin with m we can estimate the proportion of nodes for which friendship index is more than 1 we can find the bounds so it is actually bounded by 1 means a1 and 1 means a2 and this 1 and a2 differ in the upper bounds of the inner sum they are highlighted in red so what do we do with it here we plot the upper and lower bounds based on the results of the theorem so as you may see these the value of bounds depends on the gamma the exponent of the power low and m the minimum amount of nodes in network so this is plot of the bounds of kappa which is a share of nodes for which friendship index is higher than 1 or the share of nodes which have friendship paradox and these were theoretical results and now I show empirical results for simulated networks so these networks are based on the configuration model and as you may see I will just switch slides back and forth the results are quite similar so that's nice of course again it depends on the result depends on m and gamma which the same one thing I should mention is that well when gamma is between 1 and 1.5 then well the share of nodes for which friendship index is higher than 1 is well close to 1 it means that almost all nodes have it but then the question arises when friendship index is not equal to 1 well the share of nodes for which nodes it's present for which nodes it's not and we'll see it for real and random networks these are random networks that you are already familiar with that I've shown previously and here we see the distributions of the share of nodes friendship index is higher than 1 but based on the degree so for each degree we get the share of nodes among nodes with these degrees for which friendship index is higher than 1 or for which friendship paradox is present and well for all these networks we see that for smaller degrees friendship paradox is present however for large degrees for hub nodes almost never present and also this parameter depends on gamma if gamma is smaller than the amount of nodes with friendship paradox is higher and vice versa okay I think that's everything here and finally let's see the same for real networks well these are also quite similar yes so you see the shapes of slopes differ they aren't so beautiful as for simulated networks or you may consider them more beautiful well so yes it also depends on gamma parameter of power law but well real networks are more complex then the results are a little bit changed from the simulated networks so to sum everything up we looked at the values of friendship paradox about looked at their distributions in real and simulated networks and how it depends on degree of nodes and so in networks without degree-degree correlations network size tends to infinity we've proved that power law degree distribution because it has a finite second moment and the value of average friendship index tends to a constant divided by k however when the second moment is infinite it's not bounded then this quantity converts to a stable distributed random variable divided by this and secondly the friendship paradox is present in all networks whose degree distribution follows the power law and it depends on the exponent of the power law and if the higher minimum degree is larger then it leads to a stronger friendship paradox in network thank you thank you very much for your talk do we have questions yes please thank you for your talk it reminds me one interesting chapter in the proofs from the book book by Eigner and Ziegler and this is a chapter about friends and politicians and the theorem says that if two people have exactly one friend in common then there is a politician who is everybody's friends but your friendship paradox this also should be famous thing maybe it's somehow related to this type of theorems or not just curious yeah and just adding about this moral thing that everyone knows through some 4-6 handshakes it also struggled my mind maybe comment on this well actually friendship paradox is a known topic well it's not I who invented it of course and usually it was developed in social studies and not really in network studies maybe well their friendship index as a measure well this name was introduced recently about your exact example that's an interesting one I I can't really say if there it's the same or not it's a nice thing to check out and I'll do it, thank you wow and one more technical question you mentioned one more technical question you mentioned a bipartite graph and you also applied power law analysis to it and you also applied how to say sort it out the vertices of one part from another so it's just the same sample right thank you thank you very much do we have more questions okay thank you let's thank the speaker again and the last one is approximate density computation Dmitry Gnatov, Kamila Usmanova and Daria Kmisarova thank you for introducing our talk this is the talk done together with my former students and the lab members and also with some colleagues from institute for molecular genetics since our reference asked us to include some other examples where by clustering can be applied we included this part they are responsible for the data we are for the processing so as for the motivation of our research it was constantly multi-model clustering imagine that you have data you can think of it as a hypergraph regular uniform hypergraph where you have several types of vertices like the offers of papers marked by some tags and such a structure sometimes called folksonomy particular one because people use specific tags to mark some resources, some data but this is a three-dimensional case and a lot can be done in a two-dimensional case so here we can find the so-called three communities that is users that shares the same resources and mark them by similar resources or the same resources and mark them by the same subset of tags they are the so-called three communities or three clusters but the question that we asked was what is a good approximation of three concepts that is maximal triadic rectangles and such data and we answered this question and our paper published in machine learning journal already several years ago but in 2D case we are going back to 2D case now there are many things to do concerning the performance of similar techniques and we use as a language formal concept analysis which is rather simple language as we will see we have a set of objects a set of attributes binary relation on them and two operators called derivation operators or Galois operators saying that given a set of objects what are their common attributes and vice versa given a set of attributes what are the objects that share them all and the concept is just the unit of thoughts as in philosophy but here it's more formal it has two parts an extent and an intent all objects from A shares all the properties from B and vice versa all the objects from A these concepts are hierarchically ordered let's have a look at this small world of geometric figures equilateral triangle rectangular triangle rectangle and square and let us consider just 4 properties has exactly 3 vertices 4 vertices has a right angle and to be equilateral we can extract all the formal concepts which are just maximal rectangles in our data and hierarchically order them by set inclusion of the first component for example the concept 234C 234C is just the concept of rectangle or figures it's more general than the concept 34 BC which is just the concept of rectangles this is the tool to analyze real data for example we took all the publications on formal concept analysis performed terms extraction or maybe we use keywords and combine them to taxonomic terms like sort of topics so in the top of such lattice diagram we have 1000 papers about 1000 papers devoted to formal concept analysis and they are split into sub-topics or sub-communities of authors that write papers on formal concept analysis but also a specific sub-topic like software engineering these concepts may intersect the key property of lattices intersection and suprema here it's a bit more complicated you can also analyze real websites users those are the visitors of HSE university websites and also they read some other news like I don't know RIA news or cosmopolitan or expert.ru In triadic case as a source of this data we can use, for example, Bipsonomy German project where the authors can share their papers and tag them so we have triadic data but those were the motivating examples let's talk about bi-clustering and bi-cluster is the approximate version of concepts coined by Boris Mirkin but definitely bi-clusters were analyzed before by Hartigan, for example and bi-clustering refers to simultaneous clustering of buff objects and attributes in genetics, for example, the objects are genes and the attributes are some tissues or conditions under which specific genes can be co-expressed so this is actually a matrix where each cell is a number from 0 to 30 2000 plus something and here we can see that some of them are grouped because of their co-expressions so very large values are in red and if we consider the tissues which are how to say, suspicious to contain malignant tissues they can be the source of cancer or biomarkers of cancer the formal definition of bi-cluster is just a sub-matrix of an input matrix like a gene expression matrix serial valued one will consider only binary ones and it turns out that in bioinformatics they rediscovered formal concepts as such inclusion maximal by clusters so there are theorems saying that but we propose something which is the relaxation of such rigid notion when all the objects should share all the properties we consider just one pair an object and an attribute maybe the gene and some condition and we can apply prime operators saying that M-prime is just a set of objects that share as an attribute and vice versa G-prime is the set of all attributes which describes the object G and then we can intersect such a rectangle with the incidence matrix and count the number of non-empty cells and this is exactly the density of such a bi-cluster here is an example the geometric one so GM cell isn't here in the center these stripes the gray stripes they are full of ones and we can find first primes so to speak they shape this bounding box but we can also find the second primes and they form this green dense cross full of cells and there might be some other cells but they do not form such a cross-like structure so these black cells also belong to bi-cluster actually we may think of bi-clusters as sub-lattices in the whole lattice of formal concepts of maximal rectangles they have some properties like the density lies in the interval from 0 to 1 and actually in reality this one is enrichable so it's a bit larger but we can do for non-empty binary relation and they also can be hierarchically ordered but we cannot devise some efficient data mining algorithms like a priori algorithm for finding association rules or frequently both both items because this relation is a sub-bi-cluster the other is not monotonic nor anti-monotonic with respect to density constraint but we can set the density threshold to be 0 and consider all the bi-clusters and then the following fruitful property fulfills every concept that is dense maximum rectangle is contained in some bi-cluster in terms of computational time there are some propositions which says that the total gain is polynomial versus exponential in the worst case for finding all the maximal rectangles or formal concepts this L might be exponential in terms of the size of G and M the number of objects and attributes L is just the size of the lattice here also some example from the past we analyzed Yahoo dataset with 2000 companies and 3000 advertising terms and we applied object attribute by clustering for recommendation purposes if we generate concepts with different constraints on the A and B components that is the number of firms that advertise their goods with some number of keywords on Yahoo then for 0 and 0 treasures we obtain about 9 million concepts this is infeasible for manual analyzing for example so that's why by clustering was one of the means to reduce this number and when we change, when we vary the minimal density threshold we can obtain the number of patterns which are suitable for manual analysis and we can interpret the found by clusters as markets we do not show the first component of the by cluster they are just ideas which we do not have from Yahoo but we have the real keywords affordable hosting web hosting web and so on this is about hosting market something about hotel market the pattern here is very simple the name of the city and the word hotel we also applied object attribute by clustering to scaled data known in machine learning from UCI machine learning repository here are just some statistics some figure statistics the number of concepts versus the size of the relation in terms of non-empty pairs and we can also see how the numbers the number of concepts relates to the number of objects attribute by clusters found there is a drastically reduction up to several tens SNA related examples probably one of the most famous but small data sets in community detection is the so called so turned woman data set about 80 women and the certain part United States I believe anthropologists ask them several questions what kind of activities they share together like going to the church or to the dinner to some party the cross means that they participated in some event so it results in a bipartite graph and we applied by clusters here and compared it with clicks as communities so you can see that by clusters sometimes can capture can capture larger groups than clicks due to their sparseness so here is another example about karate club that fist in two parts after after the conflict of the I don't know the right word coach and the president of the club some of the club members decided to be with their coach the master and the other part decided to be with the president and there are some key persons here like president and this master and subgroups of people that were identified with clicks and with by clusters here I can say that by clusters are better but they also captured similar structures for three model data we have yeah okay for our free model data we have offers of papers tags and we can also analyze this with similar samples so the more focused result which is maybe not really interesting as real examples is how to compute the density of such by cluster sufficiently we were trying to use epsilon delta approximation here and chernoff-hovedenkin equality allowing us to use only some fraction of points to estimate the density of a by cluster and unfortunately this function the number of points that we should test is unbounded in the most desirable points like delta 1 the probability in threshold 1 and accuracy epsilon 0 so we can at least test it in real scenario here is a small example we have for other spars by cluster we can compute the density of this gray cross almost immediately by this formula and with the formula for n as a function of epsilon and delta this probability threshold we obtain that we need to test 10 samples we test these 10 samples and find out that among these 10 samples only 3 of non-empty cells among them and that's why the coefficient here is 0.3 and this is the size of non-gray areas together we tested the approach on free data sets so intern women, zoo and advertising the greater the density of the data set the greater the accuracy here you can see where in white cells where the fury agrees with experiment for which data set actually zoo data set this is for internet advertising for southern women it was not very stable and here also an example from genetics where we studied is chemical stroke individuals versus non-ence chemical stroke individuals and their attributes known as single nucleotide polymorphisms being attributes we found by clusters we counted their density size and purity that is the number of individuals which are not included and finding single nucleotide polymorphisms describing non-health individuals which are at risk of having a chemical stroke so later on these SNA descriptors are decoded to their identifiers and geneticists analyze them and we are in the process to publish a paper together with them where the findings were discussed with experts in relevant terms to genetics so I skip everything which is left it's just the things which was done and can be done and I'm ready to answer your questions Thank you Do you have any questions? Yes, please The complexity of the algorithm So the complexity is a linear quadratic code Actually it's linear by each of the input parameter that is the number of non-empty pairs belonging to the input relation the number of objects the number of attributes but here for maximal rectangles or formal concepts it's not linear it looks like polynomial but in fact it's not in case in case you have very simple object attribute matrix where of size 4 times 4 where all the crosses present accept the main diagonal then am I right? that seems so then this is g, this is m and let it be n that is 4 then you will have 2 power n patterns so here is the complexity in terms of the input and also in terms of the output so in the worst case we'll have even exponential complexity but we managed to use approximate patterns we lost some information but we can use it with real data with rather large data at least thank you any more questions so if not let's thank the speaker again this was the last talk of the session and now I invite you all to go to the main hall because there's going to be a closing ceremony and we're going to announce the best paper in this track as well so thank you all and let's go there thank you


I would say the list will reflect the tumultuous year that 2019 was. So I think women will see lot of new names in the list, lot of changes in ranking. I think we will see newer digital platforms and the women that had them or have been working for them in advertising media and marketing featuring in this list. So I think this time also the participation was sort of well spread almost each and every member of the jury actively participated and had a strong point of view on inclusion, inclusion and on the relative ranks.


So, building business success, multiplying, growing, how does that actually look? How does that actually manifest, not as an idea, but as practicality? So most people, when they think about growing their business, they're thinking in terms of that one thing, like what's that one thing, one action that I'm going to do that's, you know, going to make the whole difference. Now I'm not saying there's never, you know, one thing that if you do will have a really good result, but they're not looking at it like, okay, what's the next thing? They're looking at it like the thing, like what's the thing that's almost hidden, almost a secret that nobody knows and they want to use to grow. So the way I look at it is more in terms of taking the different parts of the business and increasing them and multiplying them and also taking, creating new parts for the business to tap into them. So as an example, I have a client that I talked to today and he has a business where people, basically you could say they purchase things online from his store and he needs to add more income. So he gets his traffic from Google ads, you know, paying for Google ads on searches and he needs more income. So instead of trying to find the magic solution like he hoped he would, I actually found a new avenue for him to generate income, which was the fact that people were at least once a day somebody was contacting him and asking for more information about the products and this could easily be turned into a consultation call, 30-minute consultation that would easily end in a sale, that would easily take, squeeze out the traffic a lot more in terms of the value that you get back from the traffic that you create by paying. So you get a lot more bang for your buck. So we, essentially we generated a new limb. If his business was a body, we generated a new limb that creates revenue. Charlie Munger, he's a Warren Buffett's partner, talks about the Lollapalooza effect. So the Lollapalooza effect is basically the sum parts of the organ or of the body, the business in this case, when they multiply, if you increase each of them, you get multiplied results, which means that if I have my business of coaching, I basically take it into many, and slice it into many, many parts that are all multiples of each other. So I have how much, how many views do I get? How many of them get turned into somebody who contacts me? How many people, what percent? What percent of people who contact me turn into clients? How much am I charging on average per client? How much, what percentage of them pay again? What's the average second purchase that they make in terms of how much money they put in? So there's many variables and it's in equations, like this times this times this times this. For example, the amount as a salesperson, it's like the amount of meetings times the closing rate times the price. That's how much money you make, the average price or average sale price. Now, if you multiply the meetings by two, let's say you multiply the meetings by four, so it's a big multiple. You basically get four times more opportunities to sell, so the end result would be four times bigger. But then, if you also multiply the price by two, now you get, it's not like times four and then times two and they're separate, it's basically times eight. And then you add another multiple, which is, you double your close rate. So now it's not times eight, it's times sixteen, because you took three variables and you multiply to each. So it basically builds upon itself. So the more multiple you add, the more growth you get by a large amount, sorry for that, by a large amount. So the way you want to treat your business is you want to actually divide it into every variable that goes into that equation. Again, how much money is invested? How many views? How many views turn into this? Just a long equation that includes all the factors and then you want to know what's the value of each factor. So your job is to either increase a factor or add a new factor. Because again, let's say you have the business and you have the sales and everything and now you implement a new factor, a second sale. So after the first sale, the sales person goes, hey, we also have this product which goes with the product you just bought and 30% of the time, they buy that too. So now you add, so second sale closing rate, 30% and average payment is this much. So you basically get a formula where your job is to make sure that all the variables increase and also adding new multipliers, new variables and thus you increase the equations overall value. So I hope that makes sense. And when you increase one avenue, like for example, I told him that he should double the prices and if he doubles the prices, that's a big difference on the equation because now if he has twice the sales, because he's calling the people contact, he's actually going on sales calls with them, plus he doubles the sales, the price, sorry. What that means is he's going to get four times more money from two simple actions. And what that's going to allow is it's going to give him a much, much bigger space, basically a profit margin and he's actually going to have a big profit from his campaigns. It's not going to be losing money. It's not going to be breaking even. He's going to make money from the campaign so he can basically multiply the campaign now also. So instead of investing X amount into ads, he can now invest five X because he can scale now. So you take the equation, you double the sales by two, you double the price by two and then you double the ads by five. So you're basically going to get 20 times the amount, roughly a bit less. And I'll explain why. When you increase something, something else might go down. So when you increase the price, for example, when you double the price, most likely if you double it, you're going to lose a bit of the closing rate. Not necessarily since if you're a coach, for example, and you charge $300, I'm already telling you that by upping it to a thousand more, you're going to sell more. So you're not only going to make more money, you're going to sell more people on average. But that's a video for another time, but just so you know. And if you want to know right now why, just contact me. And I have many examples of this, by the way, both me and many many students of mine. It's a fact, it's a scientific fact. So when you increase the price by two, you might get a decrease in the sales in the closing rate. And you want to ask yourself, does this increase the overall result or does it decrease it? If I double my price and I get 15% less sales, effectively what that means is I believe it's 1.75 roughly, 1.7 times more money. So is it worth it? Yeah, of course it is. It just makes sense in the equation. So use this equation technology as a tool to take your business and basically keep expanding. Again, take all the variables in your business, the percentages, the closing rates, and that's why you have to keep statistics, by the way, of everything. And when you have the full equation, now you simply have to ask yourself, what do I want to focus on? Pick one, pick a variable to focus on. Okay, I'm going to improve the closing rate. The one thing you can always improve infinitely is the amount of attention you get, meaning how many opportunities, but it's not always the right order. So for example, like I said earlier, using ads on Facebook, Google, that's a tool to get an infinite amount of attention because the more money you spend, the more attention you get. So if you can make your business profitable with the ads, then you can basically get much more attention too. So if you just, if you focus on attention before focusing on having a good enough price, having great closing rates, basically having a very, very profitable business, then there's no point in increasing the attention because it's going to be an uphill battle. Basically, imagine what I'm doing with the many videos and everything. If I want, I can easily start putting in ads and the ads basically increase the attention by a lot. And then I still get to keep fairly high profit margins because when you close one in five, you know, about one in five calls and make a couple of thousand dollars, it's pretty easy to keep high margins with that. So always begin with what appears to be the most relevant or what will open up as many channels as possible. So again, in this case, for example, if you take the closing rate and you double it and then you take the amount of opportunities you get from the attention you already get. So you double the conversions to leads and you also double the price. You basically get six times more value from the same amount of attention. So now the attention can grow exponentially by many, many multiples because now if you invest money into the attention, it's going to be very, very profitable. So you can grow the attention by times 10. Anyway, I know this video is pretty academic. It's kind of, I don't know if academic is the good word, but it's pretty technical. This is the way I look at my business when I run it. This is the way I look at my client's business. It's always, once you get started, I mean, it doesn't matter. The reason I say you have to get attention first is because until you get attention, nothing else can exist.  You can't know anything until you get attention. So do whatever it takes to get attention before anything, before even having a product, because again, it's what creates the base. You can't have anything without it. But once you have attention, now you have some statistics going and now you can actually know what to expect from the business. So I hope the video makes sense. Take it and apply it in your business if you have one. Again, just write down all the different variables that apply to your business. And your job is to either increase one of the variables or to add a brand new variable that will add new multiples, like again, like having a second sale. I hope this video helps you a lot. I know this concept of taking everything and bringing it down into variables and just a long formula. For me, it made a huge difference because business stopped being this ethereal, ambiguous thing and started being this very mathematical, direct thing that I can confront. And it allowed me to work with clients and achieve very, very tangible results. For example, you have a client that makes $1,000 a month in his business because he just opened it and I charge him $2,000 for one month, which is like, oh, wow, it's crazy. $2,000, which is not a lot of money, but it's like, okay, how do I justify this value? So I just quickly find like, oh, well, he's charging really low prices. So I just triple his price and bam, he goes up from $1,000 to $3,000, usually more because like I said, in certain industries when you up the price, it actually not only gives you more money, it also gives you a higher closing rate. So again, if you're in a consultation industry, contact me about it. I'll explain why. Let me know if you have any questions. Let me know if you need my consultation now for a free call, session for anyone who's a serious guy or girl and wants some help. And if you haven't subscribed, subscribe. We're almost at 500. Very, very fast growth because the channel is only, it was only at 400 at the beginning of the month. No, more like 25 days ago. So that's a growth of about 20, no, what I'm talking about. It's like 25% in a month, which is nice. Thanks for watching and let me know if you need anything else. I'd love to help you.


What's up everybody, Jason here for jazbyzcasebreaks.com We just sold out the last filler here guys to give away the last three spots in the mic Mickey Mantle baseball mixer with this 2022 capstone pack filler number 175 Random teams guys and again first we're gonna do the filler break Randomize the customer names teams distribute the hits out of the pack Then at the end we'll re-randomize only the names top three get in to the mic mixer Which is coming up next guys now Because it sold out tonight. We actually took out free four filler spots that we're gonna give away back to the customers that bought in So there's only 26 total spots sold. We're gonna randomize with the same dice roller for that list randomizer for the pack filler Top four get free extra spots guys. Let's roll it five to five ten times one two three three four five six seven eight nine ten ten times ten ten Alan Johan Jimmy and Alan Matsui one two three four five six seven eight nine two Jason K. Johan one two three four five six seven eight nine ten Cubs out of the Marlins So again pack filler right here guys No trading. I'll let you quickly see what you got Here now guys Tim Anderson Jaren Duran Gavin Sheetz And Taylor Ward a little new age relic there for the angels She's going to Joe B Switching scenes Let's roll the dice and let's see who's gonna win those last three spots guys five and a one six times One two three four five and six Boom six times six six Jimmy just missing out there man But top four or top three Johan is in That's one of the last four spots by guys Alan's in and Eugene congratulations Boom Just like that guys So there you go. Congratulations guys coming up next is the break itself


This is a clear message to criminal motorcycle gangs that we will take action on each and every occasion that we have evidence to take action. We now have members of the community ringing crime stoppers. We have members of the community contacting police directly in relation to the activities of criminal motorcycle gangs. We intend to take action wherever we can in relation to CMDs. It was a positive result today. It's a result of community interaction with the Queensland Police Service. Sunshine Coast Police District has made it one of their core duties as has the Queensland Police Service in targeting criminal motorcycle gang members.


Hello everybody, so welcome and good morning or good afternoon. So our speaker today will be Kazuya Unikura, who will tell us about classification of topologically non-trivial terms in action. I also realized that now it's a bit, actually, four minutes earlier than the schedule. So shall we wait for four minutes until eight, sorry, eight minutes, okay. So most people will probably connect at once. Yes, exactly. So Kazuya, do you want to test your audio also? Okay. Can you hear me? Yes, yes. Okay. It's great. Okay, so let's maybe wait for three more minutes for people to come. Okay, maybe let's start today's program. So the first speaker today will be Kazuya Unikura, who will tell us about classification of topologically non-trivial terms in action. That's welcome, Kazuya. Okay, so thank you very much. And first of all, I'd like to thank the organizers for inviting me to this workshop. So in this talk, I'd like to talk about classification of topologically non-trivial terms in action. And before starting the main part of the talk, first let me comment on the talk itself. So my talk is basically a review of physics motivation of our paper, this paper, Differential Models for the Anthocondriac Buddhism Theories and Invertible QF Days. This is a collaboration with Mayuko Yamashita, and she's one of the speakers of this workshop. And also, I put here V2 because in version two, we significantly changed the content of this paper. We improved the proofs and we also included some new results. However, this talk is just about physics motivations. And in Mayuko Yamashita's talk, she will talk about the mathematical side of the story and also developments by herself. And also let me mention two related papers. So the basic motivation of our paper comes from this paper by Friede Hopkins about the classification of invertible phases. And also, we are also motivated by this paper of Lee and Omori and Tashikawa. Okay, so let me start my talk. So we want to classify actions of quantum field theory. So we consider some field, I do not, the field by five, and we consider action. And I work in the Euclidean signature. So we go from Lorentz signature to Euclidean signature by recrotation. And this Lorentz signature action is real for unitarity, but this Euclidean action contains the real part and imaginary part. And here this 2 pi is just my convention, but the important point is that this Euclidean action contains imaginary part. And then we want to know topologically nontrivial terms in this imaginary part of the Euclidean action. So first, let me discuss some basic properties of this imaginary part. So first of all, this imaginary part takes values, not necessarily in the real numbers, but in R over Z. And the reason simply is that this action appears in the past integral exponential of 2 pi i times this imaginary part. So the change of this imaginary part by integer is irrelevant. So basically by this reason, this imaginary part is regarded as taking values in R over Z. That's a very famous fact. And to discuss other properties, let me neglect topological subtleties for the time being. And so for the time being, let me assume that this S is an integral of a local function. So this L is the Lagrangian. Then the procedure of going from Lorentzian signature to Euclidean signature is with rotation for the time coordinate. So we pick up some time coordinate, and then we change this time coordinate to minus i times Euclidean coordinate. And under this rotation, the volume form changes like this. So it also picks up minus i. And as I mentioned before, this Lorentzian action goes to this Euclidean action with real and imaginary part. And then this Lagrangian also goes to real part and imaginary part. And this behavior under recrotation implies that this real part contains even numbers of time components. And such terms goes to real part of its Lagrangian. And this imaginary part must contain odd numbers of time components because it must be multiplied by this i imaginary unit. And more generally, under reflection of this coordinate, x0 to minus x0, this Euclidean action goes to the complex conjugate, and this property is called reflection positivity. So under the assumption of reflection positivity, so this imaginary part must contain odd numbers of time components. So let me just give some example. So for example, in four dimensions with u1 gauge field and field strength f, we can consider this kind of term by using this totally anti-symmetric tensor. And then we can decompose it into components like this. Then this first term contains three time components, three zeros here. And this second term contains a single time component. So anyway, so each term has odd number of x0 components. So this imaginary part must contain odd numbers of time components. But on the other hand, it must be also Lorentz invariant. And these two facts imply that we need the totally anti-symmetric tensor to construct terms in this imaginary part. So neglecting topological subtleties, they are just described by differential forms. And also, let me next discuss another property. So let's consider the following counting of kind of scaling dimensions. So I assign dimension 1 to derivatives and dimension 0 to scalars and dimension 1 to gauge field. And more generally, I assign dimension p to p-forms. And I mentioned that we need to use this totally anti-symmetric tensor to construct this imaginary part. Then this fact implies that the scaling dimension of each term in this imaginary part must be equal to or greater than the space-time dimension. So this d is the space-time dimension. For example, in four dimensions, we have dimension 4 term and dimension 8 term given by this. And terms which have scaling dimension strictly greater than the space-time dimension are not topologically interesting by the following reason. So let's consider the scaling of the metric tensor. So this g mu nu is the metric tensor. And then let's consider multiplying this metric by some positive constant. Then a term in this imaginary part, which has the scaling dimension n, behaves in this way. So under the change of the metric by this factor, this term changes by this amount. And if this m, the scaling dimension, is strictly greater than d, then this term disappears in the limit of taking c to infinity. So this limit corresponds to taking the metric to be very large. And in particular, because this term disappears in this limit of large metric, there is no political structure in such terms. And so there is no quantization condition. So they are not so topologically interesting. So topologically interesting terms may be contained in this limit, which I denote by h. So this h is the terms in the imaginary part of the action, which has precisely the scaling dimension d. Such terms can be extracted by taking this limit. Then our purpose is to classify such h. And there are two main motivations. The first motivation is obvious. So such terms are interesting in the path integrals thing we consider integration over this field five. And another motivation comes from the description of anomalies. So let me review, let me review the modern point of view on anomalies. So in the modern point of view, anomalies in d minus one dimensions may be described by actions or what is called invertible field theories in the dimensions up to manifestly gauge invariant local counter terms. So let me explain the meaning of this statement. So we consider some anomalous theory in d minus one dimensions. For example, they can be some chiral fermions. So we consider such series. And this is anomalous. But we can cancel it. So we can cancel the anomaly by introducing the dimensional manifold. So we realize this d minus one dimensional space as a boundary over the dimensional manifold. And we also assume that the field is extended to this higher dimensional manifold. Then we put some topologically non-trivial action in this d dimensions. For example, we can put chance of terms in this bulk. Then the variation with chance of terms and the gauge variation cancels the anomaly or chiral fermions. So this is a famous anomaly in flow mechanism. And in this way, the total system is gauging invariant by anomaly in flow mechanism. And so this system has a very defined partition function which takes values in complex numbers. So the total system is completely gauging invariant. But it may depend on how to take a d-dimensional bulk configuration. So as a bulk d-dimension, we may take some manifold m and field phi. But we may also take another manifold m prime and another field phi prime. And so we have some choice of the extension to the bulk. And I remarked that here I'm treating this manifold and the field as the background fields. So I'm not doing pass integral over them. So basically, throughout the talk, I treat the fields as the background fields unless otherwise stated. So we have these choices. The difference of the two choices can be measured by computing the action on this closed manifold. So these manifolds m and m prime have the common boundary. And on the boundary, these fields are also the same. So we can glue them together to get the closed manifold. So we get the manifold without boundary. Since the value of the d-dimensional action on this configuration gives the difference between the two choices. And if this action is there in the bulk, then the partition function of the combined bulk boundary system does not depend on the choice of the bulk. Then we can consider the partition function as the partition function of the b-1 dimensional theory because it does not depend on how to take the bulk. So in this case, there is no anomaly. So this is the modern interpretation of anomaly. So the anomaly is basically described by this bulk action. However, even if this s is non-zero, the theory can be still anomaly-free if we can find the manifestly-gauge-invariant local counterterm in the bulk such that this sum is zero. And here by this manifestly-gauge-invariant local counterterm, I mean that this local Lagrangian itself is gauge-invariant. Then we can freely modify the bulk action by such a counterterm for the purpose of anomaly cancellation. The point is that this integral of this local gauge-invariant Lagrangian is gauge-invariant even on manifolds with boundaries. So the existence of such a term does not affect anomalies at all. So we can freely put such terms in the bulk. So let me give some examples of such manifestly-gauge-invariant terms.  This is manifestly-gauge-invariant in four dimensions. If we do not impose parity or time reversal symmetry, I come back to this point soon. And in this case, this term does not represent anomaly.  So this is a chance I'm on the top. So this is not the gauge-invariant in three dimensions. So it represents anomaly. So this is a description of integer quantum whole systems. So in the integer quantum whole systems. This kind of chance I'm on the bulk. And we have some edge chiral fermions on the boundary. Let me discuss one more example. So again, let's consider this term. Then this is not the gauge-invariant in four dimensions in the presence of parity or time reversal symmetry. And simply because this term changes the sign under the parity transformation like this. So this is not gauge-invariant. This is not the invariant under this parity transformation. And then consequently, a four-dimensional term like this. So this term is a theta term at theta equal pi. So this term represents a non-trivial anomaly in three dimensions. And actually, this is an effective description of topological insulators. So it is well known that this term at theta equal pi is invariant under the time reversal symmetry if we integrate it over closed manifold without boundary. But in the presence of the boundary, this term is not invariant under the time reversal symmetry. And so this gives an anomaly over the boundary theory. So, okay, so this bulk action describes anomalies. And I mentioned that this bulk-equivalent action contains real part and imaginary part. And I defined h to be the term in the imaginary part which survives in this limit. And I believe that only this term h can be relevant to anomalies. In other words, other terms such as the real part and the imaginary part with higher scaling dimensions can be cancelled by manifestly gauge-invariant local counter terms. I don't know the proof of this statement, but this is what I believe. And this h itself can be still modified by local counter terms like this one in the absence of parity symmetry. Okay, now let me give various examples of topological non-trivial terms. So this h is a function which assigns to each pair of manifold and field on the manifold, a value in r over z, so like this. And so now let me give various examples which are very important in physics. The first example is the chancellor's terms. So maybe this is the most famous example. So we fix some group and we take the field to be the gauge field of this group. Then, roughly, if the bundle, if the g-bundle is topological trivial, then this h is given by this expression. Here, for concreteness, I take d equal to 3. So this is a famous chancellor's term. And here, this k is integer. This is chancellor's level. And she is some normalization constant such that this integral takes values in integers on closed manifolds. So this is a description of chancellor's terms. And if this m is a boundary of some d plus one dimensional manifold, and if the gauge field is also extended to this d plus one dimensional manifold, then the value of h on such a boundary can be written like this. So it can be given by some integral of a gauge invariant local quantity over this higher dimensional manifold n. So in physics literatures, this is often taken as the definition of chancellor's terms. But even if this g is a discrete group, or even if this level k is zero, we can still have non-trivial values for h, which is characterized by a group homology. So such h is explicitly described by the diagram written. I don't explain the details, but in that case, this h has the properties of its value, which is evaluated on manifolds realized as a boundary is zero. But this h can be still non-trivial. Another example is Bessell-Meaton terms. Here, just for concreteness, I take the target space to be a group. And then the field is a function from the manifold m to the sigma model target space. And if this m can be realized as a boundary of a higher dimensional manifold, and if this function g is also extended to this higher dimensional manifold, then Bessell-Meaton term can be written like this way. So here, for concreteness, I took p equal to 4 and d plus 1 equal to 5. And again, this k is the level. So this is an integer. And she is a normalization constant, such that this integral takes values in integers if we integrate over closed manifolds. So this is the standard description of Bessell-Meaton terms. So this description is valid only if this m is a boundary of a higher dimensional manifold. But if this m is not a boundary of a d plus 1 dimensional manifold, then we need more data to specify this value of h. So it can happen that there exists another h prime, which also satisfies this equation if this m is a boundary of a higher dimensional manifold. Then in such a case, the difference between this h prime and h satisfies this condition. So this condition means that this difference, this h tilde, is 0 if it is evaluated on manifolds which are realized as a boundary. And such a different h and h prime really appears in actual gauge theories. More concretely, if we consider some higher dimensional, sorry, if we consider four dimensional gauge theory is SO and gauge group, then in dou energy, we have chiral symmetry breaking, and then we get constant bosons of chiral symmetry breaking, and we have Bessell-Meaton terms. But depending on the details of the UB theory, we get different Bessell-Meaton terms in the IR theory. So that can really happen. Okay. Next example is a topological non-trivial term in coupling constant space. In this case, I take the field to be a pair. This a is a U1 gauge field. This need not be U1, but for concreteness, I take U1. And this theta is, again, a sigma model. This is a scalar field. So this is a map from the manifold to S1. So this is a periodic scalar field with a period 2 pi. Then we can consider this kind of term. And here for concreteness, I take D equal 2. So this is basically a theta term for this gauge field of F. And if this theta is a constant parameter, then this is just an integral of a manifestly Gen.G invariant local term. But we can promote this theta term to a field. Again, if we promote this theta to a field, it is not manifestly a gauge invariant, because this theta and theta plus 2 pi should be identified. But this theta times F is not invariant under this shift. So this is not manifestly invariant. In this case, we can define a gauge invariant field of strength, not by this small f. So this is an extra derivative of this theta. And this is a one form on S1. And this represents a non-trivial drama homology class on S1. So we can consider this f, which represents non-trivial drama homology class. And if this manifold M is a boundary of a higher-dimensional manifold, then we can write this H in this way as an integral of a local quantity, which is a gauge invariant. And this, so this local quantity has a property that its integral takes values in integers if we integrate over closed manifolds. So this kind of term is important for describing anomalies of space of coupling constants. And here coupling constants is the theta parameter in this case. I don't talk about the detail of this, but this kind of anomalies are described, for example, by this paper. Okay, another example is APS getting invariant. So in this case, we fix some group. This group may be empty, but anyway, so let's take some group. And then as a field, I take the metric tensor and the gauge field. Then we can consider the Dirac operator, which is coupled to this gauge field, in some representation. Then we can consider the Atiyapati-Shinga data invariant of this Dirac operator. I don't describe the definition of this APS data invariant, but it is known that this APS data invariant is very important for describing nonpart of anomalies of fermions. So nonpart of anomalies described by this data invariant. I take this H to be this data invariant, mod Z. So fermion anomalies are described by this. And if this manifold M is a boundary of a higher dimension manifold, then there is an APS index theorem, which is given by this formula. So this left-hand side is the index of the Dirac operator in the higher dimensional manifold M. And this index is given by the integral of this characteristic class over M plus this data invariant defined on the boundary. So if there is no boundary, then this is an Atiyapati-Shinga index theorem. So index equals the integral of the characteristic class. But in the presence of the boundary, there is a correction term, which is given by this data invariant. So this is the statement of this APS index theorem. And because this index integers for M, which is realized as a boundary of a higher dimensional manifold, the value of this H is given by the integral of the characteristic class over this M. So this H is basically this data invariant. And this data invariant is equal to this integral of the characteristic class up to integers. So again, this H is given by some integral of gauge invariant quantity. And in particular, if this characteristic class is zero, then this H has this property. And in this case, it describes global anomalies or fermions. And finally, let me give one more example, which is sigma model anomalies. So in this case, we take some target space. So this X is some target space of a sigma model. So this can be an arbitrary manifold. And I take a field, which is a map from this M to X. So this is a general sigma model. And for example, if we consider some gauge field on this target space, then we can pull back the gauge field to M by using this F. And we can consider all quantities which are discussed for gauge fields. For example, we can consider Chan-Simon's terms or data invariant by using the pullbacks of the gauge field on X. And that describes anomalies of fermions coupled to some sigma models. I mean, so we can couple fermions to sigma model fields by pulling back gauge fields on X. And then we couple that gauge field to fermions, and then that fermion has anomalies. So that is the sigma model anomalies. And whether that is topologically non-tabular or not depends on the topology of this X. Okay, so I have discussed many examples. So now let me discuss general structure. So from various examples, the general pattern which is satisfied by topologically non-tabular term is hopefully now clear and I regard it as an empirical fact in physics. So let me state this general empirical fact. So we are considering this function H, which is a map from this manifold and field to some value in R over Z. And it satisfies the following property. If this M is a boundary of a higher dimension manifold, then it is given by an integral of some d plus one home. The formula is a gauge invariant close to d plus one home, which is constructed from the field. So this statement is satisfied by all examples, which I discussed, and as far as I know, all the examples in physics satisfy this property. Do not know a complete justification for this property over H. So in our mathematical work, we take this as a starting point. But let me mention some evidence that this is the correct property to impose. So one evidence comes from this locality and the gauge invariance. This function H is not necessarily an integral or gauge invariant local term. But it's functional derivative is given by some integral over gauge invariant quantity. As you can see this, we consider this change of this d plus one home under the small change of this field. Then this small change is described by the exterior derivative of some gauge invariant quantity, gauge invariant P form, which is constructed by this phi and this theta phi. And then the small change of H and the change of this field is given by the integral of the sky over this end is the dimensional manifold. So this is a completely local term. And this is a gauge invariant. So this may be enough to guarantee that part of the expansion is local and the gauge invariant thing we perform pass integral over this gauge phi, sorry, pass integral over this field. So here, I did, I didn't perform any explicit gauge fixing or condensation but at least formally, I believe that this is enough condition to guarantee locality and gauge invariance. And another evidence. Let me discuss the opposite to limit that the D plus one home is zero thing in this case, our condition implies that this H is zero thing evaluated on a manifold which is realized as a boundary. And such H is called the body's invariant. And in the framework of topological quantum field theory. It is known that body's invariance and invertebrate QFTs in one one correspondence. This is not important for my talk. So basically body's invariance and invertebrate QFTs. One one says one one correspondence between them. So, in QFT, we have some rigorous actions. For example, in freed Hopkins paper, they considered free extended actions. And in my paper I considered some non extended appear like action. But anyway, so we can set up actions and under these actions, we can really prove this statement. So, I believe that in the case of QFT, the understanding is very complete. Okay, now let me comment on this D plus one home. So in the context of anomalies of D minus one dimensional theories. One form is called the anomaly polynomial. So please notice the difference with the dimension between this D plus one and D minus one. So the dimension was by two. And such difference is also well known in the study of part of the anomalies. So in the description of in the description of part of the anomalies. There is a description by what is called anomaly descent equations. And it is a famous fact that anomalies in demand part of anomalies in D minus one dimension is described by some D plus one home. And this D plus one home omega satisfies this condition. So if we integrate this omega over closed manifold, then it takes values in integers. And the proof is very simple. If we consider a closed manifold close D plus one dimensional manifold, then it has no boundary. Then, in this situation, we apply our condition. So this H evaluated on empty manifold should be zero. But from our condition, this must be equal to the integral of this omega over N mod Z. From this, we conclude that this integral must take values in integers. So this is a famous argument for quantization. And some H is given by a manifestly gauge invariant local term like this. So here this alpha is a gauge invariant D form, which is constructed from this field phi. So these kind of terms are not relevant for anomalies because they can be cancelled by local counter terms. So these terms are given by an integral of a manifestly gauge invariant local term over this D dimension manifold. So example is this FHF in four dimension in the absence of time reversal symmetry. So they are not important for anomalies. And by using stock theorem, the corresponding D plus one form is given by the exterior derivative of this alpha. So this is, so if this H is given by such local integral, then this omega is exact form. Okay, now we consider these pairs, H and omega, which satisfy our condition. And we can define invariant group structure in the set of such pairs. So we can simply take the sum of two pairs, so H1, omega 1, and H2, omega 2. We can sum these two in the obvious way. For example, the sum of H1 and H2 evaluated on this field is given just by the sum like this. So I hope this is very obvious. And we can also sum this omega. I think this is clear, but let me give one example. If this H1 is given by some Chan-Simon's term with Chan-Simon's level K1, and if this H2 is given by Chan-Simon's term with Chan-Simon's level K2, then their sum is given by the Chan-Simon's term with level K1 plus K2. So the sum of these two pairs corresponds to the sum of the Chan-Simon's levels, K1 and K2. So this is the meaning of this aberrant group structure. So we define an aberrant group. So we denote this aberrant group of pairs by this symbol. So this symbol may look a bit complicated. So let me explain this notation. So this i omega is taken from some symbol in Chan-Simon's literature. And I will come back to this point later. And this BR, which appear here, suggests some analogy with drama or homology. So we have P plus 1 form and D form. And so actually I will also define another group later. And that definition is very close to the definition of drama or homology. And in this notation, there are some important data. First, it contains this G. So this G is the symmetry group, which we are interested in. For example, if we are interested in some U1 gauge theory, then this group G contains the U1 gauge group. But this G also contains information of the Lorentz symmetry group. Yeah, I will also come back to that point later. And also this X, here this X is the target space of sigma model or space of couplings. So this space X is basically the target space of scalar fields. So this G specifies the gauge field and this X specifies the scalar fields. So we defined this group. And this is the Averian group of topologically non-trivial terms with symmetry group G and target space X. And we can impose equivalence relation in this Averian group. So two pairs, H omega and H prime, omega prime, are defined to be equivalent. If they are related in this way. So if this H prime, if the difference of the H prime and H is given by an integral of D form, gauge invariant D form, and if this is the difference of the omega prime and omega are given by the exterior derivative of this alpha, then I define them to be equivalent. Here this alpha is a manifestly gauge invariant D form, which is constructed from this field. So this is very analogous to the equivalence relation, which is used to define Dramacon homology. So in particular, so this second relation, so this is very similar to the definition, which is used, definition of the equivalence relation, which is used in the definition of the Dramacon homology. So we define equivalence relation in this way. Then we denote the group of equivalence classes by this symbol. So, so this right hand side with hat was our previous group, then I divide it by this equivalence relation, then I get the new group, and I denote this group without hat. So physically, this is the equivalence. So, sorry, so physically the equivalence relation by gauge invariant D form means that we just consider these terms up to gauge invariant counter terms in the back. So this left hand side, this new group is the group, which is important for the classification of anomalies. So let me mention one important property of this group. To state the property, let me introduce the Bodism homology group of this X. So this is a Bodism group. And here in that context, this G is a group for the tangential structure of the manifold, which is considered in the Bodism theory. I don't explain the details of this point. But anyway, so we consider a Bodism group. This group satisfies the short example sequence given by this. So in this short exact sequence, this term, I don't explain the details, but this term describes invertible tqfts up to continuous deformation. And if we have such invertible tqfts, we get an element of our group. So this middle term is our group. So that is the meaning of this map from this, from this to this one. And this term is homomorphism from this Bodism group in D plus one dimension to Z to integers. This term describes the anomaly polynomial up to exact forms. So this map is obtained by integration of the D plus one form over D plus one dimensional closed manifolds. By the integration of D plus one form, we get a map from Bodism group to integers. And the fact that it takes values in integers, I explained that point before. So this is basically a direct quantization condition. So our group fits into this short exact sequence. Actually, so this property is one of the important properties of what is called Anderson duality of generalized homogenous theory. So now I can state the result of our paper. So one. Okay. So let me state the result. So one of our main results is that the group, this group, which I have defined, is naturally isomorphic to the group, which is known as the Anderson dual of Bodism theory. So this is a natural equivalence between this our group or actually this is a functor from the category of manifolds and the smooth maps to Arbelian groups. So this is actually a functor and this Anderson duality of Bodism theory is also functor. And there's a natural equivalence between them. So this is one of our main results. So I don't explain the definition of this Anderson dual of Bodism theory, but it is known to be a generalized homology theory. So, so this right hand side can be treated by methods in algebraic topology and stable homotopy theory. Why, by using algebraic topology, we can deduce many properties of this, this left hand side, which is defined in terms of topological terms. Okay. So let me describe one example. Let's take this group G to be spin times SU2. Here this spin is a spin version of Lorentz symmetry. So this spin is just a Lorentz symmetry basically. And here this SU2 is an internal symmetry group. So let's consider this group as an example. And also, let's take this X to be just a point for simplicity. So this means that the target space of the sigma model is trivial. So this means that we consider theories, feature fermionic and features SU2 symmetry, and there's no sigma model. And here this fermionic means that we consider spin manifolds. So this factor that we consider spin manifolds is specified by this Lorentz symmetry group. Okay. Then there are some very known results in the literature. So this group under some year of a body's muscle, body's muscle is very known, at least up to dimension five. And in dimension one and dimension two. The group is C2. This is C2, described by model two index of spin manifolds. And for this C2, the SU2 is not important at all. So we can neglect SU2 and this C2 described purely gravitationally. And also, let me mention that this B equal to this, this Z2 is what is called. Kitaifumayana chain in condensed metaphysics. So this Z2 is low energy limit of Kitaifumayana chain. And in three dimensions, we have Z cross Z. And the interpretation of this Z cross Z is that they describe gauge SU2 and gravitational chance of terms with levels specified by C2 integers. So this is the meaning of this Z times Z in three dimensions. And in five dimensions, we have Z2. So this Z2 in five dimensions is SU2 discrete theta angle in five dimensions. Such discrete theta angle is often important in the study of five dimensional gauge theories which appear in string theory. And in the context of four dimensional physics, this Z2 describes the weekend SU2 anomaly in four dimensions. Okay, so let me comment on the literature. This group, the Anderson theory of autism theory, is conjectured to give the classification of deformation classes of invertible QFDs. So it is conjectured by Fried and Hopkins. So our result might be seen as evidence for their conjecture. At least our discussion gives a strong physical evidence of their conjecture. Or we may also see as an evidence that topological number terms satisfy this relation. So this was basically just our assumption, our starting point. But we get this Anderson theory. So I believe that we are going to the right direction. So this property is really satisfied for topological terms and actions which appear in physics. And our result is also anticipated in early work as an interpretation of the Fried-Hopkins conjecture. And it was discussed by Lee and Omari and Tachikawa. And finally, let me comment on differential cohomology. So I mentioned that this Anderson theory of autism theory is a generalized cohomology theory. And our group with heart here. Our group is actually a new model for differential cohomology theory associated to this cohomology theory. And our model is based on differential character. And it has a very natural motivations from physics. And differential cohomology theory seems to be an important language to describe many phenomena, many topological phenomena in physics. And our differential cohomology group is very well suited for the study of such phenomena. Okay, now let me summarize my talk. So topological number terms in actions are functions like this, which assigns the values in R over Z to each pair of manifold and field. And if this manifold M is a boundary of a higher dimension manifold, then the value of H is given by an integral of some gauge invariant closed form, which is constructed from the field. And the terms satisfying this condition up to manifestly gauge invariant local counter terms are classified by the Anderson dual to Buddhism theory. Okay, that's it. Thank you very much. Thank you so much for this very wonderful talk. So, is there any questions I see one from so so so please feel free to unmute and ask the question.


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