Hi, I'm Elizabeth Gross. And I teach interdisciplinary humanities for the honors program and also service the colloquium coordinator overseeing those honors colloquia courses. And I'm very happy to read to you today from my book, This Body, That Lightning Show. It's just appearing into my virtual background, but which came out from the Wordworks Press in June 2019. And also features the amazing, amazing cover art of my colleague Nora Lovell, also in the honors program. So I'll read a few poems from This Body, That Lightning Show. And then I will share some of my other work with you. I'll start with an irresponsible fragment of Sappho, which there are several of these throughout throughout the book. I say irresponsible because while I do read Greek, much of the Greek is missing in the fragments of Sappho. And in some places I've taken permission to fill in some of the blanks with the words that I think belong there, even though there's absolutely no way to know. Fragment 20. On the stock brightness and with luck fate will take harbor in the black earth. Sailors might lift in big gusts to dry land. And might sail heavy things like wind and everything raining, if this work dry land. In slopes of Thera, after the fresco of Akratiri Thera, 16th century BC. And this one has an epigraph also from Sappho, but too small for me to translate in any way that changes the beautiful work that Ann Carson did. Fragment 162. With what eyes? And it's a question. One. Atlantis or not, accident in the form of a goat discovered the city. Famous and lucky, the goat fell through centuries and centuries of volcanic ash. Archeologists followed in all. Did the goats survive? Do goats have the kinds of eyes that see color? Two. The only way to make something last is to forget about it for a long, long time. Three. We just bought a copy of the ancient fresco, a birthday present for my father on a lark. The red orange sky rides heavy on white mountains winding just over the antelopes, lapping heads hung up in the room days before mandatory evacuation. That sky, the only solid shape. Should we take it with us along with the insurance papers, the family photos? No, leave it on the wall. That one must be my voice. My family didn't know the story, what they survived, painted animals accustomed to loss. Four. 21.5 hours to Dallas, stopped in our car in an endless line of people waiting to run for our lives. Five. Before Akritiri spewed into the sea, the citizens packed up their jewelry or whatever and fled their painted halls. If they died in their ships, no one knows about it. Six. Then flood, then return. Drive to understand what happened here, but keep the windows up. No one should breathe this. Twisted trees choked by saltwater and muck holding up the unexpected. Chairs, boats, cars, the sky is the limit. Tiny pyramids of mold and dust piled up on all our picture frames, not one of them crooked. A hole in the ceiling of my parents' house, the approximate size of coffin, me underneath thinking lucky, lucky, lucky. Looking clear up to the blue plastic tarp and the light shining through. Seven. The strong black marks around the antelopes painted eyes took everything in, as tree bark darkens after rain, gathering depth, or as the eyes of a living deer recede wetly from this world into other, quieter worlds, caught by surprise just after sundown, which belongs to them. Eight. When I ran away to the archaeological museum on a one-way ticket to Athens, I met those antelopes, original eyes at the top of the stairs. I wasn't expecting them. Didn't know they'd been transported from what was left of their island. Wherever they stand, they guard the house, shadowless, holding up the walls. I stood under their gaze for a long time, except there was no time. Everything was protected. This body. This body, that lightning show in the wide back window, that window box of dirt and last year's roots, that old saw, waiting quiet in the shed, that noisy mini factory of hungers, those counting seconds before thunder, the television remote on low batteries, the metronome, the practice of sight reading, the wind under the floorboards, the hard rain pooling in the window sills, the reddening of certain kinds of fruit, the handmade bowl with fingerprints left in, the loud cicada dusk, all questions, the thread, the roped off border, the string instrument played pizzicato, an off key. One more from this body, that lightning show, which although it came out in 2019, is quite old work for me. I had the pleasure of reworking with a very talented editor at the Wordworks, but mostly these poems were completed in 2010 or 2011, and much of what was going on then in my work, as you've heard a little bit already, is processing the aftermath of Hurricane Katrina here in New Orleans in my own experience of evacuation and displacement following the storm. So this one picks up in that story that after returning to New Orleans, Levy return. The riverside is quiet as a sleepwalker, but overhead there is a racket of green parrots in the electrical transformer grid, invisible except occasional ambassadors coming or going, but loud. Either it's the warm that draws them or the hum of power. Are they still set up in houses in their dreams? The new generation, all wild now, not knowing they weren't from around here. Late afternoons, I walk the low ridge of the flood wall. From the riverside, the city is just wires crossing the sky, a bicycle riding the horizon, horses running circles at the electric tower's base. Let the light leave me in tall grasses that sometimes appear when the river is low. So now I'd like to read a few poems from Dear Escape Artist, a chapbook that came out from Antenna in 2016. And it's very close to me because it was a collaboration with a dear friend and very talented visual and book artist, Sarah White. We letter press printed and hand bound the edition, letter press printed the covers. And the work is also full of her gorgeous ink illustrations showing you a few of these in places where it interacts with the text as well. So I'll just read, I'll just read a few of these. Dear Escape Artist, I was watching underwater for your last big thing. Saw you pick the lock with the same frayed rope that tied you up with. Was there a they or do you do it to yourself? I'm always imagining a they. Perhaps this is something we have in common. I wish we could talk it over, high up on a ledge, feet dangling just to pretend we're not holding on for dear life. Dear Escape Artist, my research tells me there are at least three ways to die in an escape or die performance. Drowning, suffocation, falling and occasionally electrocution. But this was something else. Despair. The word calls up a fanting couch. The word is weak. There are times the mind invents a rescue helicopter and it's ladder flinging out to it like a tongue just to get anywhere else. Dear Escape Artist, I had a dream this morning I was you. The trap was set. It was the kind of dream that feels continued from another dream. Mine or someone else's bleeding through. I was in a ferris wheel in black and white. It was a famous movie, a theory of evil. At the highest point, everything so still below paused almost except a single kite whipping the gray air. It's hard to watch the struggle as if its neck could break. The dots move slow on the ground, predictable in circles. Why not squash them? A man says, who is also me. I had to exit the conversation before we started coming down. Dear Escape Artist, lately I can't sleep at night so I construct an elaborate escape, build it up in layers around myself like a wasp. I start with simple rope and then add chains, then glass, a weighted tank with tiny holes drilled in, open to the tide that rushes in, all inside an iron cave, suspended from a crane, draped in a blanket of bees, balanced at the edge of the world between water and the nearer parts of outer space. The airless dark, no one can breathe. I can rest knowing there will be something to do with my hands. Illustration without one. Dear Escape Artist, on the radio I heard about a kind of shrimp that makes light with the snap of its claw underwater, launches a bubble so fast it burns hot as the surface of the sun. Can you imagine letting go of a whole star? I don't know where the light goes, but it must be reflected somewhere, right? A floating plastic cup becomes a sudden moon. Dogen says the moon does not get wet when it's reflected in the water, nor is the water broken.  Dear Escape Artist, tell me another story about the world. I know what I see, so make me doubt it. What the audience remembers is the story you tell after, not the act, whatever they were looking at when they missed everything. So I'd like to close by reading some more recent works, some unpublished works. This first poem was written in the summer of 2019 when I had the opportunity to teach at Louisiana Correctional Institute for Women through the Newcomb College Institute and Operation Restoration program. I was teaching interdisciplinary humanities, like a college prep course, for students who were just entering the degree-seeking program. And yeah, so this poem came out of that experience. Passengers side window. All summer the water is high just underneath us where the highway skirts the edge of the swamp. The few trees farther out make v's of moving water where the current slowly wears them down, halfway between a living thing and the ruin of that thing still standing, a few last vertical ambassadors between us and nothing. I mean between your car barreling westward down the stream of the elevated highway and the lake. I want to say something about this landscape, what it does to me, to take it in and take it in each week, never stopping to and from the prison where we teach, losing the light on the way back in the tunnel of green before we hit the water. Sometimes after we talk and talk, can't stop as soon as we pass the last of the razor wire. We want to remember everything everyone said. Each rare human glimpse inside this place we're expected to forget because this isn't where the story is or when. The story that matters is the past, what you do to get here. I can't deny wanting to know, but I can leave it in your car with my phone, my wallet, my keys, my water bottle, my hypothetical weapons, anything that doesn't fit in the clear plastic school bag I carry to clear all checkpoints. I open the glove box, you open the trunk, this isn't the story that matters either. Their lives do not go blank like the missing horizon where lake meets sky. Other evenings after we just drive, car radio scanning for its preset stations as I search my mind for the words that might help us put away whatever we witnessed inside or understand it. Somewhere between what we can't know and what we can't say, one night the moon burns huge and orange like a thumb over the camera lens through rare breaks in the trees, high and cool and bright by the time we reach the swamp where we can really see. Just now when I mentioned the moon, I felt a moment of relief like I bent the thing I meant to say into a metaphor accessible to anyone who's tried to take a picture of the moon or explain exactly how the moon had changed them impossible. Inside the prison, the classroom is a classroom and the students are students around an ordinary table discussing what it means to be human. As if humanity isn't something outside this classroom, they are asked to prove over and over with their bodies even here lining up in the hallway for the guards to pat them down as you and I take our seats on the far side of the classroom so we don't have to watch. And now if I were to mention the roses in the prison yard, everyone would read them as a metaphor for hope or worse some thorned beauty of survival wrong because these roses are real and tended by women most forget are alive. And if I were to mention the birds tilted and soaring wild and uncountable with that image of freedom be enough to free us throw us back into looking away. These last two are my only pandemic poems which seem fit to share in this strange virtual format. So these are the newest housework, May 2020. As the world narrows, our dominion grows.  The home is everything, everything now, keeping track of which vegetables are likely to turn next in the fridge, sweeping and planning and feeding, tending to elders by phone. The weariness we carry in public places too. Are those footsteps too close? And yet I find myself following the moon. Usually I wouldn't walk at night. Beep beep a man says somewhere didn't want to scare ya. He throws back one more warning wheeling by on bike. Watch yourself in this weather. The moon, I say. But he's already turned the corner. By now perhaps you've noticed I contradict myself. Or perhaps you ran outside to gape at the moon over the cemetery like I did. Penelope waited almost 20 years to see her household piled up with death. She ruled quietly even as the plague of suitors infected the house ate everything. Meanwhile, she orbited her own life as a satellite so they couldn't touch her. Where is the epic of her life indoors? Like us, her work was slowing time and grief. Heading home, the street lamp shines brighter than the moon churning with wings. It's May. I'm too late to shut out the lights to keep the termite swarms out already worming through the house's seams. I watch from the porch as darkness swallows the neighborhood. Tomorrow I'll sweep their spent bodies into the tub and down the drain, but I'll find their wings flashing back little scraps of light for weeks. This last poem that I'll read, I just learned from the 2020 Words and Music Contest from the Faulkner Society and Podumka View. That's very exciting. This was also a pandemic poem, one of the two that I managed in this time. It's in a form called the guzzle person form. Actually, it's my very first attempt at this form. So very exciting to win a contest. Very first guzzle at the end of the world, April 2020.  Relief. Something finally stopped all of us at once, like a whistle in a schoolyard. Freeze. I'm one leg balancing. Finally stopped. The clear green waters of Venice, flowing with dolphins and swans, are just a fantasy glimpse of a post-polluted world. Our high emission flying. Finally stopped. Experts say the mask I wear protects you more than me, but they don't know the pleasure I feel. Not recognizing my own reflection in car windows when out walking. That mirror gazing finally stopped. Erasing my spring calendar, I dimly recall how many times I wished to slow down time. Not like this, of course. Now the future begins somewhere years from now, when the suffering finally stops. One of my neighbors died.  My concentration is sharp. I'm not writing. I can only read the things my students ask me to.  Alone in the house for months, I lose the sense of where my edges are, expanding until I imagine draping these walls around my body like a robe. All other daily dressing finally stopped. It was hours before Mr. James stepped out of his purple house to say his nephew passed. Relatives arrived distant until a downpour drove them close. The rain long passed when they're wailing finally stopped. On another endless video call, the birds outside trigger my microphone to unmute as my days stretch on, screen bound, indoors, waiting for someone else to finally stop the zoom. I focus on my virtual backgrounds, dolphins, light moving against green leaves, aquarium scene. I can make parts of myself disappear by drinking from a glass, reverse genie summoning finally stopped. I lost my job, not right away like so many I love who are struggling now, but after quarantine, I'm never going back to the work the office I love, our thoughtful planning finally stopped. From here, summer is an unthinkable hot blank, and yet I long to leap for it. I try to explain to an internet friend that I don't have to be this Elizabeth anymore, all that performing finally stopped. Thank you very much for your attention. In my reading, I just read and read and didn't really talk about my work, but my understanding is there will be an opportunity for Q&A. And yeah, I'd love to talk about anything there. It's a real privilege for me since I'm a poet and have been a poet for a long time, but that's not my role at Tulane to be able to share this other side of my work with this community. So thanks again to the library and especially Amanda for reaching out to me to participate in this.


This study found that transrectal ultrasound and urologist Julie Guided Pelvic Floor Muscle Exercise, PFME, was associated with improved urinary continents following radical prostatectomy, RP. This technique was also found to be an independent prognostic factor for urinary continents at various time points after surgery.


Hello, hello, welcome to my session on Ninai and Boothi-Rome, tools to generate abstract Wikipedia-like text using Wikidata items and lexemes. My name is Mahir Morshad, I go by user Mahir256 on wiki, I am a graduate student in electrical and computer engineering at the University of Illinois, and I am an administrator on wiki data and the Bengali wiki source. In the last couple of years, since the abstract Wikipedia and wiki functions projects were announced, I have been interested in getting lexicographical data ready for text generation purposes. Some of you may have seen me at previous events discussing matters which have some relation to that. Well, today I want to discuss the sorts of tasks and planning that I have found necessary to get your language to the point where text can be generated for it, starting with work on wiki data items and lexemes, then on to abstract constructors and concrete renders, and finally putting these all together. Before we do so, however, it may be worth briefly overviewing wiki data items and lexemes. So what are wiki data items? In short, wiki data items are essentially structured, multilingual, linked, and machine readable pages about different concepts. All sorts of stuff, from people and places to things and ideas alike, can have wiki data items. Information about these concepts is stored in the form of individual statements, which basically represent individual facts that we can separately add qualifications and citations to. The items themselves also have human readable names, brief descriptions, and possible alternate names that can be translated into your language. And many of them also link out to various other wikimedia projects. It's possible to get information out of all of these items using the wiki data query service. And there are any number of outside projects that use wiki data's data every day. No matter what language you do speak, it's important that wiki data items be modeled consistently well so that we can get information out of it properly. And what are lexemes? Whereas items represent different language-independent concepts, lexemes represent words and other linguistic units used in a single language, from nouns and verbs to entire phrases and everything in between. Each lexeme includes not only information about the language it is a part of, and its grammatical category, whether it's an adjective, an adverb, or something else, it also has individual forms listed for those words, which change depending on how and where they are used. And individual senses representing different meanings that a lexeme might signify when used. Lexemes, forms, and senses all have statements just like items, so that information about words, phrases, and their parts can be similarly qualified and sourced. The senses on a lexeme in particular, and the statements on those senses which link out to items and other senses, are critical for ensuring that abstract wikipedia can discuss different concepts in appropriate ways. This brings us now to the abstract wikipedia. In general, its aim is to make information accessible in more languages by essentially putting article information into an abstract language-independent machine-readable form, sort of like a wiki data item with the potential to represent more complex ideas. And then having software turn this abstract information into text in any given language. Both the information and the text generation software is still meant to be provided and maintained by a community, in the case of the software possibly hosted in the wiki functions project. Ultimately, the idea is to ensure that anyone in any language can work on the abstract article information, while those interested in text generation in their own language can separately work on aspects related to it. Now, there are two types of objects that are important for the rest of this presentation. Besides items and lexemes, of course, constructors and renders. So what is a constructor? Well, a constructor represents an abstract unit of meaning. This unit can be an entire sentence with multiple parts to be filled in, a type of phrase with a single slot, or a singleton for some concept that modifies other constructors. The machine-readable articles of abstract Wikipedia are ultimately planned to consist of constructors used in different ways. These constructors may also reside in wiki functions. It is possible that one constructor may be made to correspond to an entire sentence of an article. But the kinds of constructors that will be needed is best left a community decision once the project itself launches. Nothing stops us, however, from attempting to model potential constructors to handle different types of information in advance of the launch of the project. So what are renderers then? Well, renderers, on the other hand, take the constructors in an abstract article, transform the filled-in parts into pieces of text, and put those pieces of text together into coherent parts. In general, for a constructor to be turned into text in a given language, a renderer for that constructor language pair needs to exist. These are ideally functions, hosted in the wiki functions project, that can be called on when needed by the abstract Wikipedia. Most of these will likely involve exploring relationships among wiki data items and like-seems, to find the right like-seems to use, and perhaps configure them so that they fit naturally in the overall result. Like constructors, the renderers that will be needed are best provided by a language community, though nothing stops us from attempting to provide some of these now. So you've heard about wiki data, you've heard about abstract Wikipedia, what are Ninai and Udiron? Well, Ninai and Udiron are names that I have given to the two parts of a text generation system that I have been intermittently working on since last August. Ninai is able to take a custom representation of constructors and search for the right wiki data items and like-seems for different concepts. And Udiron provides functionality to build up sentences piece by piece, using the like-seems it retrieves from wiki data. I began writing these then because I wanted to make discussions of abstract Wikipedia much less nebulous and much more concrete than they were before. My hope was that having some sort of wiki data-powered text generation system out there, no matter how much influx it was, would not only as a proof of concept motivate people to improve like-seems and items for their own languages, but also would enrich the kinds of ideas that might be entertained when people talk about the Asset Unlaunch project. Of course, whether I have succeeded in this change in discussion tone remains to be seen. The software itself is currently written in Python, but this is because, of course, wiki functions in the abstract Wikipedia do not exist yet. Aside from this, Python is one of the languages that a function in wiki functions can be written in, and the structure in Ninai and Udiron is intended to make transplanting it to wiki functions as easy as possible, respecting the technical limitations that have been brought up when it comes to that platform. There's still a lot to be done, and the source code is out there for those who want to try using and expanding it. Most of the work I have done with Ninai and Udiron concerns Bengali, German, and Swedish, with a few digressions into other languages, but the rest of this presentation involves going through the process for adding support to Ninai and Udiron for a single new language. This single new language will be Dagmani. I do want to emphasize a few things before we begin though. First of all, the steps needed for each language are most likely going to differ considerably between languages. The decisions made for Dagmani support may not necessarily work for Igbo, or Hausa, or Chi, or indeed any other language. Second of all, while it is possible to model things one way early on just to get something working, as I'm doing right now, it is important to refine the model soon enough to ensure that it can handle whatever new linguistic features and details need to be handled later. Third of all, it is entirely likely that the resources I'm using for this demonstration inadequately describe certain features of Dagmani. And so modeling the decisions that I, as a non-speaker, have made with them may well need to be undone or adjusted by Dagmani speakers or others better acquainted with this language than myself. With these disclaimers out of the way, let's begin. We should first start by considering precisely what statements we want to make with this system. In the interest of time, and to ensure that this demonstration doesn't get bogged down in much detail, let's just make some simple assertions about the kinds of things different people and animals consume.  When turning these into abstract sentences, it is important to be able to break down their components and identify the relationships between them. Consider the sentence about monkeys and bananas. The sentence is at its core about eating, with someone doing the eating and something being eaten. Usually these two participants, by themselves, are not saying anything about themselves when they are uttered alone. They can, however, be linked by an action, to say something about both of them. One can argue that applying the action of eating to the two participants yields a meaningful statement about them at a given point in time. In a way, it's almost like to eat is a function, in this case, a constructor, which takes two participants and produces a statement. In NINI, the actual activity to eat is bled out into its own input to a more general constructor action, alongside the two participants, for reasons which will become clear later. We can transform the other three sentences to use constructors in a very similar way. Some of their components can themselves be broken down and reanalyzed into function-like formulations. In the sheep-water sentence, the relationship between much and water can be considered applying a general attribute to a noun, hence the attribution constructor. And the position in space of the sheep is in closer proximity to the speaker, hence the proximal constructor. Remember how wiki functions can host various things to be used by abstract Wikipedia? This formulation of constructors as functions taking arguments is precisely inspired by the kinds of objects wiki functions is designed to hold. Now, if you were planning to generate exactly these sentences in your own language, you most likely will not need to repeat the process I just went through. It is entirely possible that the abstract representations of the relationships I described would be the result if I started with other languages. What follows, however, is important for every language to do, possibly separately. This is where wiki data comes into play. The first thing we need to do is create lexemes for the words in those sentences, or rather we should check first whether these lexemes already exist, searching for them by going to the search bar and prefixing L colon to the lexeme we have in mind, and then expanding or fixing the ones that do exist if it's necessary to do so. Remember, we need to create only those lexemes which are actually missing. For the purposes of this demonstration, however, we will pretend that none of the lexemes we need exist, so we should create them all. Let's begin with the monkey banana sentence. We will need at least three lexemes here, the two nouns for monkey and banana, and the one verb for to eat. In each case, we can go to create a new lexeme by clicking create a new lexeme in the sidebar. There, we need to specify the word in question, the language of that word, not body in all three cases, and the lexical category of each word, noun or verb, as the case may be. Once we have specified each of these things, we can move on to adding some critical parts of these lexemes. The most important of these critical parts are those that tell people what each word can mean. These are the senses. Without senses and without an external source that might provide any meanings, a lexeme is effectively meaningless. Let's add some to the lexemes we made. We can add a sense by clicking add sense and filling in a description in at least one language. We know that this one means monkey in English, but we might say that it means monkey in each of these other languages. A talkbani speaker, rather than just repeat the word, should come by and add an explanation in talkbani of what a monkey is to this sense. We can do the same thing with these other lexemes. Once we add a sense by clicking add sense and filling in a description in at least one language. We know that this one means monkey in English, with these other lexemes. Once we have added meanings to these lexemes, we should add at least one form to each of these lexemes. While the lemma is important for identifying a word, in many languages the lemma is not directly used in a sense. Some transformation of it is used in said. In talkbani this is true of nouns, which have both a singular and plural form, which lend themselves to classification, and it is also true of verbs. But both of these discussions are a bit too long for this demonstration. We can add the base form of the verb as a form by clicking add form, filling in the base form, and then saving it. On nouns we can click add form, fill in the singular form, and add a grammatical feature singular to that form. Then we can do likewise with the plural form. We've added a lot of information to each of these lexemes, but the power of text generation is only really realized once they are connected to other things on wiki data, or rather when their senses are connected to other such things. This way, for a given concept, if we start with a wiki data item for that concept, or a wiki data lexeme in another language for that same concept, we can follow a property trail all the way back to any other language's lexemes for that concept. There are a lot of properties for this, but there are two in particular that will be useful for us. The first of these specifies for a particular lexeme sense an associated item for this sense. It links a meaning of a lexeme, typically a noun, to the wiki data item corresponding to that meaning. To add this to the sense on monkey, we click on add statement under the sense in question, and then type item for this sense in the box that appears, or p5137, which is the property ID for that property. We can then search for the wiki data item for monkey, click it, and then save the statement. We now have our first link between this thugbani lexeme and another entity on wiki data. Since other lexemes in other languages with the meaning monkey can have exactly this type of link, this means there is now a link between this thugbani lexeme and those other language lexemes. Let's do the same for banana, and then the do the same for to eat. Note that for to eat, which is a verb and not a noun, we use a slightly different property predicate for, but the logic is pretty similar to item for this sense, so trading it separately will not be necessary here. The second of these properties is useful when there is not yet a wiki data item corresponding to a particular meaning, so that item for this sense is not applicable. If there are multiple senses across languages with that meaning, it may be more feasible to just specify that one of those senses is a translation of the other. While we don't have to use it for any of these lexemes, given that there are already items for monkey, to eat, and banana, let's try linking to eat to the Igbo lexeme sense with that same meaning. For this, we copy the lexeme sense id from that lexeme, add a translation statement, and paste that id into the box that appears. Once we do the reverse operation of the Igbo lexeme, we have now established a link between those two. No wiki data items are required. If there is an appropriate wiki data item you can link to, you do not need to add translation. I cannot emphasize that enough. On the verb to eat, there is one more property that you will need to add, and more on this property is shown in the link below, but we don't need to move along to the actual act of forming sentences with renders. Before going further into it, however, it is important to discuss briefly how we are forming sentences. In short, we consider sentences as formed through attaching their words together in a structured fashion, forming a sort of tree with a root at one word, in this case sleep, and branches to other words, namely the other words in the sentence. There is a project called Universal Dependencies, which is attempted to make trees like the one you see here for sentences in more than 100 languages, using the same types of connections in as consistent a fashion as possible. With respect to the Dagmani sentences, we can observe a few things about how they are structured. For example, in this diagram of the sheep-water sentence, we see that the subject of the sentence, namely the sheep, precedes the verb, namely the drink, in this sentence. It therefore is important that when a subject needs to be connected to a verb, we must attach it to the left of that verb. This can be specified as a method in Udiron by calling a function that takes a subject and a verb and performs exactly this attachment. Because lots of other languages link subjects and verbs in the same way, there was already a separate function made specifically to do that that could be called upon. So we didn't need to re-specify everything ourselves. Just a brief reminder before going on, when you look at this code sample, wiki functions doesn't exist yet. Otherwise it would be possible to turn each of these functions in variable names into IDs and thus make the entire source code translatable. While in Udiron our setup to be as easily transplantable to wiki functions as possible, the lack of source code translatability is just one thing I could not address. A similar sort of function can be written to deal with each of the other structural relationships in this sentence. Objects of a sentence, like water here, following the verb in the sentence can be handled with almost exactly the same sort of function that was used to deal with the subject-verb relationship. In this case the object needs to be attached to the right of the verb. Adjective noun relationships also use similar handling, as does the demonstrative noun relationship. The handling of the suffix that appears with the verb in this sentence is a bit similar but also a bit different because the function in question, which is called whenever a verb must be marked for the imperfective aspect, can be written to always use that suffix rather than require a provided suffix for reasons which I hope will be a bit clearer when we go into the parts of this system that actually interface with the meanings of words. These are the renderers. If we return to the original abstract sentences and here I flushed out the sheet-water sentence in sort of the way that Ni-Ni expects it, there are two types of objects within them that need to be handled, the basic entities and the constructors. With respect to the basic entities, Ni-Ni natively has functionality, given an item like these four, or a lexeme sense, to search through wicked data properties to find a lexeme in a particular target language. We just don't have to do anything special here. Remember the item for this sense property and the translation property? Here is precisely why they are so important. This then leads to the constructors, each of which will have a corresponding renderer. By the time we need to render a constructor, we can assume that their inputs have been processed, either into words or into sequences of words. The main activity of the renderers for Dagbani will be to invoke one of the functions mentioned in the previous section, the ones that attach things to verbs or to nouns. The renderers for attribution and proximal in Dagbani are in fact as simple as that. The action renderer, however, given the potential generality of the action constructor, actually is split into multiple sub-renderers. One handles subjects, like the sheep, one handles objects, like the water, and one handles inflections, like the habitual inflection. These sub-renderers for Dagbani, luckily, are just as simple as the other renderers. It's actually possible to add custom functions that must be run at different points in the rendering process. For example, many constructors in different languages have functions that add end punctuation, such as periods, after rendering, if the constructor in question is the outermost. We can do the same with the action constructor, which is here the outermost, in Dagbani. We can now try rendering our abstract sentences. Because Nina and Udyron are currently written in Python, we need to start a Python session first. Then we need to import a bunch of stuff. Then we need to type out one of our abstract sentences. Then we need to call a method renderer on that sentence, specifying that we want to render it into Dagbani. And voila! You have now seen the basics of how abstract Wikipedia-like text generation can work with Nina and Udyron. There may have seemed like lots of aspects were presented at first, but just the functionality shown of a whole lot of sentences just like the ones I showed. I'll admit that some things were discussed rather quickly, or had been gone past. But I believe that the rest you have seen is nevertheless reflective of the most important steps to take. It took lots of repetitions and trial and error in designing the system. And by the way, Nina and Udyron are still living continually developing pieces of software that I frequently consider expansions and revisions to. But I believe that this whole process is to ensure that the system, which may well power the abstract Wikipedia, remains both flexible and powerful for all languages. I hope from this demonstration you recognize some ways that you can help right now to make text generation in your language possible. Here is a recap of some of the most important things. First of all, create like-seams. The words that you use in your language right now will definitely need like-seams if they're going to be used in a text generation system like this one. Make sure to search for them before you create them. If they already exist, try to add more information to them, and especially senses. A form or two might be nice. Link like-seam senses to items. If getting the right word is key, then you need to be able to arrive at it from other possible entities on Wikidata. Since Wikidata items are language neutral entities, linking like-seam senses to Wikidata items via item for the sense or predicate for or devinim of, as the case may be, is perhaps the simplest way to ensure that the right like-seam sense can be found. Link like-seam senses to other like-seams. Of course, not all like-seam senses have corresponding items, and that's okay. We have properties like synonym or translation or antonym or hyperonym or pertainin or probably something else I haven't heard of to ensure that these senses can still be found when starting from other like-seams. Think about how you put sentences together. Whenever you put a sentence together, no matter how simple or complex, there may be some rules as to how parts of this are done. Try to formulate these rules. They could be entirely informal or they could be based on linguistic expertise and research. Whatever the case, see how much you can capture in a sort of functional form. Think about how you express meanings. Similarly, when you come up with words to indicate a particular concept, there may be a number of different possibilities to arrive at equivalent expressions or there may be a specific manner used all the time in your language for that concept.  And with that, thank you so much for watching. You can find me both on Wiki and on a variety of platforms if you have questions about Wikidata-based text generation in general and Ninaia and Udiron in particular. Enjoy the rest of Wikimedia!


So you have a blueprint in your level and you want it to target something in your scene to make it invisible when you press E, not a problem.  To find out what that is, click on your target in the scene and on the right it will tell you what it is. Mine is a static mesh actor so that's what we're going to set it to down here. Then drag it in, get, drag out and set visibility. Once you've done that you'll need to make this variable public, compile, save. And now if we click on our blueprint object, we can use the eyedropper to manually set the target. You're done. Now every time you press the E key it will turn invisible. Hope that helps and as always I'll give a fantastic day and I'll see you around.


which I'd like to tell you. So the problem, we looked at percolation and some interpretation of what it means to have renormalization for it. The other thing which I like to do is to talk about the conformal field theory of it, which is slightly more involved. So imagine that I have on the complex plane some percolating cluster. Then I choose a domain on the plane and I ask a simple question. What is the probability that this cluster enters in an arc and lives in another arc? So if I name these points A, B, C, D, I can take this out of the percolating cluster. So I have a domain like that, an arc here and another arc here. What is the probability that this happens? This is called a crossing probability. In fact, for any random process you can define it, you are interested in the case of percolation. It is just because we are now focused on percolation, I like to ask what is the probability that this happens? In fact, one of the exercises I have given you is a similar problem in the exercise sheet that you do by simulation. So the way I organize this is control the boundary conditions. So if I let's suppose that percolation cluster is black.  In fact, now the percolating cluster doesn't have a choice other than to start here and leave from there. In the exercise I simplified it to start at a point and leave at a point. But in general, you can make it a little wider that is it can start on any point here and leave through any point there. I can, in fact, because of the Riemann mapping theorem, change that into any shape I like. So I should be able to map this to any shape I like, any old shape with just four points. It shouldn't make a difference. What I therefore need is to have a method of controlling the boundary condition to get the answer. It's only the boundary which is fixing the answer. The shape is not. The geometrical shape, its volume is not. It's just the four points because you can, in fact, by a conformal mapping shape, map it into anything you like. So at this point I need to insert something which I claim that it is some operator phi of z i. And what phi of z a does is that at a, at z a, it changes the boundary condition. In fact, I have just two boundary conditions. It can either be white or black. So if I start with this segment being black, then acting with this operator phi of z will change it into white. Then again, I act with phi of z d. And it changes the boundary condition here, again at c, and finally at b. So it's essentially these four operators which when you put in there, if you can construct and recognize these four operators, it will, it will create a setting for this entity. But I need a number because it's a probability. So I claim that this expectation value is this crossing probability. And these have to be operators from some field theory. And as you can guess, these are operators from conformal field theory with charge equal to 0. Charge equal to 0 because we know from reasons I haven't told you that this is the percolation theory. So the crossing probability for a percolating cluster to come in and leave like this is given by this four point function. And we have a calculation for four point functions. So I can simply insert it from there. So this probability p will be, this is the cross-ratio of these particular four points. And this is the hypergeometric function. If you remember, we went through a symmetry calculation showing that this cannot have any other shape than this shape. I have, of course, forgotten some terms here. Yes. Particle, no. I have a percolating cluster. Percolating cluster is in the percolation problem.  And it forms a cluster. No, in percolation problem.  And you look if a cluster goes from bottom to top. Even that happens, you are at the critical point, the percolating cluster. And then you say, OK, I take this circle and I throw it on the complex plane. What is the probability that the percolating cluster comes in and goes out of this circle? You make it a little bit harder. What is the probability that it comes in this arc and goes out through that arc? Sorry, I didn't hear that. This I cannot do. I have to go through a lot of conformal field theory to tell you exactly why this happens, that this is true. Just let's accept that it's given by this four-point function. We make some observations. This probability has to be conformally invariant, that it is conformally invariant is the case. Because if you make a conformal transformation, you can take this domain to any shape you like. It should not change. So it has to be a conformally invariant quantity. It must depend on these four points. So it does. So this is a quantity which is conformally invariant and just function of the points and not their geometrical relation to each other. Yes, this is the hypergeometric function, F21, which is a solution of hypergeometric equation. And eta is this cross-ratio. If you remember when I did this calculation for four-point function of any conformal field theory, I got that it has some parallel dependence and the function dependence. The function dependence at that time I did not specify. I just left this as a general undetermined function, F of eta. But now for this specific problem, because it is the standard classical percolation, I can specify it because I now know that it has to correspond to central charge equal to 0. So there are pieces of information which I cannot give one is, why is percolation related to c equal to 0? And how do you exactly prove this? However, we can do a neat trick. Take this and take it into a triangle, triangle of side one. So where are my four points? A, B, C, and D. So the problem now becomes percolating cluster coming up and leaving here. So these points are again where the boundary condition changing operator is acting. So these phi's are now acting on the four points A, B, C, and D on one of the sides. And I choose the sides at exactly distance 1. So it's an equilateral triangle with side 1. But this does is that it simplifies this relationship a lot because everywhere you put 1 and these things all disappear. So now it's obvious that the probability of exit is just this distance. So p has to be called x. Rotationally the same, A, B, C, D. Now, why is the probability exactly equal to x? Because if a percolating cluster comes in here and this side is black and this side is white, it has no choice other than to go out that side. But on this side, I've made this part equal to white. So it only has a choice of going out through this window. Hence the length of this window will determine the probability of it. If I make the window as big as the side D, it will certainly go out somewhere. So the probability becomes 1. It's a statement about percolation which has been tested numerically many times. And it is strange that it's true, but it is true. There is a comfort. Yes, will you get that by conform? No, there is no problem with sharp points on the boundary. It's, in fact, there is a general theorem which says that you can do that. And you actually, in complex analysis, can take a boundary with a smooth arcs to one with points, a polygon. You cannot break the boundary if you are deaf, that's what I mean. You cannot break the boundary, but you can make it sharp like this, make good points on it. Okay, the problem is that we might exit from the same side we have, and with fixing the boundary condition. You see, I can, it's true that I draw these shapes, but essentially the percolation comes in through the whole side, and the option of going out the same side is not available. It has to go out through this window which I give it. So you can also imagine it here like that. In fact, a percolating cluster coming in here, going out there. The boundary conditions, the probability, I see it is just one, right? I mean, if you fix the boundary condition, that can go out in this way. No, the idea is that you have a percolating cluster, you throw this triangle on it. So it is possible that you have this situation. You have this situation, don't you? So the probability of doing it hitting this side plus the probability of, sorry, I understand what you mean. I should not have said white here. Yeah. Okay, it's not obvious that it has to be X, but it is. There is the transformation which takes this into that, has the effect that takes this hypergeometric function into just X. To go into the conformal field here of percolation, you have to admit a lot of difficulties, but we saw that just like Ising, percolation has a renormalization group and it has a CFD representation. Next. My play by what? You should apply another parenthesis, without being, and in the denominator, the parenthesis, this is not the frustration, I mean. What is missing? Z of D, Z of D should be Z of A. Okay, the cross-ratio has some rules that, okay, it's not correct. You must assume that the probability does not change under conformal. The probability does not change under conformal. And it is an assumption, or is proven? No, we accept that percolation at the critical point is conformally invariant. How? Well, it is critical percolation, it's not under. So it is conformally invariant. So if you ask a question about it, the answer should be conformally invariant. And the answer in this, when I ask this sort of question, is where are the points? Where are the four points? The only thing that matters is the position of these four points with respect to each other. So intuitively, if the segment is a bit larger. Yes. The other one becomes smaller, sorry. Yes, yes, exactly. Or you can, it doesn't matter if you make this domain, if you change this domain by this shape. The four points are in the same place, but the arcs change. Still, you get the same answer. That is with different unit cells of different size. They're just a conformal transformation of. That point is true. As I said to you yesterday, I know this problem. It doesn't have an obvious answer. If it has, I don't know it. You are right. The details of the lattice should not matter, especially when I'm at a critical point. There is something missing there. I cannot quite get hold of it. So obviously, this sort of problem will not depend on the shape of the lattice, because what is the lattice is changing is just the critical percolation value. And that is not an invariant property. For instance, in critical temperature, you can change things with changes to critical temperature, but does not change the exponents. Yes. Much together, many circles, and in India, I'll form a big cluster. Similarly, I can do in case of triangles, and I might expect the same kind of threshold probability in both the cases. Then the PC is coming out to be same from this argument for different kinds of unit cells. Yes, I'm not sure. I don't know with that sort of argument if you can change the value of PC. And you may be able to, but I haven't thought about it. Yes? It's invariant under conformal transformation. Probability of crossing, yes. But in that case, you say P is equal to x. But with conformal transformation, I could move the point C in the segment BD. Yes. Not forbidden, so I could modify the probability. Yes. That's true. So it's not. Sorry, when you change x, if you change C and bring it here, you can take C and bring it here. But then that is not, you cannot change that by conformal transformation to itself. You cannot do this by conformal transformation. You have that, there you're changing something about the physics of it. In the same sense that here I can add this arc, but if I move, if I decide to move this point here, this is not a conformal transformation. It is changing the definition of the problem. I don't think so. It is, in a sense it's obvious it's not because if you change it, the cross-ratio will change. That's the cross-ratio is supposed to be invariant. Okay, so I'm going to stop here and start a new chapter in this course and that is to look at Schaum-Lufner evolution. So the next two lectures, that is this lecture and tomorrow, I will spend on SLE and then I will stop. On Thursday I will just, I will use Thursday as a day to solve problems. No new torture. So that as much as I can get this in to today and tomorrow is my luck. So this guy, Schaum-Lufner evolution, usually in the literature referred to as SLE-COPPA, is a very powerful for analyzing critical curves. When I say critical curves, I mean curves which are scale-free paths and this happened at the point of critical phenomena when two different phases meet. Also critical paths, as I said, in the beginning of my lectures, appear when you have random, random paths such as the self-avoiding walk. So in fact, I have by this method a way of producing many critical paths by just changing COPPA. So I change COPPA, COPPA when I have COPPA equal to two, I generate loop-raised random walk. When COPPA is eight-thirds, I generate a self-avoiding walk. For COPPA equal to three, I generate the critical ising interface. Another path which is called harmonic explorer comes out at COPPA equal to four, percolation comes out at COPPA equal to six and the uniform spanning three at COPPA equal to eight. And perhaps it's not, these are not all of them. There are other paths as well, some which I know fall out of this range and some maybe have not yet been discovered. So it offers me a very powerful tool to discuss. And therefore, a methodology on the complex plane is necessary to deal with it. And then the methodology is a very strange way, if you like, or innovative way to look at a path on the complex plane. So usually we are used to referring to a path on the complex plane by its tip. So gamma of t is a complex number and it starts at some point on the real axis, hence gamma of zero is equal to A and it goes up and from t onwards it can also continue. This is the usual way to think about it. However, what Lovner suggested was doing this. He said, let us find a mapping of the complex plane to itself such that this random path comes down and is absorbed in the real axis. What is meant by the hull here is any region of the upper complex plane that the motion of the path has restricted. Restricted in the sense that it is no longer available to the path. So I have such a map which absorbs the path into the real axis. This means that it has to change with time because with time the path changes. So for each value of t, I will have a different complex function which absorbs the path and the areas which it has made inaccessible to itself. Therefore, g of zero of z is z. Why? Because the path has not existed yet. So the only map you need here is the identity. Just maps it to itself. It is possible that the path gamma comes and touches the x axis as it has done here. Not a very good drawing. It looks like it has crossed it but it really just touched it. It is allowed to touch the real axis and then continue again. Again now you see a hull has been formed. This is a bit more complex than the previous hull but still it is something which is not accessible to gamma that is this path cannot go back in there. The hull copper is now something bigger and more complex and it's not just the path but some areas of the complex plane which have been excluded by the motion of the path. What Loveder succeeded in proving was that for even for these sort of situations there is a map which absorbs all of that into the real axis. So this map g z of t still exists even for this kind of a hull. We also put in some more conditions and g t of z and then it becomes unique. The other condition we put on g t of z is that at infinity complex plane is essentially the identity. So it has a Lorentz expansion at infinity is starting with z meaning that I absorb this copper this k into the real axis but if you go far away from real axis I don't do anything. The infinity is left alone. All these would not be much fun if finding g would be very difficult. However it's not t is time yes. Well it's actually I call it time but it's actually not time. It is a real number which counts along the path. t can be finite for z infinity. It can be so for that t has to be infinite. So we are always looking at this at finite t but very large t. So the point is that at finite t the infinity is left untouched. Okay if this differential equation didn't exist it would be a waste of time talking about g because finding g would be very difficult. The genius of Lovner is that all that is explained you can just solve this differential equation and the answer does all that you want. Very, very powerful result. It's an amazing result. So this equation says that I solve this differential equation with the boundary condition g zero of z is z and g at infinity has that expansion. So the answer comes out unique for any given a of t. A of t is called the driving function.  So I need to go back to this, to my standard understanding of what a path is. So my standard understanding of a path is this guy, gamma of t. What Lovner is saying is that in fact this gamma of t is by g of t is brought back into the real axis or there is another way you can look at it. You start at origin and you apply g of t a step by step and you build your path. So which is the other expression below. And in this way I have a method of describing paths on the complex plane. The last equation is a formal writing. So g of t is applied to zero for a small t. Then you repeat for the next year. Go epsilon ahead in t and then repeat g of t. So it's really, I should have, this is really should is something like this. G of delta t on origin and then g of two delta t on this and so on. Okay, let's do a very simple example to understand what is going on. So I take a point, I take a constant value for a and that gives me a differential equation which is relatively easy to solve. So I see I have a factor round there. Two times t minus p. No, no, sorry. I think that it has a two here and that's where that two is coming. So solve this to get that shape. However, I know that if I set t equals to zero, I should get the z and t equal to zero b determines the value of t at zero. So I have made a shift in time. So this is easily solved to get this formula. So the final answer is this guy. Gt of z is a very simple function of t and z and of course it's simple because the driving function was taken a constant. I can expand it near z equal to infinity. I get the right asymptotic behavior and at t equals to zero, I take the positive square root. A is canceled and Gt of zero z is just set. So this is a solution, an algebraic or a solution to the differential equation but what is it geometrically? Yes, in the what? Yes, yes, yes. This particular equation. In the exercises in the homework, as you say, I asked you to solve it for a driving function which you like. No, there is no partial differential equation to solve. It's just an exact differential equation to solve but for the constant it's easy for any other function you may have to do it numerically or you can maybe in a clever way find an analytic function other than the constant which you can solve by hand. So what is it geometrically? This solution, what is it do? It's a path which starts at A and just goes up, just goes up. So gamma of t is at any point at the position A plus IB, A is fixed, B is to root t. Just goes up and as I said, gamma of t is the action of inverse of G on A which has an obvious reason. It's because at this point, Lovner's equation becomes singular on the right hand side. So at the point where G equals to A, you have singularity. So that singularity is the tip of your path, gamma of t. Hence, the tip of the path is at G minus one of A. Where is the rest of the path? So when G acts on this complex plane, what it does is that it takes gamma of t to A on the real axis. It's obvious from here. G of gamma is A. What, where does it take A to, it takes it to some point further back. So it's actually taken, what it has done is that it has taken this path and absorbed it into the real axis. Relatively easy to believe, very difficult to believe when you have a complex stochastic process. But for this simple segment map, it is easy to believe what is happening. Hence, we can do a little as well and see that the origin is actually gone here. In other words, there is some point back here which is acting as the origin. Now, as correctly pointed out, this is the exercise. Two functions. One is the sine of t and the other is t sine t. You put it in there and see what sort of lovner paths you get. It is interesting paths come out. But they have the property that they don't touch. The path does not touch itself. It's a, in other words, it's a simple path. It does not, sorry, cross itself. I shouldn't say touch. It does not cross itself. It is a simple path. There is no point of crossing. And as you choose different functions, you will see that it has no point of crossing. Now that was lovner 1924. Then we time translate forward to 2000. Schram made an observation that if you put in, instead of the driving function, a Brownian motion, you get something interesting. When you put in a Brownian motion, you no longer get just the path. You get a collection of paths. You get a collection of paths, which are stochastically or generated. So he said put Brownian motion instead of a. And of course, this is Brownian motion with variance equal to one. So I put a square root of kappa to get any variance I like. And now the question is what do I get? I get random paths like that starting at a point on the real axis. Usually we take it to be the origin and it goes up. These paths are random paths which don't cross themselves, but it's not a self avoiding path. Self avoiding random walk is in this class of paths, but it's not all of them are that kind. It's a concept which at least for me was a little, took me a while to digest. It is a path, it is random, it doesn't cross itself, but it's not a self avoiding random walk. It can be for a special value of kappa, but in general it is not. It is statistically different. The only similarity is that it doesn't cross itself. So in this way I can generate a lot of paths which are not self crossing and they are random. Hence it's a very good candidate for critical curves or interfaces of interfaces, random interfaces. So here is, I could have given this as an exercise as well, but I thought it is harder. Just put in different values of kappa and see what you get. So for different values of kappa for equal to one, three and six, these are the paths you get. So we notice that there is an obvious qualitative difference between here and there. And I will argue that kappa is smaller than four which is here and kappa is bigger than four which is here are qualitatively different. We will get to that point. Okay, just a slide about Brownian motion in case there is someone in the class who doesn't know what is a Brownian motion. Brownian motion is a stochastic process which has following properties. It's continuous, its increments are independent random variables and in fact these increments have a Gaussian distribution. There are these BT and BT plus H are normally distributed. It has the property that this probability distribution function is a solution of the diffusion equation. Hence it is conformally invariant. In other words, if you take a Brownian path in a domain and you map it to another domain and hence a phi of gamma and phi is conformal. Again, phi of gamma will be Brownian. In physics literature we are used to describe its distribution by this path integral. Strictly speaking, it's a wrong thing to do because B is not differentiable, it's just continuous. But like many other things we do in physics, we do this. And maybe in this representation it's easier to see that now any mapping of B by a conformal map will give us another Brownian distribution. However, Brownian motion is allowed to repeatedly cross itself. It's the motion of a Brownian particle and if you've ever seen it under a microscope it continually crosses itself. SLE doesn't, when it goes inside the Lovner equation the produced path does not cross itself anymore. So B of t as a candidate for critical curves although it is conformally invariant is a bad candidate because we cannot have self-crossing in interfaces, critical interfaces. We are dealing with two dimensions and it's very important to note this property of Brownian motion that it is recurrent. It repeatedly comes back to the origin and that is going to play a very important role. That's this, they are. Why they are?  This is the property that interfaces have. Now the contribution made by Schramm, I should say that he actually called, in his paper called this stochastic Lovner revolution but it was this S and this S are in the right places so now we call it the Schramm-Lovner revolution. Yes, yes. And then we see that it really, the final line reproduces quite well the boundaries in critical domains. But this thing, in the sense that the complex construction that we built to obtain this curves are physically related to the problem or it's just by chance that finally we reconstructed such complex lines so that by chance they reproduce the boundaries or there is a deeper connection between the construction and the physical properties of them? In a, there is a deeper connection and you are jumping this presentation a little. There is a deeper connection but still you could say that even that deeper connection happened by chance. I don't know how much Schramm knew that this connection is going to be made. He just observed that these are conformally invariant distributions. The observation which was made later and I'm not sure who made it, maybe Karl did it was that the theory of these curves is related to conformal field theory. And since conformal field theory is related to critical phenomena in two dimensions there must be a relation between these guys and critical phenomena. However, this connection is not complete. I mean, not all critical phenomena can be described in this way, just some of them. And the connection to conformal field theory is obscure, that means not all quantities of conformal field theory can be explained in terms of these, just some. But one of the things which we are interested in which is the fractal dimension of these curves comes out to have very easy expression. They have in common the scaling events so this common feature connects them up. Okay, so Schramm claimed that they have two properties. One is the Markov property. The Markov property says that if you have a domain like this and you have an SLE path going from R1 to R2, you choose a point on the middle tour. Then you make a two-step calculation. You first do a SLE mapping, bring tour to the edge. Then it is true that if you take this gamma one and you first absorb gamma one into the edge, then tour to gamma two is again conformally invariant. So that whether it goes from tour to gamma two is independent of how it came to tour. So this is the Markov property that these paths have. And the other one is of course the conformal invariance of it, that is if you take a distribution over a domain of paths which connect R1 and R2 and you make a conformal mapping, it changes the domain to D prime, changes the path to phi of gamma and it changes the points to phi of R1, phi of R2 which are written as R1 prime, R2 prime. The probability does not change. So this is in shapes what I just said. Conformal invariance means that you make a mapping with these two end points and the path connecting them from D to D prime and you get new points and a new path and a new domain. The probability distribution over the new domain is the same as the old domain. So this is the hall which I already explained that as the path moves out of the real axis as it comes out here, it takes some parts of the complex plane which are then not available to it. And obviously what is available to it is what is left out. I didn't make this obvious. In this theory, because of the way we set up the differential equation and so on, we specifically work with the upper complex plane. And so of course, arbitrary. I just need to define a real axis and then everything works above it. Okay, now let's take the Loewner equation and make a transformation on it. And that is define a new function which we have called F here and put it in Loewner's equation. We get something simpler which is this guy. What I now have here is the time derivative of the Brownian motion. Therefore, this is a white noise. So I have now a Langevin equation with a drift force and a white force, white noise force. And we know how to solve these differential equations in physics. This particular one is called the Bessel process which is by the way very useful in financial mathematics. It has been used for a long time in financial mathematics. But for us, I mean people who don't do finance, what is important in it is that it has a drift force which is one over F. So actually a one over F force derives the particle away from the origin. If this was not here, I would just have a Brownian motion. F would be just the Brownian motion. And the Brownian motion has the property that it plays around the origin. So the Bessel process we know in physics is the balance of between these two forces, the deterministic drift pushing it away from the origin, the stochastic force bringing it back. So let's take these two steps separately. I can assume this to be zero. So I set K kappa equal to zero. Sorry, here I have done it the other way around. First, I ignore this guy. Yeah, I ignore this guy, that's true. So F squared d by dt one half is equal to two. Therefore, F squared is four dt. That kappa there is unnecessary. I mean, it's just a force of habit when I write a diffusion equation, I just automatically put a constant here. I don't need it. So what does this say? This is that you have a path which is going to infinity like a square root of t. And this is what I expected with this repulsive force. Just goes to infinity like a square root of t. Alternatively, I can forget about that. And so this and that will give me a force which comes back. So question is, when do these two forces equal each other? Of course you need a better proof, but the implication here is that there is a point for exactly kappa equal to four. Here I have a returning process and here I have a path going to infinity. And these two forces equalize exactly at kappa equal to four. So three regions can be identified. One is for kappa equal to four so that we have a path which starts at origin is a random path and a simple path and it goes up to infinity. Above four, and above four it's a path which can touch itself, it can touch the real axis so it will cut out a hull and it's a growing hull as gamma of t goes up to infinity, the hull grows. So still the path goes towards infinity but it gives you a growing hull like that. Now there is from somewhere else I know that kappa equal to eight, it becomes a space filling path. That means that it visits every point on the space as it goes up. So essentially I have three phases for SLE. Below four which is this sort of random path not touching itself, exactly at four which is a shape somewhat like that. And above four but smaller than eight which it becomes denser and denser here until it becomes totally dense. Another property of the path is that I can ask what happens if I scale time. Scaling in a space was accepted because we are at the critical point so you know that a scale invariance in a space is needed that is a scaling in the z direction. However you can ask what happens if I scale it in the t direction. t is the time variable, it goes along the path so if you scale it you are actually going up or down in the path. The flight noise has this scaling property that if you scale it by a squared, a comes out. You can take that and show that the novena process has to have this particular scaling. That g has to scale by one over a when you scale time by a squared. And therefore it follows that the hull will also scale with a like that. Yes, it doesn't matter, it's a function so you define a new function as g minus a and that goes in the denominator. It's a very normal operation on stochastic differential equations that it is in the denominator does not play any important role. So another question which we can ask is the locality of it. Is the path local or it knows of its entire existence elsewhere? So one question is that is it a random process which sort of takes this tip and then pushes it a little further ignoring the rest of things which are on the complex plane. Or suppose I have a domain in the complex plane a very far from my path and my path at some point has been in there and has come out now and is continuing here. Is it, is there, what is the condition that this gamma does not know about a? If it knows about a then it's a non-local entity. It knows about all its past as it moves up. You may want to say that for some physics processes I like to have one which is blind to its past. I will jump the calculation and just give you the answer that if kappa equals to six, it will be a path which is local. It doesn't see its past. So it can, the tip of it just follows a Brownian motion. Only one value of kappa has the property that it is local. So locality requires kappa equal to six. Yes, there was a question. Say again. Yes. Yes, we mean the path, right? Yes. I had some slides to make this calculation but I had decided not to give you the mathematics of it. So to ask if the path knows about a you look at the expected time to hit a and then you do that calculation on that and you see that if that expected time to hit a is a divergent then it will never hit it and it doesn't know about. The alternative, the sort of dual question to that is that if I require the path to not visit a fixed domain A in the upper half plane. A similar question, a slightly different from not knowing where it is and you would expect that this to be related. Again, some calculation and the answer comes out that restriction requires kappa equal to eight thirds. Eight thirds. So you might guess that these two numbers are related and in fact you are right because the SLE has a property called duality and I want to see not duality means. So take an SLE path, it is going up into infinity, it creates a hall and then I can make a cover for the hall which is this red path. In fact, this picture gives you the impression that my SLE path is the red line which is actually not, it's the blue line. So there are, when you construct an SLE path you have two dual paths. One is the covering of the other and this happens only for kappa equal bigger than four because smaller than four you don't have such a process. If you look at this now you see that this path which is the cover of this other path is an SLE which is not touching itself, it's a rather simple SLE and this is in fact the case that you have two pictures. One is an SLE path which is going to infinity, rather jagged and complex and the other is the path which just traces out its perimeter which is this path and they are both SLE, this is an SLE, this is also an SLE and their couples are related by this relationship, yeah. The restriction is that we want a path not to visit a part of the complex path to just not go in there. It's different from the other one that it has a section of itself that it sees or does not see that it moves independent of it but here I have an area and I want this path never to go in there. Now the duality says that they are both SLE paths with kappa kappa prime equal to 16. If you think of their phases of SLE the minimum was two, the maximum was eight so that minimum, maximum are related by this relationship two times eight being 16. The other way to look at it is that these two paths have fractal dimensions and if you calculate their fractal dimensions and multiply them by each other you get this relationship. What is amazing is that this relationship before SLE was known. So DH is the whole fractal dimension, DEP is the external perimeter fractal dimension and for a critical phenomenon this was known. However the explanation comes as these guys can be interpreted as SLEs. So this case six times eight over three is also 16. That means that these two paths, the locality and restriction are dual to each other. Okay I can think of SLE as a stochastic process and it is because I can write a Langevin equation for it. So I must also be able to write a Fokker-Planck equation for it. So if PSI is the probability distribution function of SLE it must satisfy this differential equation which is the Fokker-Planck equation for this guy here. Now you look at this and you say I've seen this differential equation somewhere else. And where have you seen it? It's the level two null vector which I gave you when I was telling you about null vectors except that this coefficient is now given in terms of kappa. Hence you suddenly observe that the PDF of SLE is in fact something which satisfies the level two null vectors and it's therefore a wave function or a distribution which you can get out of CFD provided you fix this constant kappa over four. Okay we fixed the constant kappa over four in front. Two amazing things happens. One is that you get the central charge of the CFD in terms of kappa and the other is that you get the conformal rate of the field associated, the H21 field associated with this C which is just six minus kappa over two kappa. This is in fact a very revealing thing. It is the question you asked a little sooner and getting here that there is really a deep connection because of this simple observation between CFD and SLE. So I can perhaps get a lot of calculations of SLE out of CFD by using this connection. Now this connection, these expressions are interesting. One of them is this that they see vanishes for kappa being six or being eight thirds which are these dual pictures. The other one is that the H21 field has conformal rate equal to zero because at kappa equal to six. So when you're dealing with kappa equal to six, whatever it is, you have a zero field and zero central charge. But we know that is because half an hour ago I was telling you that percolation has C equals to zero and H21 equal to zero of the fields which I introduced. There is another property here which I wonder if I have given. It's not obvious but this expression for the central charge is invariant under this transformation. So if you change kappa to 16 over kappa, C does not change. So I can now just make a table of the central charge and kappa and for each central charge, of course I have a statistical physics model which I can write next to it. And now I expect this to be related to this SLE and these are very famous models. The looper is random walk corresponds to kappa equal to two self avoiding walk or KPC level sets to eight thirds. A spin cluster boundaries in the Ising model or W03 level sets. This is tungsten oxide. Double diamond model, harmonic explorer, level sets of the Gaussian free field. They all correspond to central charge one on kappa equal to four. FK clusters, Ising model, but FK clusters corresponds to 16 over three. Percolation cluster boundaries corresponds to six and it so happens that 2D turbulence also corresponds to kappa equal to six. And finally the uniform spanning trees which fill out the space as you know are related to the sand pile model and shortest distance on the UST of sand pile model is the looper is random walk. So this is the other limit where kappa is eight. So these two theories are dual by this understand. This third column is still something I have to do. That is in terms of this knowledge that I have, I can construct the fractal dimension of these curves. Only one which is obvious is this UST at the very end, uniform spanning trees.  This is a two dimensional curve. These ones I have to show you how I drive, but I want to stop here. Thank you. Tomorrow will be the last part.


Good morning Hank, it's Tuesday. So I've been thinking a lot about the world's largest ball of paint, which is located in the tiny town of Alexandria, Indiana.  Like the world's largest ball of popcorn is in Iowa, the world's largest ball of stamps is in Nebraska. There are several competing world's largest balls of twine from Kansas to Minnesota, but it's the ball of paint that interests me most. So back in 1977, this guy, Mike Carmichael, painted a baseball with his three-year-old son. And then they kept painting it for, like, hundreds of coats, and then they started to invite neighbors and friends over to paint the ball. Eventually strangers showed up and Mike would invite them to add layers of paint, and now, 40 years later, there are more than 25,000 layers of paint on this baseball. It weighs two and a half tons. It has its own little house, and every year more than a thousand strangers show up to add layers of paint to it, which, by the way, is free. Mike even provides the paint. Anyway, I think the world's largest ball of paint has something to tell us about the creation of art. Like, usually we imagine art as a story of individual geniuses, right? You know, Shakespeare or Leonardo da Vinci or whomever uses, like, their innate brilliance to expand the human landscape. Now, sometimes we acknowledge that circumstances play a role in the emergence of great art. Like, for instance, for Mark Twain to become Mark Twain, he had to grow up on the river that separated America from itself during the war that separated America from itself. But mostly we think the work is done not by the times, but by these heroic individuals who, like, push us forward and lift us up. Now, to be clear, I do believe in genius. From Mark Twain to Jane Austen to Toni Morrison, there are some artists who are just uncommonly great. But I don't think genius is a simple trait, like having brown eyes. I think it's more of a continuum, like having empathy. And also, I think the worship of individual genius in art and elsewhere is ultimately misguided. Like, Thomas Edison didn't invent the light bulb. It was being invented all around him by lots of people, and he added innovations to it. And Isaac Newton didn't discover gravity. He pushed our awareness of it to new places. I think lots of us, and I include myself in this, by the way, worry that whatever our work is, it won't matter because it won't be remembered or because it won't rise to the level of genius. But maybe that makes individuals too important. Maybe in the end, art and life are more like the world's largest ball of paint. You carefully choose your colors, and then you add your layer as best you can, and then eventually it gets painted over. It gets painted again and again until there is no visible remnant of your layer of paint, and really no one knows about it except for you and maybe a few people close to you to whom you told the story. But that doesn't mean your layer of paint is irrelevant because it permanently, if slightly, changed the larger sphere. Right? Like, the world's largest ball of paint looks nothing like a painted baseball, and you're part of the reason. Whether you made a YouTube video that only a few people saw or wrote a short story that only a few people read, you've still played a role in shaping this many-splendored ball of paint we're all living with. So you add your coat of paint, or hopefully several coats, and hope that you've made the world more beautiful. And yes, eventually you will be painted over, but you still matter. Hank, thanks so much to you and all the VidCon staff and volunteers for an amazing weekend in Amsterdam at VidCon Europe. I'm gonna enjoy a couple days of vacation, and then get back to painting. Hank, I'll see you on Friday.


Hey guys, this week in the rundown, the Billet-Based Distribution Admin has been released and we have an interview with FleetBeldo about it. And we're taking a look at the Navy's review of rating titles. If you caught last week's episode, we talked about Billet-Based Distribution or BBD. The BBD initiative is designed to better match sailors and their skills to billets across the fleet. I was able to talk to manpower personnel training and education Fleet Master Chief April Beldo about what BBD means to the fleet and its implications in the future. Here's a bit of that interview. What will a better manning fit do for the Navy? Do for sailors? Well I think when we talk about any of our critical NEC billets, the command will be able to fit their needs to the sailor that's coming on board. So when the activity manning manager sets up their BBD profile, when they ask for a sailor they'll get exactly what they're asking for, that critical NEC will be filled. It's almost like a one-for-one swap. Check out the full interview on Navy Live. Also, if you want more information on BBD, check out NavAdmin 016-16 on NPC. Finally, the Navy plans to do a review that will focus on removing man from job titles while making titles more relevant for today's Navy. Next week I'll be talking to Mick Pond Stevens about the review and his plans to implement a focus group that will help look at this. Be sure to catch the rundown next week for the latest on that. Well, that's all we have for this week. For any questions, send us a message at usnpeople at gmo.com. For the Chief of Naval Personnel, I'm MC2 L.J. Burleson. Thanks for watching.