So welcome to this morning's session. We are the third lecture by lecture by Percy Dived Okay Okay, so Let me just give you a quick reminder what we've done so far we have Discussed the following that a remand hillbill problem Sigma V Involves an oriented contour our convention Plus side is on your left as you go along and V is a jump matrix, which is a invertible matrix at each point of the Contour such that the matrix V and its in inverse are bounded over the whole Contour the kind of contours we look at are going to be what we call composed contours or contours Composed curves, which are finite unions of arcs. In other words, homeomorphic images of the interval 01 and They had additional properties these each arc was rectifiable or locally rectifiable That enabled us to introduce on any contour Sigma We could introduce C come to H of Z say to be the integral Of H of s d bar s upon s minus z and this is over the contour D bar means DS over to 2 pi i So because we have rectifiable con contours we have a measure on each of the arcs We have a measure theory. We can integrate and Just with these assumptions we know that We can introduce the operators C plus minus which are the boundary values as You approach the point Z From the plus side or the minus side and that is equal to one-half of H plus i over 2 times a Hilbert transform on H and We always have that C plus minus C minus is the identity and This is true for all Lp Where P is bigger or equal to one and less than infinity But if you want these operators C plus minus or H to be bounded in Lp now P will only run from bigger than one and less in Infinity you need another property, which is called the Which is the property that the C gamma little little call it C gamma Which is equal to the supremum over all Z belonging to the contour and all numbers are which are positive Times the ball of radius R around Z intersect with the contour divided by R This quantity is finite. So You take any ball around any point Z So you could take a point like this you take a ball and You intersect with the con contour you compute its arc length Divided by R and the supremum over Z and R should be fun finite Such a curve is called a Carl Carlson curve is called the Carl Carlson constant This is finite if and only if H or C plus minus Belong to the bounded operators and Lp Also, whenever you have just this over here these bound boundary values are non-tangential Limits Okay, so now we can begin Speaking concretely about what we mean by a Riemann Hilbert problem and So we always have Composite curve of these kinds are not going to say anything more more about it now we say a pair of Lp Z functions F plus minus belongs to and This is just notation Boundary C Lp if and only if F is equal to C plus minus of some H Where H belongs to Lp, so that's a definition so that means If we define F of Z to be CH At Z For Z belonging to C take away the contour. This is called naturally the extension of F plus minus off the contour so those extension of F plus minus of You notice that this H is necessarily unique because What we have to have yeah, this is So F plus minus right equals that So if I have this pair here It's given by C plus C minus so because of the property that C plus minus C minus is the identity I'll keep putting the pluses Because of that you see that H is just F plus minus F minus So H is unique Okay, now I'm going to introduce two kinds of Riemann-Hilbert problems and both are used for different purposes, but they are equivalent to to each other So let me just give the following So we fix P less than one unless bigger than one less than finding and We're given Sigma V and a given Sigma V and a Measurable function F say We say M plus minus belongs to F plus Boundary C of LP So this means if I take M plus minus minus F It can be written as C plus minus of some function H. There's some function H Solves the Inhomogeneous Riemann-Hilbert problem of type 1 and LP So it's inhomogeneous Riemann-Hilbert problem of type 1 and LP if M plus equals M minus times V on the contour So the function has this property if you take away this function F for just a measurable function It's not in any LP space or anything, but just M plus minus minus F is equal to C plus minus of some function H and it has this relation almost everywhere on the contour okay, so We say so given Some function now which belongs to LP of Sigma we say M plus minus which belongs to the boundary and LP solves The inhomogeneous Riemann-Hilbert problem of type 2 and LP if M plus equals M minus times V plus F almost everywhere one second So you have these two different things now you notice the big difference between them is that M plus minus is something which automatically has an analytic continuation above the off Sigma and M plus minus might not because you don't know anything about F Now these are useful in many different ways Okay Okay now at V equal V minus inverse V plus the any Point wise almost everywhere factorization of V V plus minus V plus minus inverse belongs to L infinity now This is just a point-wise factorization. There's no Analysti attached to it now you should think about it in in the following way you should think of yourself in the context of Suter differential operators where you're obtaining an a priori Picture of what V is going to look like which will then be useful for further analysis So in other words you have this freedom to factor it point-wise and Achieve different goals in how you choose all the results that we're going to be speaking about going to be Independent of how you make this choice and I'll make this clear We write V plus because our density plus W plus and V minus as being equal to one Identity minus W minus so these are going to be bounded Okay, and we introduce the following operator CW we let W be the pair W plus W minus CWH is just C plus H of W minus C minus H of W plus and this belongs to the bounded operators in LP Okay, you've got a matrix valued function everything is of size k k bar k You take your function H you multiply it From the left on to W minus Then you take C plus of that C plus of course is applied when I write C of H I mean if H is a vector if H is a matrix and you just mean C acting on H I J each component And you do the same thing here now because this is bounded W minus is bounded W Plus is bounded and C plus and C minus of bounded this makes for a bounded operator and As I said right in the very beginning That as a analytical problem a Riemann-Hilbert problem is all about Solving singular integral equations on the contour so we're getting closer to that point Okay Now I just want to draw a little Important Diagram now these are going to be equivalent and You use one equation or the one point of view or the other depending on what you want to achieve This is going to be Connected with trying to solve this equation this on the other hand Is going to be useful for deformation theory? see over here in plus and minus always have automatic analytical continuations so Depending on what you want to do you use one version of Riemann-Hilbert theory or the audience here is a theorem Here's a theorem so suppose F times V minus one belongs to LP and P is less than one and bigger than infinity then M plus M plus plus if solves In the homogeneous Riemann-Hilbert problem of type Okay Of type one if M Let me put it like this Okay. All right, so M plus minus. Let me put it like that Okay, am I saying this correctly? Okay If M plus minus solves the inner homogeneous Riemann-Hilbert problem of type two and LP with F equals F times V minus the identity Conversely If F belongs to L2 F belongs to LP then M plus equals M plus plus F and M minus equals M minus Solves in homogeneous Riemann-Hilbert problem of type two P if This object here solves the inhomogeneous Riemann-Hilbert problem of type one and LP with F equal to C minus of F So the first part is Really very very trivial the thing I want you to pick up from this is the obvious point if you solve the one Riemann-Hilbert problem you solve the other and vice versa I'm going to leave this proof as the full proof as an exercise, but the first the first part is really very trivial as so if M plus minus belongs to LP And M plus Equals M minus V plus F Where F is equal to F times V minus 1 Then this is M minus V Plus F V minus 1 so that means M plus plus F Equals M minus plus F V So if you define this to be little M plus and This here to be little M minus you've got M plus equals M minus times V and M plus minus minus F belongs to the boundary So that's a triviality To go the other way around is strange enough a little bit more subtle Because you can't in general reverse this to go if I know a little F I know capital F, but if I know a capital F, I don't know little F was this might not be in Invertible, so I'll leave it for you to just Check that through Now Okay, now the connection To a normalized Riemann-Hilbert problem is simply the following we say M plus minus Solves the normalized Riemann-Hilbert problem sigma V If it solves the In homogeneous Riemann-Hilbert problem of type 1 and P with F just to be the identity function It's another words. I'm saying that M plus equals M minus times V and M plus equals the identity plus minus plus boundary You notice that with this definition you obviously see that if you take the extension now of You define MZ to be 1 plus C so this means it's equal to Identity plus C plus months of some H, so you just define it to be this Then this function here solves what we called formally a Riemann-Hilbert problem It satisfies this jump condition that goes to the identity as Z goes to infinity In a trivial way So this is the precise meaning of what we define to be Formally a solution of the Riemann-Hilbert problem. All right now Where does this operator come into the picture? There's a very nice and cute Calculation so let F belong to LP and M plus minus Equals F plus C plus minus H and M plus Because M minus times B. So in other words M plus minus solves the inhomogeneous Riemann-Hilbert of type 1 with this function F. So we've got M plus Because M minus times V minus inverse times V plus for any factorization pointwise almost everywhere factorization We define mu to be M plus Times V plus inverse which is also equal to M minus times V minus inverse This is bounded And Now we make this definition H of Z by definition is just C of mu W plus plus W minus So mu is a matrix valued function on the Condole you multiply on the right by this and you take the Cauchy transform of this object now here comes Perhaps the main calculation of the whole theory very simple, but extremely important if I look now at H plus That's going to be C plus of mu W plus plus mu W minus and That's equal to C plus mu W plus Plus C plus mu W minus and now we use the fact that C plus minus C minus is the identity So that means that H plus now it's going to be C plus mu W minus Plus C minus mu W plus plus mu W plus using C plus equals C minus times times that this object now this object is what we called CW mu And then we've got here plus mu W plus That's CW minus the identity mu plus the identity Plus W plus mu Which is C mu minus one mu plus V plus Me and we've got Sorry mu I'm putting it on the wrong side mu V mu now This is what we the CW minus one Mu And this is what we called This is how we defined mu. It's equal to M plus So we've got this Simple calculation, but that's what we get and we get similarly H minus is going to be CW minus one mu Plus M minus H minus So we get that So that means if we look at this combination M plus minus one minus F minus H plus minus that's equal to one minus CW mu Minus F. So the minus F I've added to both sides and I've just put the I've taken this put it on this side Put the one minus C minus on the other side. I've got this identity Now by assumption this object here belongs to the boundary of C and LP and the same thing is true for that So that means that the whole left-hand side belongs to This quantity here. So that means that we have that M plus minus minus F minus H plus minus is equal to C plus minus of some function H But by this relationship, this is independent on the right-hand side of plus or minus So that means that C plus H is equal to C minus H But we know that C plus H minus C minus H is just H So it must be that H is zero Which means that The left-hand side there is zero which implies That one minus CW mu equals F So there you have the fundamental connection between the Riemann-Hilbert problem and a particular singular integral operator equation on the contour. This is the fundamental connection Keep losing this. Now conversely So let me just summarize quickly. We've shown that the inhomogeneous Riemann-Hilbert problem of type 1 is equivalent to knowing how to solve that of type 2 Now we begin to make the connection to this operator 1 minus C is CW And we see that if we can solve the inhomogeneous Riemann-Hilbert problem of type 1 We can solve equations of the form 1 minus CW mu F Now the converse is true that if 1 minus CW mu equals F for some mu belonging to LP F is given then if we define H C mu W plus plus W minus if then if we make this definition we have That H plus minus equals F minus F Plus mu V plus minus Mu is here mu is the solution of this equation before we define mu Over there So if I solve the inhomogeneous Riemann-Hilbert problem of type 1 and I define mu in this way Then that mu Is going to solve this equation Solve an inhomogeneous problem of type 1 or 2 and I get a solution of that equation now If I have a solution of that equation I'm saying I reverse this little calculation here, and I see that this function here H has these properties and if we now set M plus minus to be mu V plus minus We see that M plus Equals M minus times V by the definition of these things and from here we see that M plus minus is equal to F plus the boundary Operator or C plus minus of some function H So if we solve this problem We see we obtain a solution of the inhomogeneous Riemann-Hilbert of type 1 now So Not only are these true algebraically, but they also true and analytically So you see I'm not going to write this fact out. It's obvious That if we solve this problem here And we obtain a solution here Where we've got a bound on M plus minus in terms of the norm of F Okay, so let me just write Write this out Let me call it a theorem that F belonging to P of sigma at M plus minus solve problem of type 1 with P F given M plus minus solve to P With F given by F times V minus the identity then one minus CW inverse on F Is bound by C times M plus minus P one minus CW inverse on F Is bounded by some other constant Plus minus That's F Such a relationship follows very easily from the algebraic facts because mu is expressed in terms of M plus minus So all of this we dealing with three equivalences if you can solve type 1 or type 2 Or you can invert the operator 1 or 1 minus C If anyone of those three three things is known The other two immediately follow their equivalent Now what you see here is they not only algebraic facts But you have these analytical facts which follow directly from the algebra and if I would know for example That the solution of the type 1 problem Was bounded in the natural sense for example of M plus minus NLP is bounded by some constant times norm F Similar thing to that I would know immediately from here that I have an a priori bound


Hello everyone, here is today's video and tonight I decided to play Fifty Nights at Freddy's and for those who never ever heard about this game it is a horrible game I actually expected to put it on the channels of other YouTubers but I never played the game and I really wanted to play it but I am an easy, timid person so I don't know how good this serious movie progress but we will see we will see, start the game so we need help yes, I really don't like the look of this shit ok, let's start the game what happened what? what? so I I can move the view what? do I need to click on something? where is it? so I can control the screen of the camera ok so he said that he wanted to record a message for me he said that he actually worked in this office before and he is in he is working now and he knows that he can be a little timid and I don't even need to say good, good so now he wants to give me a message of the company a message to the pizza of Freddy's it is a pizza so I think that magic and other things are happening what the fuck he just started talking about what happened but he found people moderating in this pizza what the fuck there is wind so I can I can read when I look at it good, good oh, what the fuck I have energy and it seems that it is something after something because it sees ok, good that is a message for the that is a message, good, good I am here and you can see because it sees you in the angle and that's it I don't know if it is a fact that some of the dolls in this restaurant actually have died in the last eight or nine years I think I forgot the date but later they said that it is a surprise that people can experience the fact that the previous part of the episode was a death oh, good, so the dolls If they see you during the night, they want to put you in another cup because they think that you are the intern of the cup and of course that's not a good situation because probably you are very busy Now let's talk about the fact that your eyes are looking at your head simply you have to often say to the camera and confirm that there is a problem So, is there anyone who is close? It seems that not Why can't I see that chamber? What is that? It's nothing, nothing, nothing Oh really? So we have three people in the first chamber I'm just... Oh no, it's not the first one What is that? Is there people?  There are people Isn't there anyone in the chamber? What is that sound?  Oh what? I don't know how to play this game because as I said I saw a few videos about it but really I'm not ready for this Oh what is that?  No, no, no, no Don't use it that much Oh, you have to double click on it What is that? What is that? No, no, I don't like that I totally don't like it Oh fuck, I can't simply do that Is there... Anyone really is there?  What is that sound? It really is there I can see it Why can't I simply do it?   Oh What is that? What is he doing?  Really, really, really Do you want to dance in the big round in the people of the world? What is that sound? I can hear it I can hear it I don't like the sound What is that sound?   What?  They don't move It seems that they can only move when you don't look at them So you have to often look at them But when you look at them you use your energy So you I only have 19% of my energy and it's always I think that I got the night No, that was easy Really the second night I'm not ready for the second night Oh well It's the phone again In fact, where is the phone? I can't see it So he said that if I can hear this message I'll see you in two days Oh well And now he says that the phone is more and more active when the week progresses And he prefers a phone called Freddy and he says that he often comes often goes on the stage I don't know But I think that that black shadow is a cube but it seems that not In fact, I think that it's just a hole in between the tables What is that? I don't know He says that the cube that is in the pirate egg is actually more active So you don't have to worry about that Oh well What is that? Oh hello, how are you?  Oh well, my friend just came Oh well I completely forgot that when I looked at the camera or the screen I used my energy What is that music? I think that I never wanted to go to the party of a child in my whole life after this game Where did you go? Where did you go?   What is that?  I didn't do that There is poop I really don't like this feeling which I have now in my... I almost said cat cat What is that?  Oh good Why did I do that? Why did I do that? I don't sleep I am an Esperantist What is that sound?  Why did I do that? You have to be very careful about a big bullet Really How did I How did I choose to play this game?  Where did the poop go?  I don't know where I can listen to music from this room Where is the pirate? Where is he?  Do you know that I don't like you? Again?


The Navy announced Thursday it is reinstating the enlisted early transition program. According to a new NAV admin, the program allows eligible sailors in targeted ratings to apply for a voluntary early separation up to 24 months prior to the end of their obligated service. Available quotas are identified by rating, pay grade, year group and Navy enlisted classification. For the list of quotas and more information, visit the Navy personnel command website. Military Spouse Appreciation Day is May 9th. We want to say thank you to all the spouses in the fleet serving their country on the home front. Just like service members, military families pack up their lives to go wherever they're needed when the nation calls. The Navy is stronger because of you and your support. You are essential to mission success around the globe. Read more about these stories at Navy.mil. From all hands update, thanks for watching.


Hey, Psych2Goers. Was there a moment that you wish you could forget? Do you wish you could have gone back in time to make a different choice? Regret is a melancholic experience. You might look into your past, play out alternative scenarios, glamorize the ending you longed for, only to return to reality feeling a little depressed.  Number one, living out your parents' expectations instead of your own. Did you give up your dream job for something else? Perhaps you've always wanted to be a musician, an artist, or a park ranger, but gave that up. Living out your parents' expectations is something many people are guilty of. You may be afraid of disappointing your parents so much so that it affects how you approach some of your major decisions that you make in life, such as your career path or who you choose to be with. In letting people's expectations tie you down, you may be silencing the voice at the back of your head that wants to grow another way. While everyone's situations are different, it can be beneficial to set aside some time to truly think about what your goals are regardless of what others want from you. Number two, not asking that person out. You ever have a crush on someone but never got the chance to speak to them? Romance can be a tricky thing to maneuver at a young age. You might feel anxious about the prospect of rejection, so much so that you never end up making the move. According to a survey from an article written by Adrienne R. Camilleri, romance beat out family, education, and career as the most common regret that people face. Number three, overworking. Do you sacrifice a lot of your personal life for your work? While it isn't inherently wrong to work hard, many people do so without thinking about why they do it. Hours spent in the office can detract from the time that could be spent doing the things you love or what the people you love. In fact, according to the book, top five regrets of the dying, working so hard is one of the common regrets that elderly have. Number four, letting friendships fade away. Are you still close with your childhood best friend? Whether it's someone you've known since grade school or someone you just seem to be on the same wavelength as. Everyone has that person who played a large chapter in their lives, but sometimes you might find that you go from hanging out all the time to barely once every few months. It's sad, but losing contact with someone is something that can happen in a snap. And for many older folks, reminiscing about the good old days and looking back at how friendships fell apart can leave us our taste in their memory. Number five, hiding your true feelings. Was there a moment you chose to hide your actual feelings even when you wanted to explode inside? While it might have been easier to keep quiet at the time, being able to get things off your chest can pay off in the long run. When you hide your feelings, you prevent others from forming a genuine connection with you. This can perpetuate a cycle of loneliness and withdrawal that may make you feel worse both mentally and physically in the long run. And number six, not accomplishing enough. Is there something that you've always wanted to do but never got the chance to try? We all have an innate desire to feel accomplished and successful no matter how grand or little it may seem to others. Perhaps you want to learn how to ride a bike or grow a flower garden. Whatever the case, it's always ideal to listen to your heart and fight for the things that you want and believe in. By not pursuing the little or big goals you set for yourself, you're limiting yourself from truly making the most out of your time here. Do you have any regrets? Let us know in the comments below. If you found this video helpful, be sure to like, subscribe, and share this video with those who might benefit from it. And don't forget to hit the notification bell icon to get notified whenever Psych2Go posts a new video. The references and studies used in this video are added in the description below. Thanks so much for watching and we'll see you in the next one.


Hey guys, welcome back to Mill Prep Monday. Today I am making bacon chicken and ranch wraps. So I'm Kristen. I am sister number two out of the six sisters and I love sharing with you my Mill Prep ideas to hopefully make your life a little bit easier and to eat just a little bit healthier. So before I get started on anything, don't forget subscribe to our channel. You'll be able to see our Mill Prep Mondays, our Tip Tuesdays and of my favorite are Food Fridays. So with this chicken bacon and ranch wraps, say that 10 times, bacon, bacon, chicken, ranch. Now these these wraps only take about 10 minutes to throw together and then you have lunch ready for the whole entire week. My favorite tip on making these is grabbing a rotisserie chicken from the grocery store. It makes having chicken on hand so fast and so easy. Alright guys, let's go make these chicken bacon and ranch wraps. So first I'm going to cook my bacon. Now I like to use turkey bacon. You could also use the bacon that's already pre-cooked so you don't even have to worry about this step. But I really like turkey bacon.  It's okay if they touch each other a little bit because they will shrink down. And I'm going to preheat my oven to 400 and then bake it for about 8 to 10 minutes. While it's baking, I'm going to get everything else ready.  Now I've washed this so it's clean. Then I'm going to put two pieces or two lettuce leaves into each bowl.   Now you can use rotisserie chicken. This is the chicken that I had from last week that I had some extra that I already cooked up so it would be so quick and easy, ready to go. Once I'm done chopping, I'm going to split them up into about four equal piles and then just put each pile into two of the leaves of lettuce. Now they don't have to be perfect. Just try and make them as equal as possible. Next I took two tomatoes, chopped off the ends, and then sliced them up to put them on top of my wraps. You could also use cherry tomatoes on this recipe too. Just chop them up pretty small and put them on. They would be delicious. And then just try and evenly distribute them to each lettuce leaf. Alright, my bacon is done cooking. They cooked about 10 minutes because I like them a little bit crispier. And now I'm just going to take one piece of bacon per lettuce and crumble it up a little bit and put it right on. Like I said before, you don't have to use turkey bacon. You could even use bacon bits that you get in the salad aisle. Now when you're ready to eat these, drizzle them with a little bit of ranch dressing. I'm not going to do ranch dressing right now because I don't want them to be all soggy so I'm just going to put the lids on. Or if you're packing lunch for the go, you could grab a little container, fill it full of ranch, and stick it in there too. Need some more help planning healthy meals? Then let us help you by signing up for a healthy menu plan. You can get 20% off your whole entire order by using the code Facebook20. Thank you so much for joining me today. I hope this meal prep has helped you and that you'll be able to eat a little bit healthier this week. And don't forget to subscribe to our channel to check out our meal prep Monday, our tip Tuesday, and our food Friday. Okay guys, see you later.


Okay, so the trade deadline, as you know, is quickly upon us here. And there are some teams that seem to just be stuck. Chicago being one of them, 22 and 25, ninth in the east right now, and we know the rumors. We've talked about them. It's like two seasons now with the Levine and the DeRosin and all that. But they played a little bit better lately. So are we blowing it up? Okay.  Blow it up. Listen, if you're going to let Zach Levine go, free DeMar DeRosin as well. This is, my position is coming from a personal place. I want to see my brother have an opportunity to compete at the highest level in the later years of his career. I don't want to see him be wasted away there with floating around in the eighth or ninth spot. Give DeMar DeRosin an opportunity to compete at a high level. Blow it up. Yeah. And this has been rumored since last year. And the teams haven't done it. They re-signed the contract extension to Billy Dobbins, so they have their coach moving forward. And this is a team where it's not like a young team, like a San Antonio or a building team. This team is poised to win right now and they're not winning. It's not working. No matter what the system is, the offense, the character of the guys, whatever, this hasn't worked. You can get a lot for these guys too. They're talking about you can get two first round picks for Alex Caruso. Imagine what you can get for DeMar DeRosin, for Levine, for Vooch. So they have assets that teams want. Blow it up because they're not competing this year. Okay. That's two right there for blow it up right off the top. How about the Nets next? 19 and 27, they're 10th in the East and there's interest in Dorian Finney-Smith, Spencer Dinwiddie, and McHale Bridges. Send them to the Nets. Blow that up too, I guess. That sound effect you're doing? We'll blow it up more than Chicago. At least Chicago has the guys that can go and surprise a team in a playoff series right now. This team has no chance to win. I love McHale Bridges. I think besides, and Cam Johnson saw it as well. And the best thing for them is that Ben Simmons continues to do it. He did last night. But with that contract, he's got a hold on their situation there. But yeah, guys like Spencer Dinwiddie, Dorian Finney-Smith, these are guys that contenders want, these are guys that contenders can use. They have even more pieces, I think, than Chicago. They're not going to win with everything with Kyrie and KD and James. This team is now in full blown rebuilding mode. Blow it up. Guys will always want to come to New York and create and see. Let me ask you a question. Who do you think the best players on the Brooklyn Nets? Bridges. You think McHale Bridges? Okay. I agree with you. I don't know if we blow it up. I think we refocus. Who do we build this team on?  You keep McHale Bridges. You keep the two cams, and you build from there. And so I think they just need to re-center their attention on some of these younger guys opposed to, I love Spencer Dinwiddie. But I think it's McHale Bridges' team. I love Dorian Finney-Smith. I think you can get something valuable for him. The two cams are still very young. You build around those three pieces and keep moving. And again, they're talking New York. You're always going to be in on free agents. All right. So that's a build it up I heard. All right. We're split on that one. Kind of, sort of. Hawks, Lou. 1927, 11th in the East. And the names in that, of course, are Dijante Murray and Bogdanovich.  This is tough for me. This is tough for me. I want to see this organization be successful like no other. They embraced me at the end of my career. I thought I wasn't going to enjoy my time there. But I ended up loving my experience with the teammates and building with those guys. But I think it's time to blow it up. I think it's time to reset. That group has been together for a number of years now, have had a lot of highs, had a lot of lows. And right now, they're in extreme low in a year that they're supposed to be turning the corner and being more successful. We're two years away, two years out from East of Conference finals appearance. And so for this to be basically the same group, sending 11th in the East, it's not working. Blow it up. And this team isn't that young anymore. You're looking guys like Deandre Hunter, Trey Young, like they've been in the league now for enough time to expect wins and it hasn't translated to that. When you look at this team, they have the talent. They have the guard play. They have Capella and Akungwa. Akungwa. Akungwa. Nailed it. They have the, I love Bogey, too. Like they have Siddiq Bay. And it doesn't make sense to me that this team's not winning games because they have a little bit of everything. So on the blow-up side, I do think... They've changed coaches. Like it's everything. Yeah, they've changed a lot. All the tools are there. It's just not working. So I don't think they have to blow it up per se, but I think they have enough pieces and assets to move two or three of them and still be in an okay place. Who do you move? Yeah. I mean, I think it's the obvious one. He's won. But like, what do they do with Trey Young? Is he their guy still? Yes. They move Trey Young. That's blowing it up. That's, yes. But then you still have the Jalen Johnson, the other players that you don't have to go through this full tank rebuild mode. And what can you get for Trey Young right now? That's kind of interesting to me.  You can't. Are you going to build through the draft and just stack up assets like Oklahoma City did? I think they have so much talent that even if they do decide to trade two of these guys, they're in an okay place. All right. All right. Raptors 16 and 30 this season. Raptors 12th in the East. And of course we already know that Siakam and OG are out. Are they, is this, they're blowing it up in process right now? They already have. Okay. Is that what you're doing? They finished the job. They've got this one guy. His name's Scotty Barnes. Yeah. Everyone else is on the child boom block. So I think they're already in the process of it. They've already moved Siakam. They move OG. They get back assets like RJ Barrett. But this is a team that, again, they're also, they have the talent. So it's not like we're looking at like a Charlotte or a Washington that's just stuck with these horrible contracts, they're not going to win for a long time. They have solid players. So I, when you say blow it up, I don't mean blow it up and go for the number one pick because they're so talented, they're still going to win certain games. But that's almost worse sometimes. Yeah.  So they're kind of a lot of teams in this gray area. The gray area. Six. Yeah. 24 and 24. Well, that's right there. You just stuck a 10th in the West. So they got Jordan Clarkson, Collins Sexton, Laurie Markinen. Do you keep all three?  What do you do here? Is that a tricky one? You know what? I don't know. I don't know. Maybe by the end of my statement, I haven't figured out. But if you're 24 and 24 in the West with so many good teams playing good basketball, that's pretty decent. I don't think they're playing, they're playing under par. I think they're, they're playing pretty decent basketball, considering the circumstances. You've got about six or seven teams in front of you that's supposed to be in front of you with where you are with talent wise and where your, where your group is. And so I don't know if you blow it up. You have a lot of good pieces, but I'm curious to see what they do at the deadline and see if they can get better or get some pieces for, for Collins Sexton or a Laurie Markinen or somebody there. So I don't know if you blow it up. I, I built it. They had that stretch. Last year, if you remember, I had that kind of Orlando. This year, type start where it's like, whoa, what are we doing? I don't even think they realized that was possible or a marketing kind of turns into this household name where he's an all star. So I don't think they blow it up. I think if you can sure go give, go get Jordan Clarkson and go get some things back young to grow at the Walker Kessler's with the Keyonte George. These young asses they have. Sure. But again, now there's a reason we're asking about these teams because they're all stuck in this area where they're not quite good. The Lakers are a 500 team. We're not saying blow it up for the Lakers. This team doesn't have the expectation level that the Lakers do. And they're still right there at 500 as well. So I say you build it. And there's just different, like I think the Lakers no doubt can still win a playoff series. I don't think the Utah Jazz can win a playoff series. That's the difference.  This last one did not see having to ask this in the last several years, but the Warriors 19 and 24, 12th in the West to say they're trying for a fifth ring. Obviously they're trying, but not like this. This has to be blown up. Right. So let's face the facts. They're not going to win a championship with this core anymore.  And that's sad. But this dynasty again, we almost just stop talking about it because it's just not the same. Oh, it's sad. Are they really going to blow it up and trade Clay Thompson and trade Dremel Green? Probably not. So then the question is, who do they get rid of? What can they get back for an Andrew Wiggins? What can they get back for anybody else? I'm trading everybody if I'm them except Kaminga and Steph Curry. Kaminga has now showed me enough where he's a building block for the future. He's versatile. He's so young.  He's keeping him. Everyone else figured it out, but we have to find a way to maximize Steph Curry for the next two or three years. And they can go and get free agents that want to play with Steph Curry for the next two or three years. So again, I think who can they get for those guys? Are they really going to kind of shake up the world and trade Clay Thompson? Like I can't, I just can't see it, but it's probably the best option at this point. I think that's the only option. Wow. I think that's, I think that's the only option at this point. Like I like to compare to Kobe. You know, you have such a successful run with Shaq and that, that group and then years later, it's not going your way. They bring in a pile of salt. They bring in all of these other pieces and give you another opportunity to have a championship run and it worked and it was successful for them. So I think that's the route you go for, for Steph Curry. You give them one more chance. You give them one more hurrah with a completely different group. This is a, this is a, a, one organization. If Clay Thompson or Draymond to where to be moved, I'm sure they'll give them an opportunity to be successful and compete somewhere. End of an era it would be. By the way, Kaminga moving up to the untouchables list. That's something. You know what? I wasn't a big fan. I've watched him play during that time that Draymond Green was out and he can play. He's getting more confident. He's getting, he's so bouncy. He moves without the ball. He plays well. He knows this game. He doesn't take really bad shots. He doesn't take a lot of perimeter jump shots. And he's so young. If that keeps developing, he can turn into something real special. That was almost sincere sounding. That was, that was, I don't know. And there he goes. Oh, we're going to take a quick break. When we come back, which of today's defensive players could slow down prime MJ? Oh, I love these. I love these.


Our next consideration is going to be building and maintaining rapport. The importance of rapport is that within our communicative activities, we're asking the students to talk to each other. If they feel comfortable with each other and with us, then that interaction is much more likely to be useful. So, how do we actually build and maintain rapport? Well, it's easiest if we consider two stages of the course itself. What we can do at the start of the course and what we can do throughout the course to help build and maintain that rapport. So, at the start of the course, it's very useful if we ask the students to create a name card and to make that name card visible to everyone. Secondly, we need to try to do some ice-breaking activities that will allow the students to interact with each other and perhaps give a little bit of information about themselves. Once we move into the course itself, there are a number of techniques that we can use to help maintain that rapport so that students are comfortable with each other when doing communicative activities. So, throughout the course, use pair work as often as possible or indeed small group work that allows for interaction to take place whenever possible. Don't let single students dominate. Thirdly, allowing students to correct each other will often help to maintain the rapport within the class. Perhaps finally here, try to personalize all activities wherever possible. Quite often, you'll be taking activities from coursebooks and if those coursebooks, if you take the activity and white out the names of people given within those activities, substitute those for the names of the people in your class so you have personalized it for your class, then that will help to build and maintain rapport within the class. Our final consideration here then is going to be discipline within the classroom. From your own experiences at school, you will know that some teachers have more discipline problems than others. Now there are no set rules which will work for all situations that you find yourself in, but there are some things that we can do to stop problems rising in the first place. One of the major causes of problems is when students do not respect the teacher and there are some things that we can help to build and maintain that respect from our students. Perhaps of the major things that you should consider, it is very important that you are always seen to be fair, that you are punctual, that you are always well prepared in terms of your materials and activities, that you do not make threats within the classroom and then not carry them out. Also here, it's important that we show respect for our students in all situations. And this can come down to very simple things like when we give homework, we should make sure that we take that homework in and that we mark it promptly and give it back. And finally, one of the major things that we can do to help maintain the respect of our students is to always be enthusiastic. Our final consideration here in terms of discipline is going to be your response to problem behavior. Your responses are actually critical as to whether the problem is going to be increased or decreased. Here's a few simple things to remember in terms of your responses to discipline. Firstly, it's very important that you act immediately before the problem can get worse. Obviously, people's ideas of discipline problems will be different in terms of their severity and so on and so forth, but wherever possible, we should try to use non-verbal techniques first. If, for example, two students are talking to each other while you are talking, then just stop. Look at those people who are talking and it's very unlikely that they're going to continue to do so. So without saying anything using non-verbal techniques, we can avoid this type of behavior. Next, it is very, very important that you always keep calm and that you never shout. From your own experience, you're probably aware that there's very little to be gained by shouting. Make sure also that you keep within the school discipline code. Make yourself aware of what that discipline code actually says so that any responses you have to discipline problems, you're not yourself moving outside the actual discipline code of the school or language center. Perhaps finally here, what we might say is, although it can sometimes be difficult, try wherever possible to use humor to dissipate discipline problems. It would be very nice if we could just give a list of things that you would need to do in order for you to never have any discipline problems in your career, but that list does not exist. Most of your responses to discipline problems will be learned over time. You will find out what works and what does not work. But when you first start, if you keep these sorts of ideas in your mind, then it does mean that discipline problems shouldn't escalate.


Hi everyone and thank you for giving me the opportunity to speak today. I'm Katrin, a Senior Technical Product Manager at Amazon Lab 126. I've been a PM for about eight years now with almost six years in robotics. Before I get into the meaty part of this talk, let me tell you a little bit about myself and my path to launching a consumer robot. I studied media technology at Elmino University of Technology. It's a small university in the middle of Germany. During these studies, I developed a very strong interest in the usefulness and usability of technology. Often when I'm asked, or when I have asked engineers, why are they building something? I got a response similar to the response in Big Bang Theory because we can. To me, this was not really the right reason. So I started doing research and usability engineering and followed through with a dissertation on user experience engineering. During the research, I noticed in order to actually make an impact and to reach the right audience, the thesis needs to be targeted at product managers, not at engineers. And this was my very first touch point with product managers. As part of the thesis, I got to interview highly successful product managers to understand their major challenges and what they would need to define more human-centered products. With their responses, I got more and more interested in that field and decided in order to make an impact myself, I need to become product manager. Hence, I accepted a management trainee position at RobotBarsch in Germany that allowed me to get glimpses of different business units and the overall workings in a relatively large corporation. During this program, I really got fascinating opportunities to manage innovative products from the idea on and I became the product leader for a voice-enabled smart home hub. Also, the program allowed me to come to the amazing Silicon Valley and let me stay here to get kind of my product to an important prototype development stage. I'm not going to go into the details, but this product did not launch as well, a popular voice-enabled smart speaker swiftly gained market dominance. However, this led me to my next adventure and the opportunity to be a product manager for Curry, the adorable home robot, my first chance to work on an autonomously moving character in the home. Curry's value proposition was more emotional, so not utilitarian as its goal was to bridge the gap between people's fears of having robots in their homes to welcoming like a robot companion in their families. Curry's mission was to bring smiles to its family members with moments the robot captured autonomously throughout the day. I'm also not going into the details here either, but this robot didn't launch. It was a pretty hard time for consumer robots. So I went on to my next adventure. To round up my PM experiences, I wanted to finally launch the products of features I'm working on. So I decided to follow an offer from Fetch Robotics to work on intralogistic robots that were already on the market. Although not in the B2C space, so no consumer robots, I was able to collect valuable launch and post launch expertise. And this time, there was no other reason besides Amazon knocked on the door. And basically, without being explicit, asked me to be a PM for a consumer robot. I could not say no as my heart was still wanting to launch a consumer robot so badly. And overall, my professional goal was to launch one of the first home robots that can become a companion. So here I am, the team announced Amazon Astro in September this year. And yeah, this also concludes my journey to finally launching a consumer robot. Enough about me. When I was asked to present at product school, I not only felt honored, but I also wondered what would be of interest for the audience. Unfortunately, I was not able to ask you that question. But I learned that most of you are aspiring PMs, so I'm giving it a shot with the following takeaways for this webinar. From my personal expertise or experience, what are the qualities and skills of a well-rounded consumer robot PM? What is a robot experience? And how do we create a robot experience? And believe me, this takes a village. Before I dive into the qualities and skills of a consumer robot PM, let me briefly define what I mean when I talk about consumer robots. For a consumer robot, the target user is the end user.  The robots I worked on at Fetch Robotics, where the target user is more like a warehouse worker, a very special type of person using the product in a very specific context. Why is this important? Because it is important to understand that the target user well, specifically their needs, goals and limitations, with respect to the robot's context of use. It's also important to understand the target customer, so you know who would be buying your product to keep the business going. In the consumer robot field, this is typically a normal consumer like you and me. If I use the warehouse robot example again, though, the target customer would be the warehouse owner or manager. Also, I already mentioned the context of use earlier, so for the consumer robots I'm referring to, the context of use is more in the home with focus on everyday life. And key features include autonomous mobility, a character AI that learns to become their user's companion and be useful throughout their day. Examples are Curry, to some extent vacuum robots, although they're missing the companion part, however they get the usefulness pretty right, and Astral. Now, since I defined the product category a little bit better, we can talk about the skills needed to be a well-rounded consumer robot PM. And I want to do this on the example of my launching a consumer robot journey. First and foremost, I feel there needs to be the passion and curiosity about consumer robots, user needs and emerging technologies. Secondly, the PM needs to be able to innovate and execute, think about solutions for the needs and problems identified and create a prototype to validate assumptions on need or problem fulfillment. Thirdly, prioritize and communicate. The well-rounded PM is able to make judgment calls on priorities for features and bugs that are typically quite complex with various dependencies and is effectively communicating their strategy, requirements and prioritization to the team, in fact, to various stakeholders. I further learned that it is very important for a PM to not only listen very closely to their users and customers, but also to their stakeholders in order to make the right judgment calls. With that, it is important to empathize with users, customers, partners and other stakeholders such as engineers, sales, marketing and designers. And lastly, this is something that Amazon looks into deeply too when selecting their PMs. The well-rounded consumer robotics PM needs to have strong customer obsession that means decisions will always be made with the best interest of the customer in mind. And of course, we also need very technical, deep technical knowledge in order to be able to dive deep into problems and solutions. And that concludes the qualities and skills of a consumer robotics PM at least based on my personal experience. So let's shift gears a little bit and dive into the more interesting part of this webinar or meaty part. With the title, Creating Robot Experiences That People Love, I hope I was able to get all of you thinking, what does that mean? Specifically, what is a robot experience? Good question. Let's start with what a user experience short UX is. You probably all have heard about UX, but as a refresher, the International Organization of Standardization, ISO, defines UX as a person's perceptions and responses resulting from the use and or anticipated use of a product, system or service. They also note that this includes all the user's emotions, beliefs, preferences, perceptions, physical and psychological responses, even behaviors and accomplishments that occur before, during and after use. It's adding a lot of psychology to it. But also they note it's a consequence of brand image, presentation, functionality, system performance, interactive behavior, assistive capabilities, as well as the user's internal and physical state. But although this captures UX well from a psychological perspective with a focus on the user, it is important to add how the UX is influenced by business needs and technological feasibility, which I find is greatly summarized in this model of ideas, design, thinking methodology, and this is specifically relevant for PMs. In order to create user experiences, PMs need to balance business needs, technological feasibility and user needs. But now how does this translate to robot experience? Well, I'm taking this very well thought through and standardized definition of user experience and personally, so this is not standardized, define robot experience as a person's perception and responses resulting from the interaction with and or anticipated interaction with a robot. So this representation kind of outlines the dynamic nature of UX and also RX, so the robot experience. By creating anticipated experiences, we also influence the momentary experience as emotional reactions are evaluative feelings based on the ability of how the robot is able to meet the expected or anticipated experience. Furthermore, this evaluative feeling needs, feeds the reflective experience, post interaction and influences future interactions with the robot, which again feeds the anticipated experience of future interaction. So all of these aspects deserve their own presentation and definitely deeper consideration, which I don't have a lot of time for, but let me spend a few seconds to briefly speak about each of the aspects. So need fulfillment and feature promise are influenced by brand, system, properties, user characteristics and context parameters. They form the motivation to use the robot while interacting with it. Users are perceiving functional and non-functional characteristics of the robot, novelty, value, as well as obstacles in control. And this perception leads to measurable emotional reactions specifically like balance and arousal in the short term, as well as mood and sentiment in the long term. And I'm pointing this out as measuring the RX is important to validate your RX assumptions. And with this, I want to conclude discussing the definition of RX. It is important to understand what defines it in order to not only measure it correctly, but more importantly, in order to create it. So that leads us to how do we create such robot experiences? It was mentioned before, if you remember, but they are more central to an experience than previously pointed out, psychological needs. I'm truly convinced that this is the basis and key to creating experiences. And my theory is backed by a popular group of psychologists called Sheldon et al. who argue that fulfilling psychological needs leads to positive experiences. After various experiments on which needs actually create positive experiences, they boil down the list to a bit more of a handful of key needs. Autonomy, independence, competence, effectiveness, relatedness, belongingness, self-esteem, self-respect, security control and pleasure stimulation. This list already provides a pretty good framework to think through and should also overall provide a basis for you as a PM to operationalize those needs for your specific product robotic area and target user group. I'm not going to go into those details, but rather provide examples of robot features that help to fulfill those specific needs. So example for autonomy, independence, voice interaction, or the variety of responses and content, the need for competence, effectiveness can be fulfilled with a feature like find my keys like an IoT integration or in general intelligent mobility, so the ability of the robot to autonomously move around. The need for relatedness, belongingness can be fulfilled in many different ways. For instance, two-way talk when you're utilizing the robot, but also maybe a companion app with it. Staying nearby, which is more kind of the robot person direct relationship while the robot is staying close to a person or the character in order to improve building that relationship. So I suspect you're getting the idea. I'm not going. I'm not reading what is on that slide, but I hope that these examples can give you a good first step into thinking about the psychological needs and how they can translate into robot features. Although this is a great framework to have as a basis to creating experiences, it doesn't get us to an experience yet. So what do we need to know or to do to create robot experiences? And I'm looking through the experience driven PM lens here and now we'll bombard you with this flow. I call this the IREEP, the iterative robot experience engineering process. There with me, we will go through it step by step. And you will see a lot of the steps are likely familiar to you. I simply want to make sure that I provide you an applicable flow that incorporates all the previous learnings. So you will be able to create great robot experiences that make people's life better in the not so far future. Let's start with envisioning the robot experience, the very first step. Goal of this step is to scope and identify our X criteria that are known typically based on evidence as such as user research or thought to be drivers for your specific robot. In this step, it is important to define a visionary goal. That means defining a long-term vision, including a time frame that explains why the robot is supporting people in the future. Typically, that vision is based on fulfilling those earlier mentioned psychological needs and defining this visionary goal helps to communicate the product's conceptual idea and provides the starting point for building a roadmap for product development. So very important.  You decide on a strategy that is either market driven or market driving. And I'm sure you know all about that already. So I won't go into those details just so you kind of find it in the right step within the process. So based on your vision and strategy, you start defining your requirements. In order to do so, you need to have a clear criteria or in general clear criteria for greatness or great experience. Those also help to provide metrics for our X evaluations and to understand users' personal goals. Understanding personal goals help you to define use cases, write your user stories and to prioritize your features. And you guessed it, a general context for these goals are provided by the needs you have identified to fulfill with your robot. Let's dive deeper into specifying your RX requirements. So the goal of this step is to specify the perceived usability and attractiveness of the robot by breaking down the high level psychological needs into kind of neat items and then relating them to actual product features. The general result of specifying that RX is a clear understanding of that usability of the desired product that you incorporate into very first design drafts. And this, on the other hand, builds the basis for implementing the RX and therefore for the concept, prototype or product to be evaluated. So implementing the RX is a fun one that I personally leave to the engineers. At least this is not a very typical PM task. However, as a PM, you want to work extremely closely with your engineers and your designers, and you want to help your partners, your engineering and designer partners, to prioritize features, triage bugs, maybe revisit the customer experience or the flow in order for the features to be truly usable and desirable to use. On we go. Now, since we have some sort of a design concept, prototype or product, we need to evaluate whether our planned RX, in fact, creates these experience by collecting user feedback regarding the anticipated and or actual experience. Starting early, such as evaluating rough prototypes and mockups of potential designs will help obtain a deeper understanding of your user needs and provide initial feedback on those design concepts. Results of evaluating the RX affects about how the concept, prototype or product is able to fulfill the specified needs as well as the overall visionary goal. They provide further indications to improve the refined, defined RX. In that case, PMs go back, revisiting their requirements and specifications. So this is back into the loop. But if findings reveal that need fulfillment is similar to what is planned, the iterations will end. And that is it. Although this was rather high level, I hope you were able to take away an overall framework on what defines a robot experience and how to create the experience. With that, I really thank you for your patience and I'm curious to hear or read from you any questions and comments you may have. Thank you.