If you drive back and forth to work on this particular route, you all know that you get into a habit of driving You don't even have to think about it anymore. It just happens You can take the right exit stop at the proper places do everything It's all habitual because it's become a habit. You're not even thinking about it in the dunya It's not that bad of a problem although sometimes it is where it really is a problem is in our dean and This status of being in a state where we're doing things habitually And not thinking about what we're doing is called rafla heedlessness and it's one of the root causes of all diseases We've all had the experience of when we prayed or I won't say all but many of us has had the experience of when we pray and We go through the entire prayer and we do everything The father the sunnah them and do every aspect of the prayer We're doing it right outwardly if somebody looked at us. They would say mashallah. They did a good prayer Inwardly we were thinking we were on the other side of the world We were thinking about something else But we performed everything how did that happen because we got into a habit of doing that prayer in that proper way We're not thinking about it, and then we're not getting the benefit out of that prayer


Okay, is that not what we're all here for?  I know you're giggling Stop it. It's horrible. What are you doing? You're it's a waste of energy. It drains you.  I Know all of you're doing it. All right, put your hands up right now. Who's jerking off? Come on There you go. See that that's good. I like that honesty Everybody All right now This is good. Avoid the POA mindset P. O. Mindset. They said, yeah, you have to plow. You're gonna keep trying.   Okay, so Doesn't mean not to try. Okay, but there's a difference between the girls flirting with you And maybe she's interested or she's not interested do not waste your time with girls who are not interested in you Believe me if they're looking away, they're avoiding your questions.  Great girls don't want you to plow You're just wasting it. Stop it. Okay, that's the whole P way thing. Oh, the other thing is P way mindset is like you'll open a girl and then you'll just run away immediately You're not you'll be open or oh, I don't think she likes me and you leave don't do that either Okay, just because you can talk to another 50 girls.  Okay Right, so let me just emphasize because I think I was gonna do this later Try and and see if you can get like a genuine Connection when you talk to girls really look for that genuine connection. See if there's something there. Is there something there? Do you really like her?  Don't waste your time All right, one thing I want to teach you guys. I think I have time for and that's it The three musts this is The one thing if you just do this one thing this will get you late a lot this one thing Okay, there's only three things you have to do For in every interaction to genuinely have a real shot of Hooking up with a girl. Okay, really simple genuine compliment. You must let her know She's your that you're attracted to her very simple could be anything doesn't matter what it is She has to know you find her sexy. Okay, that's one second thing. You must pull the trigger Okay, pull the trigger means actually asking her out if you're on in the daytime asking her out Let's get a coffee now. Let's let's go bowling.  Okay. That's number two number three curiosity. Okay You really want to succeed with women you must show and take a genuine curiosity in women What is their passion? What makes them tick? What do they love? What do they hate? Who are they? What's their plan? They had a million dollars. What would they do? Okay? If a girl really feels you're genuinely curious about her and you really want to get to know her That is the most powerful thing that will get you laid on its own. Okay, especially with these other two ingredients. All right, so Here's what's funky.  Okay Can anyone guess what the sentence is? All those three ingredients anybody? Okay, I'll tell you sometimes I make students suffer and I make them guess and I make fun of them.  Whatever you're telling her. She's hot. You're gorgeous. Okay, you're pulling the trigger Let's get coffee.  You're sexy Let's get coffee right there. You've done it. You've asked her out. You've told her.  Okay, so when you're in interaction, you don't know where to take it You don't know what to do.  Let's get coffee. What are you doing right now? Okay, that's simple Not difficult. We'll get you laid Can't believe you guys didn't even take a guess at the sentence Right, I believe I'm out of time This is my slide for whoring myself. See I have to put that in there because normally I don't do this Available for coaching.  I'll see you next time


What we're doing today is some experiments to look at actually measuring the performance of the air drops. The water drops that come from the aircraft and things like the spread pattern, the coverage, the amount of water, so that we can try to understand the relative effectiveness in terms of wetting the ground and helping to control fires. We're measuring the air drops in a series of hundreds of cups that are laid out and they capture the water from the aircraft drop and then we go through and retrieve those cups and measure the weight of every single one. From the drops already we're already seeing the nature of the water column as it drops. The heavier water droplets first followed by a wider area of mist and that's all really important for wetting the ground to suppress the bushfires and cool them down. Different types of drops might have different effectiveness and different purpose depending on how the fire is burning and where.


Hello friends, I am Sanjay Gupta. In this video, I am going to demonstrate you how you can swap elements of two 1D arrays using pointers. Before starting, you can note my information. You can follow or subscribe my YouTube channel through the URL youtube.com slash sanjaygupta underscore tech school. You can download my programming app Techimus, which is available on Google Play. Now I am going to demonstrate you the code which is implemented in front of you, which will swap elements of two 1D arrays using pointers. So in first statement, you can see I have declared some variables A and B both are arrays P1, P2 are pointers and I is a variable which will be used to repeat some set of instructions with the help of loop. After this variable declaration, I have implemented three statements in which first is printf, which will display the message enter 10 elements of first array on console. Then through this for loop scanf statement will be repeating 10 times and all the 10 elements which will provided by the user will be stored inside a array. After completion of this loop, the second segment will be executed, which will display enter 10 elements of second array message on console and next 10 elements of second 1D array will be stored inside B array. After reading elements of A and B, I have to assign addresses of both the arrays into P1 and P2 pointers. So for that purpose, I have used P1 equals to A and P2 equals to B statements. So here you have to notice that name of array provides base address of the array. So A is providing its base address into P1 and B is storing its base address into P2. Now I can access elements of A through P1 pointer and B through P2 pointer. So for swapping purpose, I have used this loop which is repeating 10 times and here these three statements are available which will swap elements of A and B arrays with the help of pointer. So here asterisk means value at address. So when I will be writing asterisk P1, it means P1 is containing an address and I want to receive the value of that address. So for that purpose, I have written asterisk P1. So asterisk will provide the value which is available at the address and the address is stored inside P1. So P1 and P2 both are pointing to some addresses and their values will be received with the help of asterisk sign. So this way all the elements are added and subtracted and the results will be again assigned into values of P1 and P2 pointers. Now for pointing to the next location, I have added P1 and P2 by 1. So initially P1 and P2 are pointing to the base locations of array. To move to the next location, I have incremented both the pointers by 1. So this way this loop will repeat 10 times and all the locations of A and B arrays will be interchanged or swapped with the help of pointers. And this method is implemented without using third variable. So after completion of this for loop, I can print the results of A and B arrays with the help of their names. So here you have to see that I have received elements of array through array name and now I am going to print the swapped values again with the help of array names. But for swapping purpose, I have used their addresses with help of pointers. So now if A and B will be printing swapped values, then this operation is correct. Otherwise, this is incorrect. So now I have to check whether the program is working properly or not. So I'm entering 10 times 1 in first array. Now it is asking for the 10 elements of second array. So this time I'm entering 4 in second 1D array. So you can see the output. First row is printing 4 and second row is printing 1. And here in this printf, I have printed A first and then B. So A is printing 4 and B is printing 1. But I have entered 1 into A array and 4 into B array. So this way I have interchanged values of A and B arrays with help of pointers. So this way you can swap elements of 2 1D arrays using pointer. You can use any particular method either using third variable swapping or without using third variable swapping. So I preferred without using third variable swapping method. So I hope you have understood how you can swap elements of 2 1D arrays using pointers. If you want to watch more programming related videos, you can follow or subscribe my YouTube channel through the URL youtube.com. You can download my programming app Techimace which is available on Google Play. Thank you for watching this video.


I have YouTube live across the board.  If you really understood Keto, you would understand, did you know age of 30, your brain? One of the things that my story, I've been Keto for 20 years, I've been Keto since the majority of my entire adult life. And primarily for my brain and for some of the past. New birth.


Hooked up Yo what's poppin people welcome back to another episode of kicking their bass TV today We're about to do some crazy fishing guys. This has to be one of my best days of fishing ever I'm actually filming this intro backwards. This is just insane. Do not skip through this video guys We have some awesome content for you guys to watch here on the channel today today We're actually fishing some backwaters for some big red fish. Maybe even some trout some flounder But our main target today is redfish. We're using some artificials I'm gonna show you guys exactly what we're throwing what we're doing today And we're just gonna try to hook a lot of these big redfish I'm gonna tell you guys we pulled up in my truck or Cody's truck and Instantly we saw some activity in the water And so I ran to the back grabbed my rod and you guys are about to see what's about to go down By the way, if you guys are new to the channel hit that subscribe button hit the notification bell Also hit the like button if you guys have been enjoying the content and if you want to see some more videos like this This is a banger now. So let's go ahead and hop into it Got that camera, dude.  Oh my goodness My goodness Cody. Oh my goodness, brother.  Are you you're actually playing with me, right? Did he's way over on this thing?  Oh Cody oh It's a big boy You might be a 30 inch or Unbelievable man. I'm freaking believable. There's a lot schooling in here He's not like a giant, but he's a dang good. Oh My god, look how beautiful Look how beautiful and golden he is barely hooked. Oh my goodness, man. Oh My goodness first cast of the day Beautiful red fish right here. Just so beautiful really pretty one. He's not a massive Red by any means but just a beautiful beautiful fish You can hear him drumming all up in them right there. I cannot believe that First cast and we got a beautiful red We just pulled up our truck guys and we saw some fish twirling and me and Cody jumped out of the truck Really quick grab the rod and first cast he slammed it, but that's a pretty red We're gonna go ahead and get him back in the water. He's good and healthy and I'll see if we can go catch another one What a beautiful catch What do you got to say about that Cody that was intense that was so sweet man start off the video First cast with some action like that. You just cannot beat it guys and that's my first red since we went surf fishing We're gonna see if we can go get another one. Let's go ahead hot back in the water All right guys, we're gonna get back in the water if you guys are wondering what I'm throwing just a little fourth ounce Lead weight. It's a little tiny swim bait on there. Very simple and basic got it on the kick in their bass combo Which is dropping this Thursday in two days.  There's I Just don't know how they are once you catch one like does it spook some of them off? But there just seems like there's so many fish in this area. I just can't believe you bit it first cast And that's that's just insane to me small one. Yeah. Oh, I came off That was probably 1415 inch or those are those are pretty small There's so many fish on this bait right here ceiling hook up.  Oh my goodness, dude Unbelievable I might have to quit bass fishing after this guys. This is this is just so much fun Throwing this new kicking set up to it feels so good on this rod very lightweight. Just look at that Can't beat that drag rip. Oh, that's another big and Cody. Oh Dude, they're so pretty and golden man. Look how pretty this one is. Oh my gosh. Look how golden he is The prettiest red I've seen All right, let me just get you up here. Oh, he's golden dude Golden if that beautiful red man, just the gold markings on these fish are just so beautiful And man these fish fight hard too. He's a little bit smaller than the first one we caught Still just a beautiful red.  What a beautiful fish. Thank you, baby Very important to get these reds back in the water pretty quick He's also got to be careful with some gators today. Last thing we want is a gator to come up on the bank But holy cow Cody, this is just man.  Look at these fish man. This is unbelievable I mean these fish are chewing on bait everywhere right now.  You know what I mean? Like watch me not get a bite on this color. They just want that natural Because I have had two boils on me and they didn't come in. Oh, this is a big boy big big boy This is the biggest one yet. Oh my gosh Nice fish coming in already. Oh, yeah, the biggest one yet. Oh Yeah, good one good one. Oh, baby Don't get over there. That's what that other one was doing. It's kind of got a Let them run their way out There you go. See him start to take off to the right. Oh, that's a good one Come on, baby. Get out from under there. Oh my gosh That's a nice one. That is a nice red.  Oh Man, he pulled off Wow, is that a good fight though you cannot complain of that These cheaper hooks guys, uh, they're kind of bending out a little bit which I hate but Man, was that a good fight? I know we didn't get to catch the fish, but oh I'm still happy man. That was exciting. Oh I'm in the middle. Look at that. Look at that. All right, Joe You know I'll put that electric chicken on I think it's a great bait, but something about with the clouds being up today I just think this darker color right here pretty natural.  It's kind of got this Wydish gray on the bottom. I don't know. I think this color Especially with it being overcast today is killer. So We're gonna toss this around some more Waiting for the right moment There we go. There we go. Oh He just slammed me. Oh Come on now. You see him. Oh, he hit me again. He's He was just going around. Oh My god, there was a huge one right here. I just spooked right up on this grass Dude, I feel like a little girl right now, Cody.  That was so crazy I was out in the middle and I was like kind of waiting to throw in there and you could see when you know They start chasing the bait. So I threw in there and he just hit me like twice Well, I started to reel back in this little tiny grass patch right here. I Hit one on the top of the head. I'm like shoot. I flipped in there Kind of gave it a pop and he came back and I watched him eat it right at the bank That was that was the coolest eat I've had in a while. I can't tell me there's not one up on that grass So, you know one of those grass There's one on that other side. Well, there's one coming after me.  Let's go Gotta land this fish. He's going in that corner.  He smoked it. Oh Dude, these reds are so beautiful. It's like Goldie mark gold marking on So pretty here he is he about gave up not a bad one at all. It's a good fish Haha, that is a nice old red fish. Oh my goodness. Look at that dude Look at those colors Cody Is that not the goldest fish you've ever seen is in my glasses or they actually holy cow? They're even prettier without my glasses Look at that fish Thank you, buddy for eating Look how pretty that one is guys That was just a beautiful red not a giant by any means but that what'd you say? 18 inches you bigger than that he's probably 20 right? 20 inch It's a pretty fish. We're gonna get down by this water and get him back in here Look at that pretty red guys. Oh So that one was like a whole different approach, you know There's other bites that we had they're kind of chasing some bait out there in the middle Then I actually sight fished that one in front of me So I was like, you know what these little grass islands over here might be pretty good Sure enough just kind of jigging that swim bait right there and he tackled it. No What I'm trying to catch anything besides a bass like I can catch these any day of my life I just want to catch a red or a little saltwater fish and I cannot escape bass though, man That's gonna be a fat guy dude. That's that's one of them future 25 pounders done So really dude, this is heavy brackish That's wild that's pretty cool though Guys we just got our first fish At this new spot He's not a big one That's a pretty little red Look at that little guy Beautiful markings on them. This one's we were catching earlier kind of had a gold tint to him And this one's kind of like a little sweet silver guy Pretty one now. Thank you, buddy See him swim off. Oh There you go. That was awesome All right boys and girls we're back at our first little hole where we were just smoking the reds earlier Don't see too much activity. You still see a little bit of bait popping But I think we're gonna be able to get into a few. I don't know what the heck that was What is that? Those baby reds.  I like pretty decent red Flipped right in front of him He had a good runner out off the rip. Oh, yeah Not a bad red by any means Definitely not our biggest one today, but he's a good one. That was a sweet bite. Sweet eat Flip him up here. Yeah Gosh, you're so pretty dude Such a pretty fish Look at that fish right there Cody These fish are so pretty out here. It's the prettiest goldie. It's a pretty gold markings on these fish It's like they're a dang gold fish. That's why it's got like a brownish gold tint to him That was pretty I I was throwing out there You know, we saw a lot of bait moving and then all of a sudden like right up by the bank I saw a couple fish kind of twirling on some bait and I just flipped right in front of them and he ate it That's a beautiful fish right there and get him back in the water. Well guys, I was telling Cody I was like, that's probably the best drag rip we've had so far That sucker was running man.  So right when I hooked him He just went crazy Here we go Follow me in he's not a big one You barely fighting. Come on boy. Give me a rip Come on. Give me a rip. He's already worn out. Come on now You can do more than that. Oh Yeah, oh, yeah, now he's fighting Pretty fish pretty one. He's about as big as my last one. I thought not a big one, but you know a nice Good nice. Gosh. They're so dang pretty man.  It's okay. What a beautiful red guys. Look at that guy Such a pretty fish man. I won't get him back in the water. Cody just stepped on a huge pile of ants But seems like the bigger ones we caught at the beginning and now most the ones we're catching are about this size But they're still nice fish. They still fight hard and he's a pretty guy Thank you, buddy for biting Awesome fish


Kita is basically a non-profit organization. We are based in Indonesian city called Surakarta with an expertise in urban planning and citizen participation in the designs of the development of our cities. We envision a city for all where citizens are at the heart of decision making. We basically most of our work, we bridge the dialogue between the government and their constituencies by facilitating citizen participation and collaboration influencing urban policies, encouraging open access to information and providing civic education to empower urban citizens. Our project currently focus on the three sector, we call it as urban governance, urban inclusivity and urban resilience. So to explain more urban governance covers most of the project related to kind of, you know, promoting kind of participatory governance in the city. So for example, we are now working a lot on promoting like participatory design with low income community to kind of promote inclusive public space. And on the inclusivity sector, we work more on promoting kind of inclusive city working with group of persons with disability and also with other marginalized group such as informal sectors like informal traders and then also informal economy like informal kampung. And in the resilience, this where Kota Kita work pretty much with IED is on the urban resilience where we work mostly on promoting climate resilience in Indonesian cities. We work to promote inclusive kind of urban mobility where we working together with a range of several example low income community in Banjar Masin and also a person with disability to think about what kind of intervention we can do. So for example, now we are working with person with disability association to design three cycle, what we call it three wheeler motorcycles that can be used by person with disability and also design safety school zone that really accessible for children with disability as well. So we design a road street kind of design where it's make it possible for person with disability to access the school easily and in a safe manner. We have urban planner, we have also urban designer, architect, and as well as community organizer. And then also like I myself, basically I grew as a community organizer and urban activist, but I pretty much kind of enjoy in delivering like community facilitation. So that's my expertise, but then the other expert would be like mostly on the design and urban design so it's pretty good at facilitating process of participatory design and some of them are planners and communication expert. And we have also like sort of social kind of, you know, researcher, some social research at the community level as well. We work together to understand social security, social protection policies at the same time. We also have to understand some very kind of current issues around climate change and vulnerability across Indonesia and also working with other kind of expert around, you know, kind of understanding around, you know, legal aspect and national policy stuff like that.


We are going to look at two very crucial and highly specialized cells, egg and sperm cells. These lead to each and every one of us being here, hence they are so very crucial. The female sex cells are known as the ova or egg cells or ovum for one. The male sex cells are known as sperm cells. Both of these sex cells are known as gametes. Gametes are an organism's reproductive cells. They have half the genetic information that all of our other body cells have and so are known as haploid. Humans have 23 chromosomes and most of the cells in our body have two of each. So 23 pairs of chromosomes makes 46 in total, one for my mother and one for my father. However, gametes, so the sperm or egg cells, only have one of each and which one, whether it is from the mother or the father, is random. This means that each of our gametes can be different from each other, depending on the mix of chromosomes. Although the egg cell and sperm cell have this very important similarity of only 23 chromosomes, they are very different cells to look at. First off, they are hugely different in size. A human egg cell is spherical in shape and around 130 micrometers in diameter, that's 0.13 millimeters. Not very large but what size do you think a sperm cell is? Have a look at this egg cell being fertilized and you can see the difference in size. As you can see, there is a lot of sperm and ejaculation varies but contains at least 20 million sperm per milliliter, that's a lot. In comparison, on average, a woman releases just one egg per month. The reason there are so many sperm is to increase the chances of fertilization. When one sperm reaches their egg cell and their nuclei fuse, this gives two of each of the 23 chromosomes. And so makes up the 23 pairs and 46 chromosomes in total. The egg cell is large because it goes on to become a new person and so is packed full of cell organelles which allow it to create new energy and parts. The sperm on the other hand only passes on its nucleus. Let's take a look at what is special about sperm. The head is full of the cell parts that produce energy and also the nucleus. The sperm needs lots of energy to get moving. As you can see, there is a tail that it uses to swim to the egg cell. The sperm has a long journey while the egg cell doesn't move. You can also see the cap right at the top of the sperm. That's called the acrosome and contains special enzymes. These enzymes are used to break through the protein coating that is around each egg cell. Because this protein varies from species to species, this egg prevents cells from being fertilized by sperm from another species. From this video, you should now know the difference between an egg and a sperm cell. The egg is much bigger, does not move and contains organelles needed for the fertilized egg to develop into an embryo and onto a new human. Sperm cells are much smaller and more tall and there are millions of them. They only pass on their nucleus and so are able to be small. And most importantly, you should now know that gametes, so the egg and sperm cells only contain 23 chromosomes each. This is known as haploid. When the egg is fertilized by a sperm cell, the 23 chromosomes from each pair up giving the normal diploid amounts of 23 pairs of 46 chromosomes.


In 2014, Major League Baseball in conjunction with the MLB Players Association instituted a controversial rule change designed to prevent home plate collisions. Rule 713 states that a runner attempting to score may not deviate from his direct path to the plate to initiate contact with the catcher. Similarly, the catcher cannot block the runner's path in his bid to score. Some players and managers were initially concerned that the rule would alter the nature of the game. But data show that in the higher stakes matter of player safety, Rule 713 is a clear win. Using the MLB Health and Injury Tracking System, a database recording all injuries to players in the major and minor leagues, researchers from MLB and the MLB Players Association looked at how the 2014 rule change has altered the profile of player injuries. Specifically, they compared the incidents of some traumatic brain injuries or TBI's in the seasons prior to and after the change. A mild TBI or a concussion is loosely defined as any complex physiological process affecting the brain as assessed by a physician. While baseball players with mild TBI typically return to play in 7 to 10 days, there is concern that repetitive impacts have the potential for long-term consequences. 11 mild TBI's caused by home plate collisions occurred annually before the rule change was made. After, that number dropped to 2 mild TBI's per year. Meanwhile, the total number of days missed on average due to those injuries dropped from 276 to 36 annually. And while none of the mild TBI's recorded after the rule change was season-ending, nearly 20% of those occurring before the change were. The small number of TBI's recorded overall might not be enough to make any definitive claims regarding that type of injury. Notably, however, the researchers witnessed a similar trend when widening their search to any injury due to home plate collisions. Both the annual number of injuries and the time lost to injury dropped significantly. Rule 713 doesn't completely eliminate the risk of injury. Even with the allowances runners and catchers now give each other, injuries can and have happened. But the current study and others like it point to the significant benefits rule changes can provide players. Collectively, they're a testament to the ongoing balance stewards of the game must strike between competition and safety.


Hello, my name is Dr. Andrew Missildine and I'm a mathematics professor at Southern Utah University And this is my talk entitled counting show rings over cyclic groups To give some motivation on why we want to count show rings in the first place. Let me actually compare this to Comparable problem from common atorix the famous Bell numbers are actually a sequence of numbers which counts the number of ways one can partition a set of In many elements these so-called set partitions the first couple terms in the sequence are given right here These Bell name numbers are named after Eric Bell whose picture you can see on the screen right there I'd give you a visualization of what this means is consider consider a set of size of Five elements right there now it turns out there's gonna be 52 ways one can partition that well one option as you put everything together You could have everything isolated so when you see no color on the dot That means it's just a singleton and you get things like this where you put three things together leave two apart But you could decide on a different two elements which would be isolated from the rest and so this case There's a lot of possibilities here 52 for a five element set Now related to the Bell numbers are the so-called partition numbers which the partition numbers count the number of integer partitions of A non-negative integer and and so by an integer partition Well, what I mean is something like the following if we wanted to partition the number six We could partition as two plus two plus two or we could write as three plus three or we could write as three plus one Plus one plus one in other words We're looking for any way any any all the possible sums of the number express the sum of positive integers Now there's gonna be a lot fewer integer partitions and there are set partitions for the same size But the two things are related to each other as you can see We'll get to that in just a second here But when you look at say the part the integer partitions of five there are seven possibilities There's just the number five itself four plus one three plus two three plus one plus one You get the idea here and oftentimes these can be illustrated as young diagrams where the first row will be the first number The second row the number squares there will be the second number involved here and these are always written in descending order now the two things are connected to each other because the The set partitions have a very natural equivalence relationship on them We could actually say this is an isomorphism for set partitions because when one talks about a set isomorphism That is just a bijection the only thing that's left in variance by all possible Bijections is really the cardinality of the set and so if we look at set partitions and only focus on their cardinality's we can associate to each Partition one of these young diagrams so for example, we get Partitions over here where you put two together two together and one together and so you get this right here So all of these different partitions as set partitions are isomorphic and can be identified with a single integer partition I should also mention so like the integer partitions the integer numbers count the number of isomorphism classes There are of this set partitions which are counted by the Bell numbers The the number of classes is counted by the partition numbers And then if you are curious the number of elements in each class those are counted by the sterling numbers of the second kind And so there are some classic combinatorial number sequences used to analyze these questions about partitions So what I want to talk about today is what if we want to change this question to focus on finite groups? What can we do to start counting partitions of groups? Well, the first thing to kind of nail down here is that if we want to start enumerating partitions of groups What does it mean to have a partition of a group? We need a partition because the group itself is a set but with a with a binary operation Our partitions should have some respect of the binary operation and play here. Otherwise, it's just set partition Now there actually is a notion of a group Partition which in the category of groups. It's the partition object and that involves Covering a group using subgroups of that group and so that they intersect in trivial ways So there is a notion there and it seems like a strong candidate of what we want to be talking about right here But this idea of group partitions actually a very rare Phenomenon like you can do a fruit for previous groups But and others I think as well But it doesn't happen that often like for example a cyclic group could not be covered using proper subgroups. It's not possible At least not know. Yeah, you can't do with proper subgroups. And so that type of Partition where the cells themselves are subgroups. We got to do something else than that now some Partitions that do kind of respect the group structure that might be of interest counting here is take the the equivalency of Conjugates right two elements are in the same class if they're conscious of each other This is a very important partition of the group another equivalence relationship could just be automorphisms in general Sort of a stronger Relation than the conjugacy one. We could pair things together based upon their inverses Involutions being by themselves we could partition a group using cosets or double cosets if it's a non-normal group We could talk about membership of a subgroup like we could partition the group by you belong to the cell if you're in the subgroup And you part you belong to this other cell if you're not part of the subgroup And so these just give us a few examples of some partitions These are gonna set partitions that in some in some way or another the set partition is Measuring some part of the algebraic structure of the group Now all of these that you see on the screen right now are examples of a special type of partition called a sure partition or More likely called a sure ring These are named after you sigh sure Who first kind of came up with the idea and they're called sure rings as opposed to sure partitions because the written Because these objects are genuine rings sub rings inside of the group algebra Associate to the group and let me kind of explain how that is if we have some finite group g We can identify subsets of the group with elements of the of the group algebra qg and these are called simple quantities Where you basically just add together all the elements inside the subset via the formal sum of the group ring And that becomes at this simple quantity in the group Another bit of notation here if we take a subset or an element of the group ring It doesn't really matter what we do if we raise it to this negative one power inside the parentheses right here What this means is we're gonna be just taking the inverse of each element Inside that set there And so then with this bit of notation in this convention in hand We can define the notion of a sure ring so sure ring you start off with a partition of the group and This partition will make a sub module of the group ring We just take the subspace spanned by all of these simple quantities But then to make it a sure ring there's three extra conditions require First that one of the classes in the partition must be the group identity element all by itself the second Condition is that given any class in the partition It's inverse class must also belong to the partition and then finally if you take the product of any two classes in our partition the product will be a linear combination of Other of other classes in the partition so when you look at these things three things together Right, we're looking for a partition which has an identity which has inverses and which is closed under multiplication The the multiplication in play here will always be associative so we're looking for partitions that mimic the group axioms themselves and so these partitions are very group like objects and this is what we call a sure ring and So to give you an example a few examples of sure rings here One simple example is what we call the discrete sure ring and this is just you take the entire group and you partition into singletons So the group itself is a sure ring and so if we take the sickly group of order six We can partition it by just taking Everything by itself you see different colors for the different cells On the other extreme we can take what we call the indiscreet sure ring for which the Identities by itself because it has to be and then everything else is fused together Again looking at the sickly group of order six you have the identity by itself and then everyone else is in one very large class We can build partitions using automorphisms If we have an automorphism a subgroup of the automorphism group it acts on the group via That automorphic action and then the orbits associated to that group action form what we call an automorphic sure ring so for example if you take the sickly group of order seven and you take powers of two which is an automorphism you get the following three celled Automorphic sure ring as another example We can actually form sure rings using the direct product structure of the group if we have a sure ring Over we have a direct factor So she factors as h times k here if you have a sure ring over h and a sure ring over k Then you can take the tensor product of those two things and that'll form a sure ring over The direct product we call this the direct product sure ring So if you take z6 again take just take the subgroups z2 and z3 And so if we take a sure ring over z2 and as sure ring what you can see right here and a sure ring over Z3 which you can see right here take the all the possible products you get this direct product sure ring and Then as a final example here let's consider the Well, we can actually build sure rings using quotients of some kind normal subgroups So if we have a sub normal subgroup of some kind h inside of G Then take a sure ring over h and take a sure ring over g mod h and then there's a it's possible that We can kind of glue these two sure rings together to make a sure ring over The the group G and it's going to involve using cosets of the quotient and so If you were to identify the five or five points set before if we identify those points as the Five complex roots of unity then those of those 52 partitions only three of them will actually correspond to sure ring partitions We have the indiscreet one right here We have the discreet one right here and then lastly we have the This one right here. This is an automorphic one where you identify inverses together so these these four types of sure rings that mentioned so far Constituted what we call the traditional sure rings and it was shown in the 90s by London mod that all Sure rings over sickly groups are traditional. They're one of these four types And so if one wanted to try to count All the possible sure rings over a sickly group It would be very very difficult to try to go through all the partitions and decide this one's a sure ring This one's not because there's just think that that's the number of sure and the number of partitions just grows too rapidly So we need a different approach of deciding which finding which partitions form sure rings over the group And the two big things that one has to deal with here is that the direct the direct product and the wedge product constructions is a recursive Recursive construction based upon proper subgroups So you have to grapple that recursion and then also we have to be able to list the Indicomposable sure rings over a group that is those sure rings which cannot be written as a direct product or a wedge product of any kind And in this talk, I really want to focus on these Indicomposable problem because the recursion here can get a little bit crazy and we're limited on time And so I wanted to present just some examples here How does one decide how does one find the Indicomposable sure rings for a group? Well, the in the indiscreet sure ring always offers one and all the other ones are going to be Automorphic ones and there's gonna be a one-to-one correspondence between the automorphic sure rings and subgroups of the automorphism group for a cyclic group and so one has to study the automorphic subgroups of Set group. So if you take for example z5, its its automorphic group is Is a cyclic group order z4 and you're gonna see that the subgroups of z4 are gonna look like the following We'll just buy divisors you get one two and four when you go up to The automorphism group for five squared that's gonna give you z20 and you're gonna get all the subgroups You had before but you're also gonna gain Some new subgroups z5 z10 z20 and these are just gonna end up stacking on top of each other if you look for the subgroups of z10, which is the automorphism sorry z100, which is the automorphism group of z125 You're just gonna get these layers that's to start stacking on top of each other Isomorphic to each other as lattices and you see this happening over and over again If we looked at for example z7 its automorphism group is gonna look like z sick It's the cyclic group of this p-1 If you take this layer right here and you copy on top of it You get you get the automorphism lattice for z or for seven squared and for seven cubed same thing for 13 The base layer here is gonna look like the divisor lattice for p-1 And then we stack on top of it lattice isomorphic copies of that and so very recursively we can see very clearly what the automorphism groups for Ciclic groups are gonna be when it's a power of an odd prime And so if we take omega n to be the number of sureings over the cyclic groups the n We can then well for an odd prime Let x be the number of divisors of p-n that that's sort of this base case when it came to that The lattice at the bottom here We can then Using the recursion that comes from the wedge products and the recursion from that Automorphic lattice we saw on the screen a little bit ago one can actually pull apart our recursive formula for omega pn It'll depend on previous Omega p in minus ones this number x shows up a lot here again the number of divisors of p-1 And then also the the recursive relation brings out the catalog numbers There's sort of an interesting argument that I can't really go into right now The catalog number is a very famous number very famous number sequence in common torques If we were then to expound that recursive formula, we see the first 10 Iterations of that formula would be these 10 polynomials and some interesting things we can say about these polynomials They're always monic the leading coefficients one The last coefficient the constant terms always as follows the Fibonacci sequence kind of which is kind of fun and just some other things to mention that this actually shows that the number of sureings over a a Ciclic group of order pdn actually is a pork function And so this is kind of resemblance of Higman's pork conjecture that when one starts counting the Counting groups not isomorphic groups of order p to the n you have these polynomial over residue class functions turns out that sureings over cyclic P groups are also pork Which is kind of a nice connection there and if you plug in some specific numbers You can see here's a table of number of sureings for various powers of primes If we were to look like a power of two so two this has to be treated different differently as it's its even prime When you look at the growth of the automorphic lattice You see that when you get to eight it starts to stabilize that you get this little break this little v-shape That appears on each time it is because this group itself is not cyclic It's not a cyclic group like the previous ones were so it's a little bit more complicated But you can see that as the power of two increases you can you can predict how this Automorphism lattice is going to grow as well and as such you can use that to come up with the following formula This one's a whole lot more complicated as you can kind of see here as compared to the previous one Some things to notice is it is recursive right omega two to the n does depend on previous Omega values for powers of two we're looking at the proper subgroups of this group here It also relies on the catalan numbers But also it also the the Schroder numbers come out here another important number sequence That's actually closely related to the cat on long numbers the catalog numbers come back again This is mostly coming from the recursion from the wedge products involved for for p to the end There are no direct products possible But because of the non-cyclic nature of the this this lattice of automorphisms There is these Schroder numbers that come into play so these things can get complicated pretty quickly And again if you look at specific powers of two you get the following sequence of numbers So what if we want to look at counting the number of shurings when the order has multiple prime divisors Well a natural candidate, you know a sort of a simple example be look at z15 here If we try to look at the well for z15 you are gonna have direct products You're gonna have wedge products, but we want to figure out those indie composable ones How many automorphic ones can we have well the automorphism the automorphic group? The automorphism group for z15 is going to be z2 cross z4 So let's say the generator of z2 is a and the generator of z4 is b like this Then the lattice is gonna look something like the following you can look at the subgroup of z4 You'll have a the trivial one z2 z4 if you look at the group associated to z2 You just get the trivial subgroup and z2 itself and when you take the direct product of the lattice you get the following Parallelogram like shape this gives us six distinct subgroups Which will give us six distinct automorphic shurings, but the group has two extra subgroups These so-called diagonal subgroups they get their name Because of where they kind of appear inside of this lattice right here Now these diagonal subgroups come about from the following idea A is an element of order 2 and b squared is an element of order 2 if we Multiply these things together we'll get an element of order 2 and same thing when we put together a and b B has order 4 a has order 2 when you multiply them together you get a group of order 4 right there And so by both an abelian group if you multiply together elements of similar orders You can create new elements that are outside of this lattice And so this kind of becomes a tricky thing predicting when you take a direct product of abelian groups How many subgroups will you have this actually a very sophisticated problem and the the complete answer is actually not known yet? Turns out we only know a little bit about this formula of counting subgroups of general abelian groups Now if you use that you can apply that and get the following formula right here This this equate this part of the equation right here if we're counting if we're counting the number of shurings Whose order is a semi prime that is a product of two distinct primes? Then we get this right here. This is going to count the automorphisms Which comes down to counting all of the subgroups of the automorphism subgroup. We also have to count the wedge products right here and Then lastly we want to count the the indiscrete or sometimes called the trivial shirring There are direct products in this situation. It turns out every direct product is an automorphic one You don't have to count them twice now in order to get this form which is a little bit complicated here It does use Euler's tosian function and it has to do with how does the prime decompose? So if you write your prime with a it's sort of quote-unquote prime factorization if you subtract one from a prime It's no longer prime right with the prime factorization of P minus one that affects these this formula here And if you look at the this table this gives you just data for all these possible shurings right here There's we don't need to look at all of this here One last example. I want to I want to mention here is that? What have we looked at the lattice associated to for P four times a prime here? This is kind of a nice Predictable lattice here because if we take the lattice of Just Zp you're gonna get the trivial subgroup at the bottom plus something You know what is this some blob going on right there? I don't know exactly what it looked like But if we want to take the the automorphism group the lattice associated to the automorphism group of z4p Well, you're gonna get the lattice for z2 which comes from the z4 part You're gonna get the lattice associated to Zp, which is again this blob and when you take the direct product You're gonna get this this isomorphic lattice picture on top like there's this bottom layer And then there's this top layer that as lattice is going to look identical to each other But then you also have these diagonal subgroups that sit in the middle here And so if you want to count the shurings of the cyclic group of water for P There's gonna be some you have to watch out for these diagonals here. It turns out. It's not so it's not so Wicked in the situation of 4p and so as another as another kind of result here if we decompose our prime as 2k a plus one So we're trying to figure out how many multiples of two divide into two p minus one That's the factor of two is really gonna measure how many diagonal subgroups we're gonna have and so we put this together We got a cute little formula Compared to most of the formulas we've seen in this talk here. This one definitely is the cutest one here And I should should mention that These results you it was mentioned on the slides here, but these results the first couple about just the single pattern single primes Right p to the end 2 to the end. These were results proven by myself In the in a paper published earlier this year 2020 These last couple results about the the city prime p times q and this 4p case you can see on the screen here This was joint work of myself with also two undergraduate students at Southern Utah University Joseph Keller and Max Sullivan For which at the time of this recording these results will be published forthcoming probably 2021 assuming people will referee during the corona virus pandemic But we can make the projection that that preprint will be published sometime next year And so again, here's some numbers based upon that If you have if you apply that formula to the various four times p cases there And so finally just if we kind of just have some last last minute questions right here The techniques we've developed in this again, we were very very quick and we didn't talk about a lot of the recursion but In order to in order to enumerate these sure ring partitions It really could we have to be able to understand these We have to be able to predict how many in decomposals sure rings There's going to be and this has a lot to do with the number of subgroups of the automorphism subgroup of an abelian group And as I mentioned earlier, this is still a very open question We're using the so-called rank 2 problem associated to counting subgroups in abelian group Where it's just it's just a product of two Ciclit groups there P we can assume they're P groups and there there's work that's done for the rank 3 I think the rank 3 problem might have been solved I have to double-check myself before I could say that definitely the rank 4 Problem for counting subgroups in abelian group. I believe it's still quite open And so in terms of counting six assurance over Ciclit groups One's not going to be able to get any farther than the the the rank the subgroup counting problem Because that's going to be a subset of this larger problem we're in right now And so at the sort at the moment at the time of this recording The idea would be to be trying to carry this up to finish the rank 2 problem for these sure rings over Ciclit groups You know arbitrary order of P to the n times Q to the n Could we get a formula for all of those and I think there's really good hope of getting such a thing But it's it's still a little far off And then you can also ask well, what if you start getting more right just because the general Rank in problem hasn't been solved for counting subgroups and abelian groups There are special cases we could do like what if there's no repeated primes What if there's like PQR RP? You know that aren't just every of our many different primes Could we approach something like that as well? And of course, it's also natural Can we start looking at other types of groups other than cyclic groups? The problem there is that the cyclic groups are the only groups that have really a complete classification of all the sure rings over them even for small groups There are tons of partitions possible and therefore there's Potentially a lot of sure rings that could be done and we still have very kind of little knowledge on What type of sureings can appear for even even abelian groups? It's still a very very unknown thing which has some important applications One very important application would have to do is super character theory Theories because a super character theory for example, this is when you start gluing together characters of a group and you form character Theoretic like objects that we call these the super character theories and it was shown by Hendrickson that Super character theories correspond to central sure rings of the group and so be able to classify Sure rings is essentially the same problem is trying to classify super character theories And there are other applications of sure rings with algebraic commentatorics that I won't go into in this talk right now So that that finishes this talk. I appreciate everyone for watching it here I should mention that a lot of the images in this talk if they weren't made by myself They were borrowed from Wikipedia so like some of the some of the pictures of Bell and sure obviously I didn't draw those ones Though those are courtesy of Wikipedia. If you have any questions on these topics feel free to Comment in the comments below right if you like what you saw give it a give it a like click Or again if you want to have a more in-depth conversation about sure rings and topics related to that Feel free to send me an email Or again, just kind of reach out to me through the comments on this on this YouTube video. Alright, thanks everyone. Have a great day


Okay, the first thing we're going to do in this tactical decision game is orient you guys to the table. So it's important for you to understand a few things. First thing is that north is this direction as indicated by the blue arrow. The scale of the table is one mile by two miles. The fuel type here is a ponderosa with a grass understory. The rise on this terrain is approximately 1,200 feet. You can see that we have a dry creek running through the west side of the fire area and we have a bridge that crosses that creek that will give you access up into a subdivision. This is the Pleasant Valley subdivision. Our fire is located right here and it's approximately one acre, is it? Any questions? I might have missed it, but this is an intermittent stream or is there water in it? From the air you'll see that there are pools occasionally throughout this stream. Will those pools support a Mark III? They'll support a Mark III with a little bit of work. The ridge is a natural barrier. The ridge is a natural barrier. And is the black clean black? Black is clean black. Do we know if those houses are, people are in them or are they vacant? We do not. It doesn't appear as though there are any people there now, but we don't know for sure. And what resources are available to us? You currently have one other Hell Attack crew. That's the Boundary Waters Hell Attack crew to Sierra Juliet. And you have two Type IV engines and one Volunteer engine that's the mud flat Volunteer Fire Department. Okay, I'm going to go into the fire scenario. It's July 27th at 1100. The temperature is currently 84 degrees, predicted to rise to 98. Relative humidity is currently 20 percent, should drop to about 18 percent this afternoon. Wind is currently three to five out of the Southwest and it's predicted to be out of the Northwest, 10 to 15 miles an hour by 1500. Any questions? Any other weather anomalies that we should know about? Are there thunderstorms in the area? We had thunderstorms roll through yesterday, which is what started the fire. There are none predicted today. Looking at the fire scenario, it looks like this would be a high priority fire, but are there any other fires near housing developments that have a higher priority than this? There are other fires, but we haven't prioritized these fires yet. But based on the fact that there are homes here, this is a fairly high priority. What we're going to do now is I would like you guys to think about the approach that you made. We did a good recon around the fire and then landed on the top of the fire above the subdivision. Everybody's out of the helicopter now, and I'm going to give everybody three minutes to formulate a plan of action. And when the three minutes is up, I'm going to select an IC to communicate their plan of action and execute that plan. Any questions? Did you mention what we have in terms of communications? Do we have radios and who is there like a dispatch center? We could contact to get more resources if we needed them. Yes, you have two radios and you have three frequencies. You have the forest frequency, which will put you in contact with Pleasant Valley Dispatch. You have an air to ground frequency, and you have a scene of action frequency.


Visualizing single cell data in a T-SNEAM batting is fun. But what we really want to know is which clusters represent which cell types. In this video I will show you how to use marker genes to achieve this goal. Consider a data sample from 10x genomics on bone marrow mononuclear cells. The data on 1000 cells is available from single cell data sets widget and shows a nice clustering structure when viewed in a T-SNEAM batting. While this data comes from a healthy donor and a donor with leukemia, we will disregard this distinction here and will focus on the exploration of the cell types. We can distinguish between cell types using the expression of marker genes. For our data, genes that are expressed in monoclonal antibodies are good candidates for markers. We can find them, for example, in the cluster of differentiation marker handbook. From the book, I will use a few markers for T cells, B cells and erythrocytes. Let me put them down in an Excel spreadsheet. I will create a table with two columns, one for genes and the other one for cell types. CD3e is a marker for T cells. And so is CD8. And CD19 for B cells. From the handbook, I will use a CD235a as a marker for erythrocytes. Here is my short list of marker genes with associated cell types. Let's save it to the desktop. Let us use the file widget in orange to load the marker data. Orange correctly assumes that the cell type is a category and that the gene column contains text. I will use the genes widget to convert these texts to gene IDs and tell it that the genes are stored in the data column called genes. All our four genes were found in the NCBI database. I will display my list of genes in the data table to also show the cell type. In the data table, I can select any row and the widget will communicate the selection further down the workflow. Let me select the two rows with the T cell markers. Now I would like to score the cells in my data according to the expression of the selected gene markers. I will use the score cells widget, give it the data from single cell data sets and the list of genes from the data table. Score cells adds a column with a cell score to the single cell data. Try changing the selection of the markers to see how this alters the score. Now, we will use another T-SNE widget, fill in the data from score cells and set the color and the size of the dots to reflect the score. It looks like the cells in the lower right are the T cells. The cool part, however, is to have both the list of marker genes in the data table and the T-SNE visualization open side by side. Now, I can select any marker and see the changes in the T-SNE. The B cells are in the two central clusters and the rithrocytes are in the cluster on the left. And again, the T cells are in their own clusters. I could now add some more genes to my Excel spreadsheet, reload the data with the file widget and play around with some more markers. Or, alternatively, I could use marker genes widget to load markers from cell marker database. Or, select a cluster of cells to find differentially expressed genes and with those potential new markers. We will do all of these and much more in our next videos.


Aaron on base all four times tonight. You talked yesterday about how this was a whirlwind, a big week for you. What has this experience been like?  Fun to get back with the team. First game yesterday and then today. It's had a pretty good game, so it's exciting. Congratulations again on the baby. You, playing in center field, you have one of the best views for Garrett Cole. Six scoreless for him today, really setting the tone. What did you see from Garrett? I thought he was just pinpointing the spots. He was definitely hitting the spots and doing everything possible to keep these guys off balance. And, you know, he was executing. Finally, you guys finish the month of April with a 15 and six record. First place in the American League East. How does that all sound to you? Sounds good, but we got to keep it going into the next month and just keep going. Aaron, thank you very much. Back to you guys.