Welcome, everyone. We're going to get started in just a minute. Just waiting for SLP to log on. Well, goodness, it's five o'clock. This is Watch Me Work. I'm SLP. Title Watch Me Work, the me in the title refers to you. And this is where we hang out and allow you to get some work done and allow you to ask me questions about your creative process. That's all we do. I was just thinking, maybe I need to tell people what this is all about. We've been doing this show for about 12 years. We started in the lobby of the public theater where we do it live, rain or shine, come crowds or come not so big crowds. And we moved on to Zoom during the first days of the pandemic where we did it days and days and days in a row. And now we're once a week again. So here we are. What we do is we work for 20 minutes by the timer. And then we all work together silently with our mutes on. And then I invite you to ask me questions about your creative process. And if you should have a question about your creative process after the allotted work time, Lolly will tell you how to get in touch. Thank you. Yeah. So if you have a question, if you're in Zoom with us, you can ask questions by clicking on the raise your hand button, which should be in either the reactions or participants tab, likely on the bottom of your screen if you're on a laptop. If you have any trouble finding it, you can send me a message in the private chat and I will do my best to help you. If you're watching the stream with us on HowlRound, feel free to send us your questions via the public theater's Twitter or Instagram accounts or via Watch Me Works Twitter account, which is at Watch Me Work SLP with the hashtag HowlRound. That's hashtag H-O-W-L-R-O-U-N-D. So that's how you ask a question. All right. And before we get started, we will of course say thank you to the public theater and HowlRound for making this universe possible. That's right, Mo. Hands in the air. And so here we go. All right. All right. Okay. Okay. All right. Okay. Any questions? Raise your hand. Okay. Looks like Nancy has a question. Hi. Hello, everyone. Hello. So I had an experience. I went to some place and had an experience and I tried to get interest from websites, publications for a little article about it because it's about conservation and animals and stuff. And nobody was interested. But then I heard from this guy who used to write for the New York Times, and I'm not a journalist, but he did, that he got paid by ARP very well to write a piece. So I wrote to them and they said, nah, we're not interested in wolves, but we'll read it. And I made, I don't know if it was a mistake, but I wrote it with this idea, which is not ages, but I kind of used the theme of the extinction of wolves and the extinction of youth and how puzzling that is and why it drew me to go to this event. And it wasn't normally as poetic as I would like to then, but I tried to and I don't read ARP, but I figured, you know, and that it could be, this would be a good spot for people to go because you don't have to only sleep on the ground one night. It's not a big heavy camping thing. And she came back to me with a big huge no. So I just want to know in the future going forward, should one ever write with the idea of what other people would, well, you know what I'm saying, or just write it and then see where it lands because it felt even more undignified being refused by them. And I'm also so protective of the wolves, then if I had just written it and cast it out in a net and seen if anybody was interested. Right. So let me see if I understand you correctly.  No, I tried, I first I asked if anybody I made inquiry and I got no response. This one person did respond and say we're not interested in conservation. I said, well, my writing isn't like that. But then I wrote it with this leaning towards ARP ARP ARP ARP, not ARP ARP ARP is aging, you know, that society for aging where they have all these discounts and things. I'm sorry, the only one here who gets letters from ARP American Association of Aging. Oh, cool. Okay. Okay. So you so you thought, well, if I if I kind of am considerate of my audience, since it is an article that I'm pitching to them, is that a bad thing? I don't think it's a bad thing. I don't think it's a bad, I don't think it's a bad thing at all. Nancy, I think it was really smart to go on being considerate of my audience because it is after all the article that I am sort of going to, you know, angle in that direction. Is that correct? Is that what you did? Yeah. And I, you know, I would have wanted to talk about death a lot more because I think we as a culture never talk about death. And, and that's certainly part of why they have conservation to keep right creatures from dying. But I sort of danced around it because a friend who read looked at my my typos and things said, Oh, you know what I mentioned that? Oh, I mean, of course it's for people who are retiring who are closer to death. Why not mention it? But yeah, I just feel like I cheated myself and and was dishonest in that process.  But the last time I remember you talked, you said you didn't have a team.  So I'm, I'm going to, I'm going to take take things away from Nancy. Let's see.  Now, what I would say is keep sending it out though. I mean, if you only send it to ARF or whatever, right? I mean, it sounds like it would fit really well with you. Have you ever heard of tricycle magazine, tricycle magazine? Sure. Okay. And parabola.  I mean, you know, maybe do send it to more magazines that are actually might be truly interested in, in your, your wonderful work, you know, the only thing wrong that you can possibly do is to stop sending it out there. My hero, that's very good. Yeah. Yeah. I mean, I didn't come to the team to ask them last week because I was on, I went into the howl round and I couldn't get in. I could somehow couldn't figure out how to ask a question. So in future, I will ask before. Thank you. But nobody, but yeah, keep sending it out there. And yeah.  I mean, yeah, that's, that's not a bad thing. It's just, it's, it's an art. Yeah. Yeah. I don't think it's bad. Okay. Yeah. Thank you. Yeah, sure. Sure. Hope looks like Emma has a question. Hey, Emma. Hey, how's it going? Wow. How are you? Good. Thank you. Well, I first wanted to say thank you for the answer that you gave to my question, like a couple of weeks ago, because I've decided that I should have characters who want things in my plays. That feels more interesting. I'm glad. Yeah. But my question for today is, how do you decide for like any given piece of something, like what the scope should be?  And now I'm writing the third draft. And I thought that I knew kind of what it was. But then I just randomly was like, I need to add six more characters. And it's like the rest of the play was like kind of like big and surreal and weird. And now I'm adding this like six character thing that's more naturalistic. And it feels like maybe it should just be an entirely different play. But I don't really want it to be. And I'm like, I could there is like a way to make it work. But at what point do I say like, I can't keep adding elements to this or like it could just be like this ever expanding thing that has like a million different scenes and different universes. And but I don't I don't know like when to cut it off and say like, I'll save these ideas for another play. So why are you adding the six additional characters? I just felt compelled to I like, what do you mean? Talk to me compelled like, like, like I don't really I'm kind of not feeling what I'm writing. And so what is it compulsory? What does it come from? So the play as it was before, it was like all of the characters are kind of these like big archetypes, like these like exaggerated cartoonish kind of characters. And someone told me like it felt kind of brektian, which was not like it was interesting, but not exactly what I was going for. Like I wanted kind of more of like an emotional core to it. And then also I was like, I feel like having teenage girls in here would be an interesting way to explore sexuality. And so I really wanted to just put some teenage girls in there who are having like really kind of normal honest conversations about sex. Like it made like the it like made sense as I was doing it. But now it feels like I don't know when to stop adding things. Right. I hear you. I hear you. So what if what if you took the six characters out, including the teenage girls gave the teenage girls their own play, you know, and really look at the the initial play you're working on writing and get it to be what you want it to be. Yeah. Do the work.  And they kind of all over the place. So I'm gonna date someone else while I'm dating them. Right. I mean, you never know. Right. And they're dating like seven. Right. It feels like that they're dating like seven or eight people and that might be all fine and well. But at the end of the day, you just get exhausted and you don't really get your work done. Right. So instead of just going, I'm going to focus on this one relationship that I have. And I'm going to see if I can, if there's something there, you know, Brechtian someone saying is Brechtian. In my experience of the plays of Verta Brecht, they're very emotional. I don't know what they've seen, but I've seen, you know, mother courage when the death, when the deaf daughter is beating her drum on the roof and it's like, Oh my God, it's absolutely beautiful. I mean, great scene. They're beautiful scenes in his plays. Maybe they've seen really intellectualized versions of those plays, but they're great plays. So if you want more emotion in your plays, don't like, look, here's a whole another six characters and they're emotional, you know, right? I mean, that's like having like an affair when you really don't need to have an affair. You just need to focus on your partner and go, how can we work this out? Right.  But, but so look at your characters from your original, from your first, from that first play you're talking about, how can we make it more emotional or whatever you want? How can we make it more, you know? Yeah. And then draw a circle around the teenage girl play and give them their own play. Okay. Right. And then the other ones are they all, all the extra people are teenage girls. Are there the six characters are all teenage girls? Yeah. All the extras are teenage girls. Give them their own play. Okay. What's their own play? Okay.  I mean, right? Yeah. Thank you. Yeah. That's a great question. Thank you. Thank you. Thank you. Who's next? Thank you so much, Emma. It looks like Kimmy D is up. Hi. Hi. Hi, everybody. Hi. Thank you for taking the question. Thanks for being here. I didn't have a question till Emma the question. So thanks, Emma. I have been working on this play of mine for quite a while and I thought it was done. It is called Waste Management. It's because, you know, New Jersey, what else would a Jersey girl call her play, right?  It's a very dark comedy. She's in on stage. You're frozen. Looks like you're freezing a little bit. Sorry. I think you're back. Hello. You're frozen, Kimmy, I think. I can hear you.  You're very still. Oh, you're going to hear me cursing? Good.  That might help. Oh, you're back. I think you're back. I think. No. No. Maybe turn your camera. Am I back if I'm moving? Yes, you're moving, but maybe. Okay. There you go.  Can you hear me now? Yeah. Yeah, perfect. Perfect. Okay. So it's called Waste Management and the protagonist is on the stage and there's other characters on the stage, but they're really, they are her pedophile, the childhood imaginary friends that she had growing up, and reflection, which is an actor behind a frame, and that's her talking to herself through the mirror.  And I spoke to a person who's a very, you know, famous comic and writer and he says, but you've never had that issue, have you? I said, no, I've never even been drunk. He goes, so you went through all this trauma without chemical assistance. And I said, yes. And he goes, that's a way more interesting story. And that's way, every, like the other side has already been done. And since it's not authentic to you, how did you survive all of this? So now I'm in a panic, as a writer usually does. Because why not, why not panic? It's not like I have a deadline or anything, I self-inflicted wounds. So I was just wondering if I should get a dramaturg. But I don't know where else to go. I don't know what to do. And I don't even really know if this is a question. I'm just kind of floundering. Thanks a lot, Emma. So your question is, should you get a dramaturg? Yes, I think so. Something I don't, I don't know where to go or how to flush out. How I actually did survive this trauma without chemicals, even though I did it. I don't know if this makes any sense. Yeah, it does make sense. I tell you, there are two things going on here, Kimmy. There's you and there's your play. Yes. We're talking about your play. Okay. Yes. This is your work we're talking about. Yes. While your life is very important and everybody's lives here are very important, I'm going to talk to you about your work. Thank you. So what you have gone through as a person is very important. And, you know, how you got through, what you got through, how you got through it is a very important question. But I am not in any way equipped to answer and work you through, help you through those questions. Okay. Just so let's be, let's be clear. I didn't want to help with that. I was just trying to, how's my character going to get through it without, like, I don't even know how to, use my life as a tool to help my character. Like I said, I want to talk about your work. Yes. Sorry. No, no, no. It's okay. I just, I just don't want to, don't want anybody to assume or think that I am presenting myself as a psychologist or anything like that. I'm totally not. So we can talk about your play though. And we can talk about what you might need to work on your play. Yes, please. And maybe a dramaturge would be helpful. Maybe a group of actors would be helpful. I think what's the most important thing that would be helpful is to keep the focus on your work when you're talking to, when you say gather a group of actors, what you need, the main character and then three other characters. Is that, is that right? It's how many characters in the play? The protagonist, the pedophile, her reflection, and then two imaginary friends. And there are like two other auxiliary characters, but they could just be doubled up by whomever is already there. So what do you, how many actors would you need if you had five? Okay, great. So they don't even need to be actors. They can be friends. You can have five friends. Actors might be better though, because then again, it would keep the focus on your work, not on your personal stuff. And we all have personal stuff that we're going through, but I feel like it's best when we're working on our work to focus on the work. You see what I'm saying? Yeah, if you, if you hired or gathered together, five actors, right, and a director, and perhaps a dramaturg or a director who could also do dramaturgy, do a double duty there, and gathered them together, perhaps hired them in some fashion or offered trades or offered a potluck or whatever, had them over to your house or had them over on zoom and asked them to read through your play and talk with you about it as a play. Okay, that could be very helpful. Okay. And how does one go about getting a dramaturg? Where would I find? No, I'm talking about actors and a director. I think actors and a director is probably a good idea. Okay. Because actors in their brilliance can help you with dramaturgical questions. I think the point of, I didn't go through it in real life.  I'm not sure that that's a really valid argument. I appreciate that because again, Brecht was not a mother, and he wrote mother courage. Shakespeare might have been a king, but he certainly wasn't all of them kings. Right? So we have to just be, you know, be, be conscious, like we need to keep our eyes on the work. Okay. And when the personal starts coming in, if it's helpful, great. If it's not, let's set it aside and allow it its own time to be discussed and work through with the professionals that are specific to that challenge. I so appreciate that because it's really been banging around in my head. And I don't typically like to talk about, you know, what I went through. It was, it was more of, I see how so many of us have all these characters in our head that are banging around, trying to make sense out of things. And I guess I was trying to, it was more an exercise in, in describing the inner turmoil that we go through and use dark humor as a way to cope. Sounds great. Sounds great. But I think, do you, do you know how to get in touch with five actors or is there some, you know, get, you need to have actors? Okay, great. Yes, thank you. And so, and a person who can serve as the director slash dramaturge. Yes. Give your play a reading and then talk about it as a piece of theater. Okay. Okay. Yes, thank you so much. You're welcome. Love you mean it. Thank you. Thank you. Thanks, Kimmy. Lou, you're up next. Hi. Hey, how you doing? I'm good. I'm good. It's great to see you. Thank you so much. This is really, I'm going to keep it short. This is an appreciation post I want to share with you and the group because a piece I've been working on as an essay in this room for a couple of years was published this week. And I don't know the protocol, but I'd love to share it and pop it in the chat. But it's an essay about my mom, which has she's shown up here a few times and my relationship to her. And it's in a dream place that I've been wanting to be published for a really long time. And I've been working on it probably as long as I've been in these rooms. And I have other projects and longer projects, which we've talked about, but this is out in the world. And I have it to thank everybody here. And especially US LP for the space and the support and the navigation that made this really personal story be something that a place wanted to publish and put in the world. And I'm just really proud of it. So it's not the normal question and answer, but I wanted to just say that because I feel a deep appreciation for you and everybody. We're doing a dance. Yeah, girl. Fantastic. We're so proud of you. Thank you. Fantastic. Yeah. And it's like we I've brought questions here about, you know, should I care about the marketplace and what people think. And let me tell you, like I've really drunk the Kool-Aid on. I don't care. I just want to make things I believe in, but I'd be lying if I didn't tell you that it felt really good to have some outside, you know, that on the back. So I'll take it and keep working. But I'll drop it in the chat, but it's just, it's just appreciation. Thank you so much. Thank you so much. Congratulations. Thank you. Yeah. Deaf drop it in the chat. Thank you. All right. Melania. Hello, Susan Lurie. Hello, everybody. Hey, Melania. How are you? Fine. I would like, I am listening to all of this and I think that I have some answers, but I would like to hear from you. There was a person this last week that, you know, that I do my work and show up and I did my best. And it's a person that I love a lot and told me that what I am doing is a hobby. Like it's a hobby. And yes. And I don't know why, but it got to me like very deeply. And I tried to say no, but they don't pay you. So it's a hobby. And there was this. And I, I try not to enter into the conversation because I could feel that I was feeling very badly inside myself. So I put the stop. I don't want to have this conversation, but there is something inside of me that is still, you know, ruminating them these words. And I would love to hear from you. What do you think about this? Because I, I show up to my work and I do it. I know girl. No, go ahead. You go. Go. Yes. And I do it with all my heart. And I know that money in this society that we live in, it's important because, you know, it's a necessity. But to me, it's not that if I receive the money, it's going to be more important or less important. This is my heart. And I am really like breathing through my words, you know, it's something that I need to do that I love to do. And I am learning how to show up to it without being a cruel judge on myself, you know. And this space is being so important to me, your thoughts, your kindness, all the community here. And when this happened, it was tough. And it hurt me. So I would like to know what, what are your thoughts?  I'm just into, you know, become a playwright. I make up things, you know what I'm saying.  Okay. Your job is to say what you know to be true, right? What you know to be true. And if you can't remember everything, we'll remind you of some things. When I did watch, we worked for like, what, 12 years, 13 years, whatever, I was in the lobby of the public theater. And girl, you would tweet your questions in. We didn't even know what you looked like. You were some person named Melania. We got a lot of mileage out of that name. We were joking with you. You were there every single week. You were one of the people who was there every single week you were working. You were asking some really amazing questions. You were reaching some beautiful milestones. Okay. You, you were one of those people. Okay. And those of you who were there too, like Crystal and Jim and other folks, right? You know, Melania was, was always showing up. That's number, that's one of the things you can remind yourself, right? The other thing is, and this is kind of might be sound religious. I don't care. They ain't on the throne. They ain't on the throne. Okay. Do you understand your gift comes from the higher power and whoever said that to you is not the higher power. Thank you very much. They're not on the throne.  And with great devotion, right?  Okay. And I just say to myself, you are not on the throne. Okay. God is on the throne. You ain't that they are not the source of your power. They are not the source of your beauty.   And I know and if you love them, okay, I'm not, I'm not diminishing that. I'm not discounting them.  They, they are not on the throne. Okay. Okay. Thank you. Not and a hobby. What I mean, I don't even know because somebody looked that up in the dictionary online.    You know what I mean? Oh, you're not important. You're not one of the important. Yes, you are. You're important.   Am I right? Yeah, three, three. Whoa. Okay. Okay. I got one child and girl, let me tell you how I get my work done with one child. I don't know a crystal laugh and Chris has got children, right? Those of us who have other people, whether they're children or parents or whomever of spouses to take care of, we know how hard it is to get our work done. When we have children, especially children, you got three kids and you get your work done.  You know, bless the heart, bless them. Just, you know, goodbye. Oh, but also know that you're, you're, you're in, you're in good company. There are people who say mean things to those of us who, who shine brightly, my sister.  I thank God for you. You are. Well, thank God for you. Thank God for you. Okay. Yes. Yes. When we will continue to be blessings to each other, that's what we're meant for. Amen. Yes. I know. Amen. That's right. That's right. Okay. And whatever, you know, spiritual, higher power percent thing you believe in is all welcome. All deities are welcome here. Yes. Yes. Definitely. Okay. Yes. Yes. I thank God for you. Likewise. Likewise.  And this is what you're saying to me now. It's like a hug. You know, I needed it. I needed it. So thank you. Thank you. Thank you. Remember when Chris, Chris, I remember when you were going to a reading and he said, how do I show up as a professional? And we said, maybe show up as an amateur. Show up as someone who does it for love. What? A professional like a hooker? Right? I mean, I'm an amateur. I do it for love. I don't do this for money. I do this for money. You know what I'm saying? Right? Especially these days. I mean, these days, gee, things are so, you know, turn on any news channel. They're so unkind. You know, the least we can do is like, give a little bit more love to each other. Right? You might have to love that person from a distance, Melania. I'm just, you know, I got people in my life that I go, I love you, but I'm gonna love you from a distance because, you know, they can't help it. Yes. Boundaries. No boundaries. Yes, ma'am. Yes, ma'am. That's what I'm talking about. Yeah. Thank you so much, Melania. It looks like we have a few more questions from the Adams family. How you doing? Good to see you. It is so good to see you. At least life has been kicking my butt. Let's just see.  And it's, it's just, it's just a very crazy time right now. But I've been trying to like, you know, push my short film. That was the thing I was supposed to try to film this summer. It didn't work out because I didn't have enough funding. And then I met someone who was very interested and is still very interested in pushing this, this film. And yeah, the thing was, you know, we had met up a second on Saturday. It was and one of the things this person said was that like that threw me off. That was kind of like, Oh gosh, this is going to be a deal breaker. Was that, you know, the consumer or whoever's interested in buying this film or paying or paying giving to this film, it's going to want to see either violence or sex. And I was like, what? Like, you know, because it takes place in Paris and it takes place in New York. And it's like, Paris, what do you think Paris is? It's love. It's romance. It's sex. It's this. It's that. And I was like, yeah, but that's not where the story is. That's not what I wrote, you know?  Basically, it won't sell if that's not in there. And I, and I, and I was like, well, I need to, I need to digest this and kind of think through this. And I'm stubborn and I know I'm hardheaded. I know I'm hardheaded. I'm not going to put that in there because it doesn't make sense because there's not enough of a relationship between either of the characters for that to happen, because it's, it doesn't, just the way the story is, it doesn't make sense, right? But I kind of second guessed my story and was like, is there enough going on? Is it interesting enough? Do I need to create more conflict? Do I need to ramp up something to make it more over? Like, like, do I need to, like, oh, I felt like I needed to overcompensate for what I have already.  And it just, it just, it kind of took me down a notch with like, all the work, I've been working on trying to get this film like a lot along a while. And like, I've been putting my heart and soul into it. It's, you know, what I've been putting all my energy in because I really want to make this film. And it just, it just, it just, like Melania, I kind of just hit home a little bit because it was like, you're telling me that my, you know, no one's going to want to see this unless I put it, unless I make it some kind of commercialized, you know, stereotypical view of what people want to see. But I'm, I'm like, but I, when I first wrote this, I was like, but what I have is, I thought it was good. I thought it was good, you know. What's great, Crystal, is that you're, you're sticking to what you know is right. And at the same time, you're trying to hear the note underneath the note, which is really a mark of real artistic maturity, I think.  Paris and New York, and that's all Paris and New York are about sex and violence. Well, geez, okay, okay. Well, that's kind of, that's a limited worldview. And for you to look at the work and go, but maybe there's something I am missing in the story. Maybe, maybe, you know what I mean? Then it could either, it could go either way, maybe you're missing something or maybe you're not, maybe that's not the right producer. You know, maybe that's not the right producer.  So you met with this person on Saturday, you said? Yeah, like, that was the first time I met them, but yeah. But we've been in communication often. Because, because I wonder if, why don't you read the script over and ask yourself, is there another beat? Is there something I'm missing from this that could be there that's not sex or violence? Maybe there's just that, as they say, you know, producers use all kinds of language, a tightening of the news, just to tighten things up a little bit. Is there a thickening of the story that I might be missing? Is there a more, is there something that can make it more intense? You know what I mean? So they're not, are this, are, to put it differently, are the stakes high enough?  Do you know what I mean when I say that? Yeah. Ask yourself, yeah, ask yourself that question. Am I, am I coming in to the story at the right point?  Or am I coming into early and then it's a long ramp up to the story and then it kind of just makes a little bit of a hill. Right? If I came in a little later and made it more intense, is there something I can do to intensify the story? Okay. You know what I mean? Yeah. Are the people agreeing in every scene? Okay. Are the wants, the characters' desires focused enough? Are they really going for what they want? You know, use them as favorite thing to focus on what the characters want. Right. You know what I mean? Are the characters really going for what they want, like 150% or are they going like 30%? You know what I'm saying? Yeah.  So there's a note underneath that note that maybe the script isn't yet intense enough. So you can, that's what we do all the time as artists. We take a really, a note that's not so helpful and we listen to what we translate it into something that might be much more helpful to us. Okay. Yeah. Okay. I can do that. But listen to your gut. No sex scene, no violence scene. But maybe there's something else. Maybe you need to amp the whole story up. Okay. Okay. Yeah. And don't get discouraged. Those aren't necessarily bad notes. They're just not helpful. I agree. Yeah. Yeah. Okay. This is very helpful. Thank you. Okay. Oh, it's 604. We're just a little bit over time, but thank you so much, everyone. Another wonderful discussion, as always. I will see you same time, same place next week. Thank you. Thank you. Have a great week. Bye.


Okay, okay, so this lecture will be about the notion of stability which has already been mentioned here by Blam in the first lecture which is also slightly related to Blam lecture, so it's based on a joint work with nothing linear, and we'll start with a rather informal definition of what is stability and a motivation for this notion. So here's the informal definition, we say that an instance is stable if an instance for an optimization problem is stable if the point where the optimum is obtained does not change upon a small perturbation. In other words, if we move the instance a bit, the configuration for which the optimum is obtained does not change at all. And our main question of interest is the following question. Are there efficient algorithm for NP-hard optimization problems that correctly solve all sufficiently stable instances? Okay, so there are many reasons to study stable instances, and maybe the most convincing one is clustering problem, so we will consider clustering problems of the following kind. The input is a set of objects which we denote by x and a dissimilarity function d such that d of x, y is the distance or the dissimilarity between the object x and the object y. And we do not assume that d is a metric or any other restriction on d. And the output is an optimal clustering in some sense when a clustering is considered good if a similar object or closed object are classified into the same cluster. For example, we wish to find a cut, a partition of x into two sets s and its complement that maximizes the sum of distances between points that are classified into opposite sides of the cuts. Okay, so for these problems we can now define precisely what we mean by stability. So we say that an instance is stable if the point where the optimum is obtained does not change upon a small perturbation. So the first step will be to define what is a perturbation. So we say that an instant xd tag is a gamma perturbation of another instance xd if for every pair of points xy, d tag of xy is between one over the square root of gamma times dxy to the square root of gamma times dxy. That is if we get an object xd in order to generate a gamma perturbation of it, we are allowed to multiply each entry dxy by a number between one and gamma. Okay, so now we can define what is a stable instance and we say that an instance xd is gamma stable if its optimal clustering is the same as the optimal clustering of all of its gamma perturbation. Okay, so why are we interested so much in stable instances? So our main claim, maybe slightly exaggerated, is that clustering problems we are only interested in stable instances. And I'll try to justify this claim. Well, the first reason is that in clustering problem we are interested in instances where there is a clustering that is evidently a correct clustering. That is evident that it is really a partition of the data into two sets that each set have something is common. And this evidence is captured among other things by stability. That is if we move the points a bit, the optimal clustering should not be changed. So this is the main reason why we think that for clustering problem we are only interested in stable instances. And another reason is that we are not given the actual dissimilarity function because they might not be a dissimilarity function or maybe it is hard to measure it. So the real dissimilarity function is a perturbation of the dissimilarity function we obtain. And we are interested in cases where the solution of the instance we obtain is the same as the real perturbed instance. Okay, so hopefully I motivated you enough to study stable instances. And in the next part of the talk we will see some results and proof techniques obtained for this notion. So we will start with result of about k-mediums, k-means and k-clusters and other center-based clustering problems. And we will focus on k-mediums for simplicity but a similar result also for k-means. Okay, so here the input is endpoint metric space xd and I emphasize that now we do assume that d is a metric. And the output is a set of k-centers, c1 to ck that might be in x and might be in some ambient space that minimizes the sum of distances between each point in x to its center. Where the center of the point is the point in c that is closest to this point. Okay, so here we have a nice result by a watchtree, Blum and Sheffet claiming that there is an efficient algorithm for free stable instances for k-medium. It's also true for k-means and I'll try to describe a sketch of the proof. So the first step is to show that free stability entails that every point is three times closer to its own center than to the other centers. And using this property it is possible to show that the single linkage process plus some processing entails the optimal solution of k-medium where a single linkage process is the following process. We start with n-clusters each containing a single point and at each step we merge the two closest clusters where the distance between two clusters is the minimal distance between two points, the first in the first cluster and the second in the other cluster. So again we start with n-cluster at each step we merge the two clusters and at the end we finish after n-1 steps with one cluster containing all the space. So using the first property it can be shown that every cluster in the optimal solution for k-medium is obtained as a cluster in one of these steps and using some dynamic programming it can be shown that the optimal clustering can be extracted. Okay, so our next result is about metric max cut. So here again the input is an endpoint metric space Xd and the output is a cut, a partition of X into two sets S and its complement that maximizes the sum of distances between pairs of points that are classified into opposite sides of the cut. So here we have a rather strong theorem claiming the following that for every epsilon greater than zero there is an efficient algorithm that correctly solves all one plus epsilon stable instances for metric max cut and this is in some sense the best we can hope for because this problem is NP out so we know that one stable instances cannot be solved. I mean every instance is one stable and we know that we can solve these instances so this result is optimal in some sense and I'll describe its proof which is rather simple. We start by sampling log n points X1 to XL according to some distribution not the uniform distribution and then we show that with high probability there is a partition of the sample point into two sets A and its complement that induces the optimal cut where the cut induced by the partition A and its complement is the following cut on one side we put all the points that are on average closer to A and on the other side we put all the points that are on average closer to the complement of A and we show that with high probability the optimal cut is of this form and since we have only sampled log n points we can iterate over all the cut of this kind and find the optimal one. So this proves the theorem. Okay so we are almost finished. In the last slide I'll talk about future work we intend to do and we intend to work on max cut in general not the metric version that I mentioned before so far we have assumed rather strong restriction on the dissimilarity function D specifically we assume that D is a metric. It is enough to assume that D is a lift sheet but we can't throw away this assumption and without this restriction we need n of a log n stability to design efficient algorithm for max cut which is a rather large amount of stability that is usually not reasonable to assume in practice however we do conjecture that there exists some constant gamma star such that there is an efficient algorithm that correctly solves all gamma star instances of max cut which is the problem we currently working on. So sorry, when you say we need that stability Okay so we need stability That is all in order to prove we don't have a hardness result only rather weak hardness result something like that 1 plus 1 over n stability does not suffice us but nothing stronger than that and we only know to prove n of a log we know to design an algorithm that correctly solves all n of a log n stable instances or at least that's the best we know to prove for this algorithm Okay so I'll finish here. Any questions?


Welcome traders to another tick mill weekly market outlook for week commencing the 20th of June with me Patrick Monday In terms of the US next week on Monday markets are closed for Juneteenth National Independence Day the focus there is going to shift towards housing and Related markets which are left vulnerable really after the Fed policy announcements with the Federal Reserve signaling It has a strong stomach for the fight against inflation We could expect further significant interest rate hikes in coming months But by going harder and faster into restrictive territory There is a greater risk of a hard landing and a potential recession housing market is particularly vulnerable given prices are up nearly 40% nationally since the start of the pandemic due to stimulus fuel demand vastly outstripping The limited supply of properties for sale now that mortgage rates have surged higher and consumer confidence has plunged It's it's really starting to see demand weaken and supply rise the number of new home sales plunged 16.6% in April and Markets are anticipating that if there is any rebound in May That's existing home sales are measured when the keys are received rather than when the contracts are signed As for new home sales, so expect to see a big drop in May's existing home sales print This is a worrying as residential construction accounts for more than 2% of economic output while housing transactions also correlate strongly with spending on furniture home furniture home furnitures and Electronics so from a technical perspective. What does that leave us in terms of the dollar index? Well, we came just shy of that 106 target that we're looking for as a minimum upside technical target versus the potential way for Consolidation so we are looking now as the potential to hold here above the 103 handle If we do we're looking for price to extend to the upside test into that 106 20s We've got some nice momentum divergence developing and so watching there for bearish reversal patterns to potentially engage on the short side looking for a Correction at a minimum down back into the potential way for low that one 130s now Alternatively if we take out the lows at the 103 there Then I've been looking for a break of trend line support down through one or two forties and a potential then to extend down to at least test back into the 100 level and then 99 30s there that prior double top for the upside extension Then we have trend channel support back to 98 60 so we can be pivotal to see if we can hold those 103 20s As we head into next week moving to the eurozone Voters head to the polls today Sunday for legislative elections in France observers believe president manual macrons parliamentary majority could be under threat and we have really hot temperatures across Europe And that may impact turnouts in terms of data really the focus is going to be on Thursday eurozone PMI Expectations are for the June manufacturing metric to fall to fifty four point one from fifty four point six services Are also anticipated in fine from fifty five point five to fifty six point one leaving the composite at fifty four point one versus the fifty four point eight Which printed in May? It's also important that may release sort did see a down tick in terms of the composite metric But ultimately remaining in expansionary territory with the survey stating that the driving force of the expansion was the dominant services sector as ongoing supply side disruptions the war in Ukraine and subdued demand for goods restrained the manufacturing output growth this time we are looking for a A release that will show higher costs are starting to hurt the cyclical Manufacturing industry as energy prices continue their relentless surge Pickup in services as consumers rotate their spending to services away from goods as the economies continue to reopen This is also why market watches expect services sector to remain robust despite the increasing economic headwinds So from a technical perspective the euro-dollar Potential double bottom last week into those 103 fifties did see some demand come into the market Daily V-waps have flipped bullish, but however momentum remains negative at this stage So key as we head into this week is going to be any testing this 106 fifties the trend channel resistance If we get bearish reversal patterns there I've been looking to re-engage on the short side looking for a minimum test of the 102 20s versus that last corrective phase Now the alternative scenario is that we see increased Bids come into the market and take out this trend channel resistance So any move through that 106 70s to engage on the long side looking them for a test of monthly projected range resistance just below 108 and then we could also start to think about a target up into the trend channel resistance coming in 110 40s, so really going to keep see how we respond at that 106 50 for the euro this week Heading to the UK Quite a bit of data out this week starts midweek Wednesday with UK inflation Expectations are for a euro the year CPI print for made to cut 9.1% from 9% last time out Whilst the core metric is C remaining at 6.2% The jump in the April print from 7 to 9% was predominantly a Byproduct of the increase in off-gen price cap of an oven which will not be repeated in May's release This time around Look for for a unchanged headline rate of 9% and this suggests that food and energy Will likely continue to place upward pressure on prices However, this could be moderated this time around by clothing and footwear given the surge seen in May Then we head to Thursday We get UK PMIs and expecting the metric to decline for to 53 from the last 53.4% from manufacturing Tick lower to 54.2 from 54.6 The May report saw a notable decline in the headline composite metric and in a chunky drop in the services print Which actually fell from 58.953.4 the less of global noting that last round of input cost Inflation was the steepest since the index began in 1996 while the monthly loss of momentum for business activity Expansion was a survey record outside of the lockdown periods That said analysts expect more modest decline the composite release to 52.7 from 53.1 It's also noteworthy that the recent messaging from the PMIs appears to contradict the outcome of the April GDP print and therefore any optimism in the upcoming release might be questioned by market participants Then we round up the week on Friday with UK retail sales expectations after headline month-on-month retail sales to 4 1% Versus 1.4% increase seen in the prior report whilst the core metric is expected to decline to 0.2% versus the prior 1.4% the coming release will follow the April report which saw an unprecedented expansion for headline of core month-on-month metrics after two consecutive months of decline From a technical perspective for Sterling tested that long-awaited target We've been looking for that 120 tests traded down as low as 1935 before we saw decent demand coming into the market and we got the daily VWAP flip bullish heading into Thursday about Friday Saw some weakness developed and we're back now testing pivotal support here 121.50s this is going to be the line in the sand this week for the ball bear Scenario for me if we can hold this one twenty fifties then I look for an extension up into the 126.50s through that trend line resistance That's going to be a key test as well 124.75 keep an eye on that if we don't Maintain the 121.50s as support then we look for a move back down to retest prior swing lows and ultimately extend down into trend channel Descending trend channel support down below 118 on the downside So key to see how we respond at the 121.50s this week for Sterling in Japan Pretty like state of Cal alone in one release of milk really that's Thursday's CPI print Consensus is your over your core nationwide 2.1 cent versus the prior 2.1 cent consumer price inflation Lightly stayed unchanged at 2.5 cent in May for two straight months The government's expanded fuel subsidy program continues to offset movements in the by-crew prices The meanwhile obviously the key is the bank of Japan's preferred measure of core inflation excluding Fresh food energy likely edged up to zero point nine cent euro the elusman from a zero point eight cents in the prime month And obviously bank of Japan out on Friday released on Friday their Interest rate decision they are just flooding the market with liquidity Ultra-loose military policy there compared to all the major economies in terms of the central banks looking to tighten Financial conditions so from a technical perspective the dolly end tested back into that 131.40s, which we were looking for last week and we saw Decent demand coming out on Friday post that be a jade decision So what I'm looking for now is a move back through 135.40s and we have a target there 136.77 and 138.16 in extension So there's a minimum upside objectives for this move at this stage It would take a close back through 131.10 to suggest we have a more meaningful high in place That says we'll be looking for a move back down to test support to the 126.50s But for now looks like we have a bullish setup and we're looking for a new cycle highs as we head into the new trading week and we're rounding things out down under in Australia the only real Release of note this week is gonna be the Tuesday's RBA minutes Minutes from the June meeting but the central bank height rates by 50 basis points to 0.85 Remember the expectation there was just for a 25 basis points increase and note that inflation in Australia has increased significantly While it reiterated its commitment to doing what is necessary to ensure that inflation Returns the target over time the RBA also stated that inflation is likely to be higher than expected a month ago And that the board expects to take further steps in normalising monetary conditions over the months ahead With the size and timing of future interest increases to be guided by Incoming data and the assessment of the outlook for inflation and the labor market furthermore Note whether the Australian economy appears resilient although Sources suggest that uncertainty about the outlook is how household spend involves given the increasing pressure on finances from higher inflation So from a technical perspective the Aussie dollar We are still looking for an equality objective 6640 on the downside versus the swing high here at 76 60 rejected from The 70s 60 area this week So I'm looking now for follow-through back through the price cycle loads here 6820s One of the on the short side targeting that equality objectives 6640s at this stage We really need to see a break of the trend line resistance and high volume load here towards the 72 handle to suggest We have a more meaningful lower place and then we can start to think about range resistance back up into the 75 40s and that concludes the weekly market outlook for a week commencing The 20th of June as always traders plan the trade trade the plan and most importantly manage all this until next week. Thanks very much


My name is Paul Reeves. I work with the State of Washington Department of Health in the Water Recreation Program. Basically what we do is regulate pools. Flutation systems are part of that pool rule and so we have to kind of accommodate what's going on in the pool rule with the float systems. It's a learning curve for everybody, including environmental health folks. One of the most important things I was hoping to communicate to people is that everybody has a different background. Everybody has slightly different perspectives on things. And communication, any relationship if you will, takes work on both people's parts. And to communicate with the health department, coming up with clear terminology, understanding each other's terms, is going to go a long way in establishing that relationship. I honestly believe that.