Okay, so we are now going to talk about setting which will be analyzed quite extensively, basically for the rest of the course in terms of the types of mechanisms we're going to be looking at and the alternative games we're looking at. And in particular what this is known as is a setting with transferable utility. And what's looked at in these settings are situations where what people have what's known as quasi-linear preferences. And the idea before we get into the formal definitions is that there's something like money, some transferable good that we can move back and forth between agents and we know that how much that's worth to them and we can trade that off versus utility. And that gives us a nice sort of private good that we can move back and forth sort of payments in an auction or payments, contributions to a public good and we'll assume that that translates directly into some utility numbers. And the importance of doing that is it's going to give us a lot of power in terms of aligning incentives by making people's payments encapsulate the externalities that they're imposing on others in terms of decisions. So once we have transferable utility it will give us a lot of power in designing mechanisms in terms of making sure we basically price everything and we can figure out what kinds of prices people should be paying to change one decision to another decision and that's going to be a very useful tool in designing mechanisms as we go forward. So what do the formal definitions look like? Instead of just having some abstract set of outcomes now the outcomes are going to have structure where there'll still be some basic sort of public aspect to it, some decision X and then the other part is going to be a set of real numbers where we give each individual some payment or have them make a payment. So there's some transfers going on between the different individuals and so we will have some list Rn of what those payments are. So in this particular setting when we have quasi-linear preferences so people have quasi-linear so here what we're going to have is things are going to be linear in this second dimension so we can think of an outcome now as being a list of what's the public decision, some X and X and then also some P which is going to be a P1 through Pn of what those payments are and a given individual's utility for the outcome can be split into a utility function which describes how they like the X's and then also they subtract off whatever payment they're making and that payment could be positive or negative so it could be that they're paying something into the society as part of the outcome or it could be that they're receiving payments and these payments are going to be very important in designing efficient mechanisms, designing mechanisms to align people's incentives with what we'd like. So quasi-linearity gives us a lot of power. You can see where the quasi-linearity, where's the linearity part of this, the linearity part is that the preferences are always just moving linearly with whatever this payment scheme is, whatever the money dimension is. So when we start talking about mechanisms in this world then we can split the mechanism into making a choice so it's going to choose something so we've got our outcomes are equal to X cross Rn so what it's doing is it's first of all going to make a choice out of the X and then also have payments in Rn. So X and X is a non-monetary outcome and we use the term money here. It's not clear exactly what the transferable good is but there's some way of moving something back and forth which people can equate with utility so there's some non-monetary outcomes so often these are called public decisions, the aspect which is going to be common to all the agents and then we've got these private payments where each person is making a payment into the mechanism and if PI is negative then that means they're actually getting a net payment to them and the implications in terms of making this kind of assumption in terms of these preferences first of all the utility that somebody has for this outcome can be separated out from the utility that they get from the payment so it's not influenced by the amount of money your wealth an agent has and secondly people care a given agent cares only about X and their payment PI they don't care about say PJ where J is not equal to I right so they don't care what payments other people are making they just care about what's the overall decision which candidate do we pick or which public good do we pick or what decision are we making in terms of who gets what good and then what payment do I have to make and I don't care what other people's payments are to the extent that it doesn't enter into my payment okay so that's the setting and then a direct mechanism in this world is going to be a combination of some choice some X theta which comes out of X and a payment scheme as a function of the Theta's so now we announce our Theta's and then society spits back at us a public decision this non-monetary decision and then a list of transfers or payments that we're each going to make okay so that's a direct mechanism one thing that's going to be very useful in these kinds of settings and a lot of the analysis that we do going forward will be in a special case of quasi linearity and when we're thinking about the utility that individuals have so we have now we're writing people's utility overall as a utility of what the X's and the Theta minus PI of Theta right so in this X can depend on Theta what we're going to do now is we're going to make a look at situations where there's a further assumption made where instead of having people's preferences depend on the full vector of types in the society it's going to depend only on their own type so we'll say that preferences have private values or satisfy conditional utility independence if a particular person I's utility function depends only on Theta I okay so the utility for this overall outcome does not depend on anybody else's type it only depends on my own type so that means that once I know my own Theta I know everything about my preferences and what this rules out is things like investing in a stock where I'm not quite sure what the value of that investment is I don't know how well it's going to pay off and other people might have information that would be very valuable to me that's ruled out here once I know my information I know everything I need to know about my preferences and nobody else's information enters into that preference calculation okay so if we're talking about a particular candidate I know whether I like this candidate or not or if it's a public good I know whether I want that public good though so what that's what's nice about the private good setting is now instead of just thinking about Theta I's we can think of just people just telling us what their utility function looks like so we can think of the the private information they have is just a valuation function vi of X which is equivalent to this UI of X of Theta I so the Theta just becomes telling us what that function is okay so agents have a valuation function which is basically they out the value that they have of any particular allocation X okay and so then when we start thinking about direct mechanisms we can think of the space of individuals that the private information individuals have as these vi's so in particular everybody can tell us instead of a type they tell us now their valuation function and the standard notation we'll use is that people will tell us some V hat I which might be a lie and so dominant strategy mechanisms they might not always exist it could be that people are going to tell us some alternative valuation function instead of the true valuation function and so we can look at when is it that they're going to want to tell us their true valuation function so now we ask people what how do you value these different alternatives and under this private value or conditional independent you conditional utility independence condition they know their own preferences and they can tell us what that preference function is and then we can look at mechanism design and ask it when is it that possible and now this quasi linear world with these private values to get people to truthfully tell us what their preferences look like


Great River Rescue in Bemidji is helping kids become a little more pet savvy with their third annual Happy Tail Summer Day Camp. The day camp is a week long and it's basically a time for third through fifth graders to learn all about what there is to know about pets and other animals. The kids get to play with the pets at the shelter and at the end of the day they also get to explore the great outdoors and participate in learning activities. Our main focus with the Happy Tail Summer Day Camp is education. We really want to educate the kids about responsible pet care and about animal welfare overall and that's why we have guest speakers from like the DNR, from Nature Connection, from Eagle Vista Ranch to talk about horses. It's really a comprehensive look at animals and how we can be responsible citizens. Some other activities the kids get to do include crafts like making cat and dog treats and toys. They also get to do math games to figure out exactly how much taking care of a pet would cost. For a lot of the kids the knowledge is something they can take home and share with their parents. I learned what rabies were and also I learned what heartworm was. If it's a puppy you feed it three to four times a day or when it's a grown up dog you can feed it one to two times a day. Another session for the day camp is starting next week and there are still a few spots open. You can learn more about it at GreatRiverRescue.com. If you enjoyed this segment of Lakeland News, please consider making a tax-deductible contribution to Lakeland PBS.


Welcome to this chapter of the Open for Inside course, where we work on finding out how to make a good experiment. More specifically, we will address two areas. Why is observation alone often not enough? Why do we need experiments in the first place? And given that they're necessary, how do we make a good experiment? Although it's already a good start to observe the world when you try to understand how things work, we will see that we can run into trouble pretty quickly when relying on observation alone. We will see a few examples of what the source of these troubles is and how they may mislead us when we rely only on observing the world. After that, we will try to understand why it's necessary to get our hands dirty and create experiments to gain better insights. We will find out about the rationale of experiments, see a few examples from different disciplines, and then do some exercises to make our own experiments happen. The latter part, especially, will be very hands-on.


How to turn off ambient mode in YouTube with Daenerys, our five-year-old mother of dragons. This is Daenerys Venus, not Daenerys Targaryen. Ambient mode is something YouTube introduced as part of a darker dark mode, but they did the opposite effect. It made it less dark. Let me show you how to turn it off. In any YouTube video, click your settings icon and click this. Isn't that darker? Let me turn it back on so you can see. So this is ambient mode. It creates a glow around the video to match the color. It's supposed to be a cool effect and some people like it, but I don't. So again, you just click this little settings right here, settings, and then you check this. And watch this. Boom. Now this is darker dark mode. YouTube, why did you create an ambient mode and made it so difficult to turn it off? Doing some funny things. This is the YouTube help for dark mode. Click it down there. The link is down there in the description below and look at the comments on that video. Why would you ever need ambient mode? That completely counteracts the whole meaning of dark mode. I agree with you, L, the original. Please make it an option to use darker dark mode. I really want this to be optional. Don't fix things that don't need to be fixed. I agree. Camadvan 18. This is the exact opposite of what I want you to. Dark mode wasn't a problem, shaking my head, SMH. So yeah guys, the ambient mode, how you turn it on, first of all, if you want it, you go to the settings and let me move myself.  When you turn on dark mode, it turns on ambient mode right away, automatically. There's actually no setting for ambient mode. It should be right here. Sonic! Huh? What? Sonic! Oh my God. Daenerys saw the Sonic icon and that's one of her favorite characters in cartoons. Yes, Daenerys? Sorry, we're not making a video about Sonic. As I was saying, the ambient mode setting should be here, but YouTube decided let's just turn it on for you and not tell you how to turn it off because in none of the documentation here, this video, nothing here, tells you how to turn it off. They just tell you how to turn it on. Alright, Freedom Families, now you know how to turn it off. Click the settings and click this. It takes a little while to glow. That's part of the visual effect, but turn it off and now you have darker dark mode. Alright, Daenerys, is that exciting? Did you know that? Do you know what I'm talking about? No. I hope you know what I'm talking about. No! So Daenerys is my fourth daughter, almost six years old. I have a six, almost six. I am five and a half. Five and a half, ten-year-old, eleven-year-old, and a thirteen-year-old. And a ten-year-old. One of the videos I made a few days ago. And five and a half years old. Where I read your comments, I got a good response. So I'm going to read some more of your comments. Fine Gaming Connoisseur wrote 15 hours ago, hey, you're reading our comments, like you used to. It is a jolt to the start of my new year and it feels like the good old days all over again. Looking forward to seeing what freedom plans, what freedom has, what plans freedom has for 2023 and beyond. Well, our big plan is heartbeat. And in fact, I just wrote the investor deck. We're going to be pitching heartbeat to investors and hopefully raise some money. Like we raised ten million dollars for freedom games, our game publishing division. And hopefully we can repeat that with heartbeat. If not, we'll just build it as we would build it without investors. It'll just take more time because we can't afford as many things and people to build it quicker. I can't come back. But yeah, that's what's coming. Fine Gaming Connoisseur, Red Roll Plays wrote, I'm so, let me move myself to the other side. I'm so excited about the next year of deck next year. Next year's decade of freedom. So many new exciting things happening. Yes. Crazy Greg Film said, I do miss freedom. And I replied, why heartbeat will be freedom 2.0? Why do I call it freedom 2.0? Because freedom is built on the YouTube platform. Heartbeat is its own platform. It is the platform on which other people will build. So we will support networks, sub- McDonald's, yes, toys too. We will support networks, sub-networks. We will bring back monetization for blogs, for images, not just videos. We will create video wikis where you can flex your writing muscles, not just your video-making muscles, and get paid for it. We will remove the 4K, 1K completely. Gone. History. You will make money from the first piece of content you post on heartbeat. And you'll get paid a penny if you earn a penny. Just like when we launched freedom nine years ago, these were the key- A penny? A penny, yes. These were the key things that distinguished us from all the other YouTube networks. And we grew very quickly because of it. But now it's time to build the platform itself. Now we're not competing with YouTube guys. We're not creating a new YouTube. You're still uploading videos to YouTube. Heartbeat is a new revenue stream and a new concept of clipping, basically taking moments from videos. My favorite is doggie and cat. Okay, this is a bit difficult. Listen, click that eye to see the video where I explain heartbeat in 2023. I don't need to rehash everything because the narrows will not let me. And I hope you're as excited as Red Role Plays and Fine Gaming Connoisseur are. And I hope I can get you excited crazy Greg films. And you would change this comment to, I love freedom instead of I do miss freedom. Okay, we have a cat. His name is Loki and Daenerys is trying to show him in this video. He's a black cat. So it's kind of hard to see him on a black background. Okay, let me pick a lot. All right, this is Loki. This is our cat. And he's got golden eyes. He's a cute cat and the kids love him very much. I'm going to put him down before he scratches your Daenerys. The cat has already scratched Daenerys because she was a little rough with him. So naturally he defended himself, but she's learned not to be so rough with him now. Right, Daenerys? No more scratching? Did Loki scratch you again? Just once, right? Yeah. That was a big scratch though, wasn't it? Ouchie! You even were hiding from us. You didn't show us. Why? No? You don't want to tell me? I think she was embarrassed or, you know, felt like she did something bad and didn't want us to know about it. Anyway, we saw the scratch and we knew about it, so it was kind of like a hard thing to hide for her after we bathe her almost every day. So we're going to see it when we shower her, right? All right, Freedom Family. Hope you found this tip helpful on how to turn off YouTube Ambient Mode. And I'm going to be making a lot more videos for you. We're going to all help each other grow together as a family, the Freedom Family. That is the spirit of freedom. As always has been, always will be, as long as I, and who am I, as long as I remain the CEO and founder of Freedom, Freedom again, yes. And yeah, for Freedom and the Freedom Family, where we all help each other grow together as a family. And that was Kira, who just popped by. Hi, Kira. Do you want to say hi? That's my third daughter. Yeah, big family. We have babies and business growing together as a family. And so all of you are my extended, hi, Kira, extended family also growing together as a family. All right, until the next episode, hey, I went to the gym yesterday and today. Did you? I hope so because exercise is very important. Okay, Daenerys, I'm trying to finish this video. Can you just let me? Okay, thank you. Because exercise is very important, keeps you healthy, keeps you strong, and it'll give you lots of energy, even though it may not feel so good while you're exercising. It feels great afterwards. All right, Freedom Family, I am George, and you've been watching. Oh, you're dreaming but love here. Take that eye to partner with Freedom and join the Freedom Family so we can all grow together. You get many perks, like position music, you also get epidemic sound, a lot of other access to royalty-free videos, sponsorships, and many things to help you grow. Just click the links down there in the description below to get involved in our community, our forums, our Discord chat servers, Meet Our Graphics team, Meet Our Community team, all of that on Discord and the forums. What are you waiting for? Get started. And we will grow together as a family because this is the Freedom Family. You are part of it, we are all part of it, and we're all growing together. To get more, George, click that big F that will subscribe you to Freedom Central, home of the George Show. And PewDiePie gave one of you, Freedom Family, a big shout out. Click that video to see the shout out and to see our new 3D sets for you. And click that video to see what YouTube recommends you watch next.


Okay, so welcome to the speaker, Andres Rojas, who is going to talk about geometry of green semi-canonical pencils. Please. Okay, so first of all, let me thank the organizers for this school and for the opportunity to give this talk. Everything that I will explain is part of our joint work with Marty Laos and Juan Carlos Naranjo.  Assume that we have a double ethyl cover of a smooth curve C of genus G. Since the double cover is ethyl, the genus of CT lays 2G minus 1, then we attach to it the prime variety as the connected component of the kernel of the norm map, of the norm map, which passes through the origin of the Jacobian of C tilde, and then it comes with a principal polarization. This is the definition that we have just seen today. And then if one wants to consider the canonical model of this data divisor in the same way as in the case of a Jacobian, one considers the canonical data divisor in a torso in a translate of the original a brilliant variety, in this case of the original Jacobian, we can do the same if we want a canonical model of this, sorry, of this data divisor. Okay, is this canonical model C plus, which lives in a translate of the Jacobian of C tilde. In this canonical model, the data divisor is recovered as the intersection of the prime variety with the canonical data divisor of the curve C, but actually this intersection is not reduced, so one gets twice a principal polarization. Then map for use at this canonical model to classify the singularities of this of this data divisor into two types, stable and exception. Somehow stable correspond to line bundles with at least four global sections, these are points that have a high multiplicity at points in this in this canonical data divisor, so when we intersect we still have a singular point. And the exceptional singularity is a special condition of at points where this prime variety and this canonical data divisor somehow are tangent to itself. So we are getting a special configuration to get to get a singularity. And these exceptional singularities are described as follows. We have the pullback of a line bundle L on C without these two global sections twisted by an effective divisor on the curve C. The most elementary example of exceptional singularity is when we are pulling back a semi canonical pencil of the base curve C such that the pullback has an even number of sections. So for me as a semi canonical pencil on the curve C is a data characteristic. So it's a line bundle of degree g minus one such that it is square, it's a square is isomorphic to the canonical shift of C. And it is an even data characteristic which is effective. So it has an even number of global sections which is greater or equal to this positive. Under this condition we have an exceptional singularity. So Bobil used in the case of genus five, let me relate this construction with a work of Bobil, using the premap on on genus five or its proper version by admissible covers to prove that the Andriotti Major Lopez in A4 is the union of two reducible devices. Okay, this is the Andriotti Major Lopez in A4 which is the divisor, well it's the locus of principally polarized abelian varieties which have a singular data divisor. And Bobil showed that the two irreducible components of this Andriotti Major Lopez are J4 which are the Jacobians of curves of genus four and the divisor tetanul which parametrizes principally polarized abelian varieties whose data divisor contains not only a singular point but a point which is too torsion singular. Okay, so the key point especially for the irreducibility of tetanul was proving that the pre-image by the premap which in this genus is when one considers the proper version is subjective. This pre-image of tetanul which is the locus of curves satisfying this conditional both of a semicolonical pencil which pulls back to an even number of global sections. This is the pre-image and this pre-image is zero. So that when we apply the premap we get the divisor tetanul and it's irreducible. So we consider for an arbitrary genus gene to loci the loci we will call it TEG of a smooth covers of curves of genus G such that the base curve has a semicolonical pencil whose pullback has an even number of global sections. So this is the same condition that we were stating above just in an arbitrary genus and it's also natural to consider what happens if the number of global sections of the pullback is so. So this gives to another locus that we call TOG. Okay, so these two loci are irreducible divisors of IP and well there are closures in the delinear amount for compactification and GBAR are also well okay this appeared in a recent work with Carlos Maestro. So now the natural question is if we have these two loci we wonder about the behavior of the premap restricted to these two divisors. Okay and well this has been already studied in two particular cases as I told you Bobil studied the event case of genus five T5V to prove that the determined Andreotimia locus in E4 and also incidentally in a work of Izadi she proved that TO5 the odd case of genus of genus five dominates the whole A4 the whole modulated space A4. So in the genus five case we see that there are a big difference between these two divisors at the level of the premap because we call that Bobil show that this is mapped to TETAMUL to a divisor of A4 and on the other hand we have TO5 dominating the whole A4. So this is a very different behavior and actually the situation this is the situation in general. So for every year what we will have is that the event case the event divisor TEG is mapped to TETAMUL and this is not this is not very difficult to to prove is actually follows from the from the very definition but what happens is that TOG the odd divisors dominate AG as long as the dimension allows it. So for low dimensions between three and five TOG is dominating AG-1. Okay and actually for higher genus there are also differences but we will concentrate in these cases and specifically I will talk just to illustrate these differences about the event cases TEG in general the relation to TETAMUL and two particular cases of odd semi-clinical pensions which are in genus four and genus five somehow are the ones with which geometrically are richer. Okay so this does not consider the divisors the event divisors TEG the notation TETAMUL will stand not only for A4 but also in general it will mean the divisor of principality polarizability and varieties without the divisor that contains a two torsion single output. So then in general the pre-image of this divisor by the pre-map is essentially TEG. Okay in the cases of low genus up to genus five this pre-image is exactly TEG we call that in genus five this is Bobil. For genus data equivalency we have TEG plus some irreducible components of co-dimension three. Okay but essentially TEG is the divisorial component of the of the pre-image. Okay so let me also point out that in these irreducible components what is happening is that the green variety associated the abelian variety and not only has a two torsion singular point but also it contains a two torsion point the theta divisor with multiplicity at least three. Okay so it's a configuration that gives a more singular and theta divisor. Okay so rather than giving a proof of this which is not very difficult it's just following the classification of MAMFOR. Let me give an example of these irreducible components one of these irreducible components one g is equal to six. So for every smooth cubic three fold we can naturally associate an intermediate Jacobian with a principally polarized actually abelian variety of dimension five with a natural theta divisor a canonical theta divisor which has a unique singular point which has multiplicity three at the origin. Okay so in particular since the origin is a two torsion point of course the locus of intermediate Jacobians lies inside this device of tetanul inside a five. Okay well now we want to consider the preimage of this locus of intermediate Jacobians and compare it with the preimage of of tetanul. So if one wants to construct an intermediate Jacobian as a green variety the way is considering a line contained in the cubic three fold B. Okay we consider a supplementary plane P2 in the ambient P4 so that this plane is parametrizing all the planes containing the line L and what we what we are doing is projection from B into this plane so simply what we are doing is for every point of B we consider the plane which is obtained from joining the point with the line okay this is of course rational it's not defined along L that one can blow up and this is a morphine this often determinacy locus. Okay well essentially what we are doing what are the fibers of this map to every plane containing L we intersect in the cubic three fold with this plane and we are considering the intersection the intersection is the line L and the residual okay well then the locus of planes through L is parametrized by this P2 such that this residual conic is reducible so that it breaks up it breaks into two lines is a plane quintic associated to this conic vandal structure. So essentially to every point of this conic that we are doing is considering the plane obtained from joining with L in this plane intersects the cubic three fold in L and two further lines okay well if we didn't know this plane quintic by QL there is a natural covering QL tilde let's call it that essentially puts over over every point of QL the two lines the two residual lines are rising in the intersection and the prime variety of this cover is the intermediate Jacobian and this is all the possible ways one can construct the intermediate Jacobian as a as a prime variety. So if one considers the pre-match of all intermediate Jacobians one has the locus formed by covers of plane quintics satisfy an aparatical mixture okay I mean not every cover of a plane quintic arises in this way but if one puts a parity condition here then one recovers these constructions we call it RQ RQ minus following the don't have any notation I think well then what happens is that this loci RQ minus is an irreducible component of the pre-match of the TANU because RQ minus is not contained in TE6 okay mainly because the the general quintic has no semi-canal complex so this is an irreducible component and has dimension 12 because the locus of quintics well the model space of plane quintics has dimension 12 and this has a indeed co-dimension three in R6 and we have a component whose data divisor has a point has a point with higher multiplicity so this is all I wanted to say about the even case let's move to the odd case TO4 and as I told you before this map is going to be dominant actually okay in contradiction in contradiction to the to the even case the result is that this premap restricted to TO4 is subjective and actually the fiber the general fiber of this map fiber at the general Jacobian is the complement in the projective plane of the union of the canonical model of X which is a quartic plane curve and the 28th v tangent lines to this plane quartic okay essentially the idea to prove this is to use Recija's trigonal construction this is an instance of the polygonal constructions that Irene already introduced this morning the philosophy of the Recija's trigonal construction is that if we have a double cover of a trigonal curve then it's pretty bad it's pretty variety it's going to be the Jacobian of a tetragonal curve and conversely so the idea is that we have a double etal cover of a trigonal curve this is three to one this is two to one then one can associate at the trigonal curve X such that the Jacobian of X is is going to be the premarital discord and under certain generality conditions on the curve X one can reverse this construction okay so let's prove it in a in a more in a more sophisticated way but the diagram is going to be the same if we consider the modular space of objects like the ones I consider here in the left so we have a cover of a smooth curve of genus four that I will assume assume also that this is not hyper elliptic and though we with a trigonal line bundle on the curve we consider this modular space and on the left we consider and the right sorry we consider the modular space of objects like the ones presented here so we have a pair format by a curve of genus three and a g14 on X and I will assume it's base point three in order to give a morphism to p1 okay but the u14 must not not this doesn't need to be complete so then what the trigonal construction says is that we start with the modular space parameterizing the objects in the left if we forget the trigonal curve and we apply the premar to the cover then we are going to get the same ambient variety as if we apply the trigonal construction forget the trigonal line bundle and then we simply consider it okay well then the idea to find the the fiber restricted to t04 at a general curve X by this diagram that actually is a nice morphism if we restrict to a certain open subset here okay then we have to leave this element this curve X to this open subset come back the arzillas forget the trigonal line bundle and once we are here intersect with t04 well the method to do this is that we can consider true involution sigma on both modular spaces I will not give the the test because I don't want to be over time but essentially the idea is that they commute with with rathias trigonal construction so the key point is that when we are doing all this way around in order to arrive here and intersect with t04 once we are at this point of the modular space the pre-image of this prediction file of t04 is one of the fixed set of side that this involution sigma okay so since these involutions are compatible it must come back it must come from sorry from a fixed loci by tau okay and once we are in tau this is related to the geometry of x and here it's much easier to consider this fixed loci okay so this fixed component corresponds to the to the g1 force which are not complete on x so these are these are parameterized by the project plane because the g1 force non-complete are continuing the canonical the canonical bundle and then we have to discard the points of x in this p2 because they are giving base point base points in our g14 and we have to discard also the 20 determinant lines because are because are lying outside these open stops okay so i won't write anything else about this i'm sorry for the explanation i can give you more details if you want but this is more or less eight so now let me move to the case of genius five which is probably the most interesting one we want to understand how is the premap the mobile's proper version if you want of the premap restricted to t05 okay first of all let me say that donating in the description of these of these premaps found our our rational map between a4 and the modulus space of pairs format by a smooth cubic three four b and a two torsion point in its intermediate jacobia which has a certain parity condition okay and this is actually by russia is adding gave an explicit description of this by russia map and found the indeterminacy locals and somehow incidentally in this study one can find the following result of his study is that this premap restricted to t05 is rejected okay now actually the fiber at the general element of this rc plus is a partial desingularization of the curve of a curve in the final surface of lines of the cubic truth okay so this is the final surface and the curve that we are considering parametrized lines such that when we are considering all the planes through l there exists one such that the residual intersection is a double line is a double line r okay so with regard to the to the previous construction of the conic bundle this means that the discriminant quintic has a point where actually there is only one point lying over it there is a double line two lines are somehow collapsing and this produces a note on the on the corresponding quintic but the cover is admissible anyway okay the idea of the proof goes as follows don't have you describe the fiber of the premap in general not restricted to a divisor at the general element of this modular space by rational 284 as a double cover of the final surface of lines of b this is what i denote by f the fb tilde it is the 2 to 1 et al cover which actually is defined by these two torsion points so this information that gives the two torsion points but one has the curved gamma inside the final surface of lines and one can see that the pre-image of this curve gamma by this double et al cover has three reusable components one of one of them is the intersection of t05 with this general fiber so actually this component is the general fiber restricted to t05 of course and another component which is the intersection of delta zero ram this is the divisor of bobbin admissible covers of nodal curves so here are curves of singular of covers sorry of singular curves and this is the intersection of this divisor with the general actually the nagi's description of the involution here is changing sheets for the cover which also was described alternatively by zadi both descriptions are very geometric and give that these two components are exchanged by hand okay so in particular it it follows that gamma must be same because the final surface of a general cubic three four has picard run one so then what you get is that the curve gamma example the final surface and if it's pretty much where where smooth then it should be reduced okay these are consequence of of hoaching next year so gamma must be single at the picture you have to to regarded as follows we have the curve gamma and here we have the two components some of the notes of sorry some of some of the singular points of gamma leave two notes of these components but there are also singular points of gamma which actually leave two intersection points of the components okay this is the reason why this general fiber one of the two components is a partial desingualization of the curve gamma okay this is what sorry sorry andres you have three minutes left so i will finish thanks so just the final part is we cannot take more information about gamma with analysis of the divisors with the divisor 205 okay so we have described gamma this is the definition there is a plane with a residual conic which is a double line but in the same way one can define a natural counterpart which is a curve gamma plane okay it's formed by lines are such that there exists a two plane which intersects and the cubic three four in two times this line okay this somehow a natural a natural counterpart this is called classically the lines of second okay this is classically studied it's called gamma prima is known to be smooth for a general cubic three four b and also it's it's it's numerical class also one can it's easy to prove that if since a cubic three four b is smooth then one have one has a natural morphism from gamma prima to alpha okay because for every line are one can only have a plane satisfying that the intersection along this plane is is double for the line one cannot have two planes so the situation is that the curve gamma prima is smooth and actually one can prove that this is the normalization of gamma which i told you that is always singular and with a bit more of work one can prove that the only notes of that the only singularities of gamma are notes okay and these notes have a geometric meaning because these are the points which are which have two parameters in gamma prima by this by this by this normalization so i will not make the picture but you can imagine the situation of a line and two distinct planes with residual intersections double lines okay so once we are here a natural numerative question is what is the number of notes of gamma for a general curve so what is the exact number of lines satisfying this configuration and one can prove that gamma is numerically equivalent to eight times the canonical divisor and we will deduce from it the number of notes of gamma okay i won't give the details of the proof but only let me let me tell you that the way of finding this numerical class is somehow surprising at least for us because what we used is that donagis description of the of the general fiber realizes this double cover of the final surface of lines in this moderate space of admissible cover covers or if you want in the in the delinium for compactification now the fact that this space has a well has a well known picard group description the canonical class is also well known allows us to find properties of the well of the double cover but also the final surface of lines which somehow if one tries to see directly in the cubics refolders cannot cannot detect okay so expressing this funnel as a as a general fiber allows to give more information also about the cubics it's not only to say things about the print out okay and here one uses to prove this that the homology class of t o five is well known a one can compare it with with the canonical class okay using that we know the numerical class we can compute its arithmetic genus the geometric genus of gamma is that of gamma prime because these curves are are birational and computing this difference is numerical class is quite high in comparison with that of gamma prime one obtains that the exact number of nodes is 1000 485 okay so if you want to try translate these nodes into lines there are there is this number of lines for a general cubics refold satisfying this this condition and well this is all I wanted to say so thank you for for staying here thank you very much address for this very interesting talk so is this there any question I have lots of questions but maybe if you have some time tomorrow I would like to understand better your beautiful construction with the based on the trigonal reseal of trigonal construction so maybe if tomorrow you can explain it to me I will be very happy I will be glad to explain thanks okay so any remark question okay so if not we are all a little bit tired but that was a very nice talk both of the talks were very nice yes my compliments to everybody today talks were very beautiful yes


Live from Las Vegas, it's theCUBE, covering AWS re-invent 2017, presented by AWS, Intel, and our ecosystem of partners. And it's actually a little quieter here. Welcome back to AWS re-invent 2017. I'm Lisa Martin. We're all very chatty. You can hear a lot of chatty folks behind us. This is day two of our continuing coverage. 42,000 people here, amazing. I'm Lisa Martin with my co-host Keith Townsend and we're very excited to be joined by a CUBE alumni, Bob Muglia, CEO and president of Snowflake. Welcome back. Thank you, good to be back. And Kelly Munger, the director of enterprise data and analytics from Lionsgate, a great use case from Snowflake. Thanks so much guys for joining us. So one of the hot things going on today at the event is your announcement, Bob, with AWS and Snowpipe. What is Snowpipe? How do customers get started with it? Great, well thanks. We're excited about Snowpipe. Snowpipe is a way of ingesting data into Snowflake in a streaming, continuous way. You know, you simply can drop new data that's coming in into S3 and will ingest it for you automatically. Makes that super, super simple. Brings the data in continuously into your data warehouse, ensuring that you're always up to date and your analysts are getting the latest insights and the latest data. So when you guys were founded about five years ago, you are, as your marketing says on the website, a complete data warehouse built for the cloud. What was the opportunity back then? What did you see that was missing and how has Snowflake evolved to really be a leader in this space? So you know, if you go back five years, this was a time frame where no SQL was the big rage and everybody was talking about how SQL was passed in and something that you're not going to see in the future. Our founders had a different view. They had been working on true relational databases for almost 20 years and they recognized the power of SQL and relational technology but they also saw that customers were experiencing significant limits with existing technology and those limits really restricted what people could do. They saw in the cloud and what Amazon had done, the ability to build all new database that takes advantage of the full elasticity and power of the cloud to deliver whatever set of analytics capabilities that the business requires. However much data you want, however many queries simultaneously, Snowflake takes what you love about a relational database and removes all the limits and allows you to operate in a very different way and our founders had that vision five years ago and really successfully executed on it. The product has worked beyond our dreams and our customers, our response from our customers is what we get so excited about. So the saying is data is the new oil. However, just as oil is really hard to drill for and find, finding the data to surface up, even put in a data lake to analyze has been a challenge. How did you guys go about identifying what data should even be streamed to Snowpipe? Well, yeah, that's a great question. I mean, in entertainment today we're experiencing probably like a pretty much every type of business, a data explosion, we have streaming is big now, we have subscription data coming in, billing data, social media data and on and on and the thing is it's not coming in a normal, regular format. It's coming in what we call semi-structured, structured, JSON, XML. So up until Snowflake came onto the scene with a truly a cloud-based SAS solution for data warehousing, pretty much everyone was struggling to wrangle in all these data sets. Snowpipe is a great example of one of the avenues of bringing these multiple data sets, merging them real-time and getting the analytics out to your business in an agile way that's never been seen before. So can you talk a little bit about that experience, kind of that day one after you've taken these this separate data sources, whether it's ERP solution, data from original content, munging that together and then being able to analyze that, what was that day one experience like?  That word is yes, okay, and data architects and executives and leaders within pretty much every company are used to saying, we'll get to that. We'll put it on the roadmap. We can do that six months out, three months out. So what happened when I implemented Snowflake was I was just walking into meetings and going, yes, you got it, no worries, let's do it. Well, it's changed, it's not only liberating, it changes the individual's opportunities, the team's opportunities, the company's opportunities, and ultimately revenue. So I think it's just an amazing new way of approaching data warehousing. So Bob, can you talk a little bit about the partnership with AWS and the power to bring that type of capability to customers? Data lakes are really hard to do that type of thing. You run a query against it, get instant answers. Talk about the partnership with AWS to bring that type of capability. Well, Amazon's been a fantastic partner of ours and we really enjoy working with Amazon. We wind up working together with them on to solve customer problems, which is what I think is so fantastic. And with Snowflake, on top of Amazon, you can do what Kelly's saying. You can say yes, because all of a sudden you can now bring all of your data together in one place. Technology has limited, it's technology that has caused data to be in disparate silos. People don't want their data all scattered all over the place. It's all in these different places because limits to technology force people to do that. With the cloud and with what Amazon's done and with a product like Snowflake, you can bring all of that data together. And the thing that's interesting where Kelly is going is it can change the culture of a company and the way people work. All of a sudden, data is not power. Data is available to everyone and it's democratized and every person can work with data and help to bring the business forward and it can really change the dynamics about the way people work. And Kelly, you just spoke at the multi-city cloud analytics tour that Snowflake just did. You spoke in Santa Monica, one of my favorite places. You talked about a data-driven culture. We hear data-driven in so many different conversations but how did you actually go about facilitating a data-driven culture? Who are some of the early adopters and what business problems have you been able to solve by saying yes? Well, you know, I can speak in general, entertainment in general. I think that it's all about technology. It's about talent and it's about teaching. And with technology being the core of that. So if we go back five years, six years, seven years, it was really hard to walk into a room, have an idea, a concept around social media, around streaming data, around billing, around accounting and to have an agile approach that you could bring together within a week or so forth. So what's happening is now that we've implemented Snowflake on AWS and some of the other, what I call Dream Tools on top of that, the DreamStack which includes Snowflake, it's more about interrating with the business. Now we can speak the same language with them. Now we can walk into a room and they're glad to see me now. And at the end of the day, it's new. It's all new. So I say this is something that I say sometimes and kidding but it's actually true. It's as if Snowflake had a time traveler on staff that went forward in the future 10 years to determine how things should be done in the big data space and then came back and developed it. And that's how futuristic they are but proven at the same time. And that allows us to cultivate that data driven culture within entertainment because we have tools and we have the agile approach that the business is looking for. So Kelly, I'm really interested in, I love the concept of making data available to everyone. That's been a theme of this conference from the keynote this morning which is putting tools and builders' hands now builders to do what they do. And we're always surprised at what users come back with. What's one of the biggest surprises from the use cases that now that you've enabled your users? I'm going to give you one that's based on AWS and Snowflake. And a catch phrase you hear a lot of is data center of excellence. And a lot of us are trying to build out these data centers of excellence. But it's a little bit of an oxymoron to the fact that a data center of excellence is really about enabling your business and finding champions within marketing, within sales, within accounting and giving them the ability to have self-service business intelligence, self-service data warehousing. The kinds of things that, again, we go back five, six years ago, you couldn't even have that conversation. To tell you today, I can walk into a room and say, okay, who here is interested in learning about data warehousing? And you know, that'd be a great, great. Within an hour, I'll have you being dangerous in terms of setting up, standing up, configuring and loading a data warehouse. That's unheard of. And it's all due to Snowflake and their new technology, so. I'd love to understand, Bob, from your perspective. First of all, it sounds like you have a crystal ball, according to Kelly, which is awesome. But second of all, collaboration. We talked about that earlier. Andy Jassy is very well-known and very vocal about visiting customers every week. And I love their bottom, their backwards approach to, before building a product to try to see what problem can we solve. They're actually working with customers first. What's the problem? What are their requirements? Tell me a little bit, Bob, about the collaboration that Snowflake has with Lionsgate or other customers. How are they helping to influence your future, your crystal ball? This is where I think what Amazon has done. And Andy has done a fantastic job. There's so much to learn from them. And the customer centricity that Amazon has always had is something that we have really focused to bring into Snowflake and really build deeply into our culture. I've sort of said many, many times, Snowflake is a values-based company. Our values are important to us. They're prominent in our website. Our first value is we put our customers first. We are, what I'm most proud of is we've, every customer who is focused on deploying Snowflake has successfully deployed Snowflake. And we learn from them. We engage with them. We partner with them. All of our customers are our partners. Kelly and Lionsgate are examples of customers that we learn from every day. And it's such a rewarding thing to hear what they want to do. You look at Snowpipe and what Snowpipe is, that came from customers. We learned that from customers. You look at so many features, so many details. It's iterative learning with customers. And what's interesting about that, it's listening to customers, but it's also understanding what they do. One of the things that's interesting about Snowflake is that as a company, we run Snowflake on Snowflake. All of our data is in Snowflake. All of our sales data, our financial data, our marketing data, our product support data, our engineering data. Every time a user runs a query, that query is logged in Snowflake and intrinsics about it are logged. So what's interesting is because it's all in one place and it's all accessible, we can answer essentially any question about what's been done. And then driving the culture to do that is an important thing. One of the things I do find interesting is even at Snowflake, even at this data-centric company, even where everything is all centralized, I still find sometimes people don't reference it. And I'm constantly reinforcing that your intuition, you're really smart, you're really intuitive, but you could be wrong. And if you can answer the question based on what's happened, what your customers are doing, because it's in the data and you can get that answer quickly, it's a totally different world. And that's what you can do when you have a tool with the power of what Snowflake can deliver is you can answer effectively any business question in just a matter of minutes. And that's transformative. It's transformative to the way people work. And to me, that's about what it means to build a data-driven culture, is to reinforce that the answer is inside what customers are doing and so often that is encapsulated in the data. Wow, your energy is incredible. We thank you so much, Bob and Kelly, for coming on and sharing your story. And I think a lot of our viewers are going to learn some great lessons from both of you on collaboration, on transformation. So thanks so much for stopping by. Thank you so much, I really enjoyed it. Thanks a lot. It's great to meet you. Thanks Kelly, thank you. For my co-host, Keith Townsend, and for Kelly and Bob, I'm Lisa Martin. You've been watching theCUBE live on day two, continuing coverage at AWS re-invent 2017. Stick around, we have great more guests coming up.


It's amazing to see just how far the web has come Lighthouse is an open-source automated tool for improving the quality of webpages What did you do? No the entire laptop froze. No What do you do in this kind of situation? The edit of this will just be like they'll cut to me dancing And then it'll come back to you. This is exactly the kind of experience. I was hoping to give you


What's up everybody Michael here with jaspies, and we're doing our last filler for our 20 So for a 11 box baseball mixer the filler pack is a 2022 tops chrome Ben ballers pack We're giving away eight spots in the mixer with this filler. So I I've got All the names here. Thank you to this group for getting this filler done and all the teams and There's actually five full spots left guys. So if you're seeing this early Maybe go grab a full spot and we'll get this going soon, but two and a three five times one two three four and five Five times there got Josh Down to Kevin so five times again for the teams one two three four and five Five times there Match them up Make it look nice All right guys, so It's only a four card pack. I'm not gonna read off all the teams But you can look at them here. I'm gonna print this out real quick and We'll rip the pack and then see who gets into the break All right 2022 Ben baller Four card pack. Well, we actually we have something here We have something So wander rookie What's upon a time that was actually worth a good about a good amount of money and Carson Kelly Diamondbacks that's going to zap out of 75. So a little something something out of a filler can't complain about that So That was quick and easy Done with that. I got all the names back in here Good thing I looked at the screen because I didn't switch the camera all the names back in here We're gonna roll a new dice. This is gonna be to see who gets into the break Wow 12 6 and 6 12 and remember so top 8 we'll get into the mixer 12 times good luck everybody one two three four five six seven eight nine ten 11 12th and final time. Good luck guys boom 12 times 9 through 30 Thank you everybody who tried to give it a shot appreciate appreciate that but um 8 and up happy happy campers Matt Zach Oliver Brandon Craig Matt Jason and Darren All getting into the mixer nice Always nice getting into a break with a little mixer spot there, but um Yeah, so like I said guys, we're gonna run the once these last five main spots sell We're gonna run this break. So thank you to everyone who got into the filler and Next video will most likely be the mixer. So we'll see you guys then. Thank you guys


Keeping West Sussex moving is a top priority for the County Council, and tackling these things is a key part of that. Officially, they're highways defects, otherwise known as potholes. After record levels of rain and freezing temperatures, even more have been appearing all over the UK, and they can be anything from an irritation to a downright danger. The number of potholes in West Sussex can triple after heavy rain or snow. We've been watching the gangs at work to find out how they mend them and to take a look at some of the reasons that they can suddenly appear. A big problem is water seeping in between the layers of the road surface. It could be from something like this blocked stream, and even an earlier repair can then break up. If the water freezes, the expanded ice makes things even worse. Operation Watershed is a County Council initiative focused on flooding, but it also means the number of pothole patrols has been tripled to keep up with the faster rate at which they're appearing. It's a two-man gang that will go out to those areas where we're getting a significant number of potholes on a particular road, and they'll work their way along that road and repair all the potholes along it in one hit. The gangs start by cutting a rectangle around the uneven patch and preparing it for filling. There are different ways to fill potholes using hot and cold fillers depending on the size and type of pothole and what sort of road it's on. The process begins by sealing the edges of the rectangle with a spray bitumen. Then the hot tarmac is tipped in and smoothed out. The gangs, by the way, are pretty good at doing a straight line by eye. And this is the machine that hammers it all into place. It's a vibrating plate known as a wacker because, well, it delivers a whacking movement and this is the tamper which ensures the corners are properly tamped down. In emergencies, this glue can be poured in to help the tarmac stick and then there's this remarkable bag of tarmac which is actually laid cold and, unfortunately, you can't buy it in the shops. When it's finally been whacked and tamped, the repair cools very quickly. Then it's safe to walk on or even to drive a vehicle over. How long will the pothole repair last? A temporary job is done if the road is due to be resurfaced otherwise it'll be a more lasting one. What can you do to help? In an emergency, you can report a pothole by calling 01243 642 105. You can also use the Love West Sussex website or smartphone app and don't worry that someone may have reported it before you, tell them anyway.


1. I intend to discuss the essence of poetry, its various forms, and the power and function of each form. I will examine how the plot should be created for the poem to be good and beautiful, the nature and number of the parts of a poem, and whatever else is appropriate to this inquiry. I will begin in a natural way by examining first principles. Epic, tragic, comic, and dithoramic poetry are generally forms of imitation, as is most music for the flute and the harp, but they differ from each other in three ways, either in their separate medium, or in their means, or in the object of presentation. While some artists portray many different things by means of color and shape, and others use sound based on art or practice, poets generally create through rhythm, language, and melody by using them either separately or combined. Flute playing and harp playing only use melody and rhythm. This is also true of similar arts, such as playing the panpipes. Dancers use only rhythm without melody, because they are able to present character, emotion, and action by means of rhythmic movement. Another kind of art employs only language, either in bear prose or in verse. If it is composed in verse, the meter may be single or a combination. This art does not have a name, because no common term has yet been applied to the mimes of Sofran and Xenarchus, the Socratic dialogues, or to those who present their art in trimetric, elegiac, or any similar meter. Nevertheless, people are in the habit of calling them poets simply for their use of verse, rather than for what they create. They add the word poet to the name of the meter that is used, calling some of them elegiac poets and others epic poets. Even when people publish a medical essay or a work of physics in verse, they are commonly called poets. However, Homer and Empedocles have nothing in common except that they both use meter, so it would be correct to call Homer a poet and Empedocles a physicist, rather than a poet. By the same token, we would call someone a poet who succeeds in creating a work even if all kinds of verse forms are mixed, as Caramon did in his poem Centaur, a composition that includes many forms. This is how the distinctions can be made clear. Some kinds of art utilize all the means I've mentioned—rhythm, melody, and meter—in dithoramic and gnomic poetry as well as in comedy and tragedy. They differ in that dithoramic and gnomic poetry maintain their means from beginning to end, whereas in tragedy and comedy they alternate. These are the differences in the various arts by which creation is achieved. Poets present human actions. Those actions are either good or bad, because characters are generally one or the other. People differ in character because of goodness or badness. Therefore, poets portray their characters either as better than we are, worse than we are, or the same as we are. Painters have the same purpose. Polygnotus portrays people as better than we are, Pauson as worse than we are, and Dionysius portrays them the same as we are. It is now clear that all of the arts I have mentioned manifest these distinctions, and that they will differ from each other by portraying objects in one of the three ways mentioned. These differences can also occur in dancing, flute playing, and harp playing, as well as in pro—Sample complete. Ready to continue?


You guys getting some yards after the catch too, but do you feel like the flow was there with him? Like I said, I feel like everybody's doing their job, and Tana Hill did a great job just getting the ball out man. Just trying to make plays for them and we did. Coming down to the bottom of the defense, do what they did, but you guys obviously... I was crazy man, defense seems to always show up before us man. I was huge at the end and got the ball out man. Just find a way to win a game. What do you guys think of looking at, you know at this time, at the time... I mean, if I was the coach, I would have let him score because we can go down there and score. We need some time on the clock, so that's what I was thinking, but I'm not the coach. Like this week, did you find something during the 10th of the 1st? He'll been practicing with us since camp, so we've been connected. And like I said, we've been in sync, we just showed today. What was the call that he checked into that scene to you? Yeah, I had a lot of things going through my mind at the moment. I really wasn't really sure what I had, but like the last minute is just quick, but he checked, there was some pressure I think, and Cory did a great job clearing it up and I ran a quick slant. Yeah, Cory gave you a rough run there. The initial call was what for you on that one? The initial call? Yeah, I don't know. You don't know? Just so you got checked into the sand with Cory and you're well. What went about just some of those passes and the connection you guys had on a couple of those late especially? He expected me to be in the right spot and then he threw the ball where he needed to be and then I just made the catch. What did you think overall watching him today? He did a great job today. He let us in the huddle. He had a lot of confidence in the huddle that made us believe, so he was a general today. You guys seem to have some real changes to attack the ball and to go physically beat defensive backs. I know you probably relish those changes. How much do you like the idea of going in a muscle now? Yeah, we try to make the most of our chances, take the most of our chances today. The ball is in the air. We'll attack the ball. That's what we're preaching all week. Let me show it today.


I want you to ask yourself, do you feel comfortable in getting a job in the future? And this is not just a situation in Kerala, this is the situation across the country.