Good morning and welcome to First Unitarian Society of Madison. Good morning and welcome to another Wisconsin winter. And to another Sunday at First Unitarian Society, where independent thinkers gather in a safe nurturing and warm environment to explore issues of social, spiritual, and ethical significance as we try to make a difference in this world. Speaking of things that are different in this world, I'm Steve Goldberg, a proud, good-looking, multi-talented member of this congregation. And it's my special pleasure to offer an extra warm welcome to any guests, visitors, or newcomers. If this is your first time at First Unitarian Society, I think you'll find that this is a special place. And if you'd like to learn more about our special buildings, we'll be offering a guided tour after today's service. Those gather over here by the windows following the service, and we'll take good care of you. Speaking of taking care of each other, this is a perfect time to silence those pesky electronic devices that you just won't need for the next hour because you'll be sitting back or leaning forward to enjoy today's service, which I know will touch your heart, stir your spirit, and trigger one or two new thoughts. We're really glad that you're here today, and we'd like to invite you now to join in a moment of centering silence so we can be fully present with each other this morning. As we gather to worship together, I bring words from the Gretchen, from the Reverend Gretchen Haley. In a world that feeds on moral outrage, we are here to cultivate moral courage. In a time that prizes picking sides, we gather to draw a wider circle. And in a culture that teaches us to get for what we give, and to ask what is in it for me, we come to practice generosity, and to remember we are all in this together. And we are all in this together as we sing our first hymn, number 212, We Are Dancing Sarah's Circle. Please rise for spirit. We are dancing Sarah's Circle. We are dancing Sarah's Circle. We are dancing Sarah's Circle. Sisters, brothers, we can find, we can find our history. Please remain up for our lighting of the chalice which is printed in your order of service. Again from the Reverend Gretchen Haley, we say, in the midst of life's bitterness, we choose to sing, to give thanks, to laugh together, and to be keepers of beauty, to offer a place of belonging for all who come in gladness and in pain, to resist the push to the next moment and the next, to slow down, to breathe more deeply, to feel a part of something greater for this hour and in this space. Let us be the change we wish to see. Come, let us worship together. Please turn to your neighbors and give them a warm welcome. Once to see a story up close, good morning, it's so good to see all of you. I am seeing you with my eyes which have circles in them. Two circles, we have a pupil and an iris, yes. And today we are talking about circles and our circles are everywhere and that's what this book is about. It's called All Around Us, but before we read that book I want us to do some circles with our bodies. So make a circle with your hands. You can do this out in the audience and at home too if you want. A circle with your hands, can you see the circle? Now turn your fingers down on the top a little bit. Do you see the heart now? That's why I think that circles are about loves. Now let's make a circle with our hands, let's give ourselves a hug. It's a very small circle. Someone said it's not a circle. I guess you have to use your imagination.   And then there is the moon up in the sky that is super round. So we're going to hug the moon. You have to use your imagination, don't you? Yeah. Then we just kind of bring our hands down and rest. So those signs, those movements go with a song that Drew is going to teach us after we read this story. So this story is called All Around Us. It's about circles. I know. Yeah. I know, he says. Grandpa says circles are all around us. We just have to look for them. He points to the rainbow that rises high in the sky after a thunder cloud has come. He traces the colorful arc with his hand and says, can you see that? It's only half the circle. The rest of the circle is down below in the earth, where there's water and light and new life. That is the part of the circle we cannot see. But in my mind, I try. She was using her imagination just like we were. Grandpa and I work side by side in the garden, planting flowers and pulling vegetables.  It's interesting to think about circles in the garden. This is what Grandpa says. He saves the stems and leaves and seeds to bury back in the ground. This is another circle, he says. What we take from the earth, we return. Then he draws a circle on his belly. Can you do that? And then he draws a little circle on mine and says we even have circles inside. So we have to use our imaginations for that too.  Then they go outside for a walk in the neighborhood. And they start looking for circles. Now do you see any circles in this room? What do you see? Lights that chime over there, that gong, my earrings, the candles, the microphone tip. I saw a special circle over there this morning with our musician. That was pretty cool, a drum, yes. And in this picture, do you see the sun? That is a circle too. Look at this. On the next page we have our eyes, just like we were talking about earlier. We stare at the green and brown rings in each other's eyes for a long time and then we laugh again. These right circles are everywhere. I'll show you one more important circle before the big ground moon comes out, says grandpa. We walk way back in our yard and it is under a tall pecan tree. Grandpa seems sad when he sits here because this is where we bury the ashes of our ancestors. I don't remember them, but he does. Then our bodies return to the earth, he says and pats the ground with his big hands. Can you pat the ground? But that's only half the circle, that's the part we cannot see. Finally, we walk to the front and water our smallest tree. Grandpa planted it for me the day I was born and everything that fed me while I grew in my mother's belly is buried at the roots. I love bringing water to the apple tree. It is already taller than I am. I'll pat my head. Some people last night said our heads are circles. Do you see my child? He says we have new life with you. I am part of the circle too, the part that we can see, just like a rainbow. And our mouths are kind of circles and we're going to use our mouths to learn a new song with Drew. And you and I are going to help with motions, okay? This is where you help with the circles that we sing. I have a reading from Bruce Marshall entitled Radical Hospitality. He writes, let me suggest an image, a table, a long table where people gather to eat. It doesn't have to be fancy with expensive china and chandeliers hanging above. In fact, it's better to be less imposing. Maybe a picnic table outdoors on a warm day, imagine that. When I was growing up in central Illinois, we often had summer dinners outside. It gets hot in that part of the country and we didn't have air conditioning. By the approach of evening, the day's heat was still trapped inside the house. But outside, cool breezes began to set in. My mother and father, sister and I, and my grandmother, who lived upstairs, gathered at the picnic table outside for dinner. Dinners outside were different. The air was fresher. You could breathe deeply. Everything came more easily and it often continued after the food was gone. We could relax and be ourselves. Usually, it was just the five of us at the picnic table for dinner, but sometimes there were visitors, relatives, a friend, someone new to town who my parents thought to invite. To accommodate them, we brought out more tables and set them in a row. On one such occasion, a visiting relative from Germany had his first encounter with watermelon. He exclaimed in surprise, I have never tasted anything so wet. What I'm envisioning for this imaginary table is a table with plenty of room. We'll set places for each person we expect to join us and we'll put out a few extra settings for others who might arrive unannounced without an invitation whose names might not appear on the guest list. Isn't that a little frightening to include strangers who might be disruptive or dangerous or might not share our social graces? Well, yes, it can be uncomfortable, strangers at our table. In our lives today, we are taught to fear strangers, turning on the TV or the online news or read the paper. Strangers blow up airplanes, compete for us, for jobs with us, steal our money and our identities. We devote considerable energy to protecting ourselves from those who are not like us. So here we are. Excuse me, here we are walking. Here we are welcoming them to our table. But this is radical hospitality, hospitality that returns us to our roots, and the roots of hospitality involve not just inviting friends and family, not just those who you share outlook and value, but also strangers and outcasts. In the Christian story, Jesus was accused of inviting people from the margins to his table, sinners, tax collectors, those who would normally not be welcome at a dinner party. In radical hospitality, we greet the stranger. We invite them into our lives, even though it can be uncomfortable. We honor that person's worth and dignity and our own. As we open ourselves to who they are, what their stories are, how life looks through their eyes, we stretch ourselves to accommodate this stranger's view of the world. As leaders, we offer hospitality even to strangers we do not fully understand. Even the stranger, deserves to be heard, has value and receive welcome. There is something special about saying circle round. For me, it conjures up images of campfires with marshmallows, complete with tall tales and laughter spewing forth. Or maybe circle round brings up images of a raucous family reunion with the storyteller at the center, captivating the imaginations and the memories of the listeners gathered around. In either scenario, there is a real sense of belonging. Today we gather around the warm glow of our chalice to hear stories about belonging and expanding and love, and so that we may consider the impact of these stories on our lives and remember that everything is held in love. Belonging is our theme for the month of October, and it's not much of a stretch to see how circles represent belonging. Consider all the ways we use that word circle. Social circles, political circles, journey circles here at FUS allow for small groups spiritual deepening. I also think of people singing in circles and making beautiful music together, or dancing in circles like how we were dancing in Sarah's circle earlier. And listening circles, they are a part of a method for restorative justice. All of these circles are examples of belonging in our various communities and subgroups. It sure feels good to belong, doesn't it? I recently came across a post on Facebook that takes that idea, that feeling of belonging and it augments it. Unitarian Universalist Minister Reverend Scott Taylor notes that, the true blessing of belonging isn't that you get to come inside the circle, it's that you get to participate in expanding it. The truly healing question is not just where can I find belonging, but also how can I become belonging for others? That's a wonderful and curious question. How can I become belonging for others? How can we here at FUS or elsewhere in our lives become belonging for others? Well, maybe that is what UU Minister Bruce Marshall was talking about in the reading that I offered earlier. Radical hospitality is about becoming belonging for others. It means putting out a few extra places for others who might arrive unannounced. And it even means being uncomfortable with strangers at our table, so to speak. This feels particularly timely because last night we had our first potluck. On the second Saturday of every month through most of the program year we will be having these community meals. And as is the case for most community meals where I attend, it's a little awkward at first. When we engage in radical hospitality, we feel uncomfortable with the folks at our table, the folks who have circled round. But that's okay. Marshall reminds us that radical hospitality is in the roots of our Unitarian Universalist faith. He references how Jesus was accused of inviting people from the margins to the table. Sinners, tax collectors, those who would normally not be welcome at a dinner party. Jesus was becoming belonging for the social outcasts of his day. In many ways that was his theological statement. You too belong here. You too are saved by love. We Unitarian Universalists follow in that tradition when we honor each person's worth and dignity as well as our own. We open ourselves to the strangers who are among us. We open ourselves to their stories, to how the world looks through their eyes. We stretch ourselves to accommodate this person's view of life. We are expanding the circle to become belonging for our neighbors. We also see this expansion of a circle when we fast forward 18th centuries from the days of the early Jesus movement to the days of Edwin Markham. Born in 1852, Markham was poet laureate of Oregon from 1923 to 1931. In Unitarian Universalist circles, we know Markham for the short poem he wrote, the one that gets recited as an example of universalist beliefs about love, salvation, acceptance, and belonging. Complete with the original male pronouns, it goes like this.  But love and I had the wit to win. We drew a circle that took him in. This redrawing of the circle, this redefinition of boundaries of who is in and who is out, this is powerful work indeed. Our Universalist ancestors offer us a radical understanding of belonging, a belief that there is a love large enough to include everyone. Let me muddy the waters though. While there may indeed be a love that is big enough to include everyone, that does not mean it is easy or simple. In fact, I have some hard questions to ask about circles and belonging. What about, for example, when we are the ones about which the campfire's tall tales are being told, when the funny stories told by the powerful are actually harmful lies about the powerless? Or what if family reunions are not just uncomfortable but harmful to our health? Or perhaps we're not even invited because we've been disowned. These sorts of circles are about not belonging. For some of us, we're not even in the circle, and that is painful. Similarly, there are experiences about boundaries and belonging that go beyond the personal to the political, the historical. It is, after all, the weekend before Indigenous People's Day on Monday. What does it mean to belong given the historical context of colonization in which we live? Who belongs? And where? Back in June of this year, officials of the University of Wisconsin-Madison and elected leaders and citizens of the Ho-Chunk Nation dedicated a new heritage marker that was placed on campus, on Bascom Hill. The plaque was a joint effort, and it reads as follows. The University of Wisconsin-Madison occupies ancestral Ho-Chunk land, a place their nation has called Dejope since time immemorial. In an 1832 treaty, the Ho-Chunk were forced to cede this territory. Decades of ethnic cleansing followed when both the federal and state government repeatedly, but unsuccessfully, sought to forcibly remove the Ho-Chunk from Wisconsin. The history of colonization informs our shared future of collaboration and innovation. Today, UW-Madison respects the inherent sovereignty of the Ho-Chunk Nation along with the 11 other First Nations of Wisconsin. Let me repeat that year, 1832. That was a year that the Ho-Chunk people were forced to cede this territory, including this land on which we are worshiping today. 1832. That was just 20 years before the poet Edwin Markham was born. So the question is, who is drawing the circle? Who is in power? Who is deciding? Who is in? And who is out? The Reverend Alicia Ford is a contemporary Unitarian Universalist who gets at some of these same questions in her piece, We Are Not Guests. Though lengthy, it is worth sharing in its entirety. She writes, am I a guest here, here in this house? Are you? Are we guests here, here in this house? And whose house do we inhabit? In the small world of our lives, the borders between us, the easements, fences, gates, hedges, they serve to delineate, to separate us, to remind us of where my property begins and ends, and where your property begins and ends.  You've worked to own this small plot of land and the house erected on it. You have claimed it, it is now part of yourself, your definition of self, your identity. If I cross over your fences, I am a trespasser or a guest in your house. What does it mean then that in 1845, the United States crossed over into Mexico and took half of that country, took land, resources, labor? Was the U.S. trespasser or guest? Are there to be no consequences for taking what does not belong to you, she writes? Should we simply forget whose house we inhabit? To speak of hospitality in immigration often erases historical context. The actions of the past that have led us step by step into this current predicament. Professor Miguel de la Torre writes, perhaps it might be more accurate to speak of the responsibility of restitution rather than the virtue of hospitality. Hospitality in this case implies that the house belongs to us, that the land, the resources that are part of this house is ours, and we who now live here are being virtuous in our willingness to share. It erases the history that would have us remember that those who cross the border today, those choosing to brave the harsh conditions of the desert, those who face the possibility of death, imprisonment, deportation, criminalization, they are doing so because the U.S. once crossed their borders to extract their resources and labor. It is for them a matter of survival. It is for the U.S. a matter of restitution. Reverend Ford's continues, the prospect of restitution is scary. Where do we begin? With Mexico? With Native Americans? With territories? With the descendants of those who were enslaved? How do we acknowledge and address the complexities of our history present and, if we're not conscious, future of dominance? What would right relationship look like? What would unilateral conditions and considerations would make restitution possible? And for us, unitarian universalists, what would it mean for us to shake off the idea of hospitality as a central principle that is often attached to immigration and delve into the concept of restitution? Whose house do we inhabit? For we are not guests. Nor are we hosts. What then is our responsibility? So, we have some unitarian universalists who are advocating for radical hospitality for the expansion of the circle. This call implies an inner circle identity or positionality. Other UUs call for drawing the circle wider, even if it means we are drawing the circle from outside of its original location. And still other unitarian universalists acknowledge the limits of a version of hospitality which is attached to immigration, one in which we hosts are being virtuous in our willingness to share. This call acknowledges power dynamics and advocates for a larger justice, one grounded in taking responsibility, one based in restitution. Because we belong to a faith tradition that values the inherent worth and dignity of every person, and that believes in a circle big enough for everyone, a circle large enough to hold us all, then it seems to me that it is possible to listen to all of these calls at the same time. Yes, we should absolutely offer radical hospitality when we are in a position to do so. And yes, we should absolutely draw the circle wide enough to include even those who have done us wrong without condoning their actions. And yes, we should absolutely take responsibility to offering restitution, and in doing so help to repair the circle. Like we were sharing with the kids, there is a large, a love large enough for everything to belong. I'm held by this love. You are held by this love. All that we love is held by this love. Indeed everything, even that which is beyond our comprehension, is held by this love. Now that song ends with, may we rest in this love. May we rest in this love. And as we rest in this love, may we be renewed, for there are circles to expand. And together, we are called to do the work of this world, ensuring that everyone knows belonging. Blessed be, and amen. One way we help to expand the circle is by sharing our offering each week. And this week, our outreach offering goes to Native Vote, which in 2011, the Wisconsin conservation voices worked with the Bad River Band of Lake Superior Chippewa to stop an open pit mine produced near their community in northern Wisconsin. So that partnership turned into a highly successful nonpartisan voter engagement project that has since spread to many Wisconsin Native communities. And our offering today will be shared with that organization. I invite you into a time of giving and receiving. Thank you for including your generous giving in our circle of First Unitarian Society. That same spirit of giving and completing the circle is exemplified by the people who volunteer to make sure that these services run smoothly. So let's make sure that we express appreciation to the following individuals for their volunteering today. Running the sound system to make sure you can hear everything. Thank you to Creel Zeering. Thank you to our lay minister and Smiley. Our friendly, upbeat, smiling greeter today has been Gal Bliss. And our ushers, Marty Hollis, Cynthia Nolan, Paul Abramson and Prudy Stewart, thanks to all four of those individuals. And providing radical hospitality in the kitchen, preparing coffee, Bissnitschke and Teresa Rademacher. Staffing the welcome table, you'll find Mary Bergen to answer any questions you might have. And our tour guide is John Powell. So again, if you're interested in learning more about our special buildings, John Powell is the consummate tour guide and he will host you over here at the windows right after the service. Just a couple announcements. Please be sure to leave your hymnals in the chairs so that the 11 o'clock participants can enjoy them. The second announcement involves another kind of circle, the journey circles. And Karen mentioned those briefly during her remarks. The signup for those journey circles continues. These are theme-based small groups that meet every month and there's room for more of you in those journey circles. You can find information and registration form in the commons following the service. And you can see how gray the day is right now. But at 12.30, there'll be a ribbon cutting to mark the opening of our solar panels. And maybe that will invite sunnier skies in the future. So 12.30 this afternoon for that ribbon cutting, so endeth the announcements. Each week we take time to hold in our hearts and in our shared space the cares of this community, which if you would like to write in our book, it's outside of the sanctuary every week. Today, no, nothing was written but that does not mean that we do not bring things on our minds and hearts with us into this room. I know my week has been full and I invite us into some time just to consider all those in our lives who are impacted by worry or health issues, by fear or concern, by hurt. And to also hold up the joys of new jobs or new life, new possibilities, celebrations of love, the circle of life has so much for us to experience and together we hold that. May we remember that no matter what we are holding, we are not alone in that. We are part of a web of life that makes us one with all of humanity and all of the universe. May we be grateful for the miracle of life that we share and the hope that gives us the power to care, to remember and to love. And in the spirit of community, we get to sing together one final time. Him number 155, circle round for freedom will be our closing hymn. 155, I invite you to rise in all the ways that we do. The melody is printed in the middle staff. That's what I'll be singing. You can sing whatever you want. Let's do that one more time together. We prepare to move back out into the larger circle of the wider world. May we remember that we circle round for freedom so that we can keep the circle whole for everyone. We extinguish our chalice remembering in the words of John Donahue that to belong, to be human is to belong. Until we circle round together again, I invite you to go in peace. And before we do that, I invite you to sit down for one last gift of music.


You know 2006 But basically what is happening is the entire revenue is now getting squeezed, you know And that is why we are having this whole debate. I think the whole The the the entire assumption behind GST was that it would lead to a huge Buoyancy and revenues, you know, then then the states don't have to so so so you had first the 42 percent formula You increase the devolution from the from the center and the second was GST and and let's not make a mistake Every state supported this Okay, now there's no point in saying that It's not there and and and many states many many states said that, you know, since it's destination base So therefore we'll all benefit. Okay, so I don't think anybody went thought through this thing completely See on pay on paper something like GST makes absolute sense, you know I mean, it's a it's a wonderful thing that, you know, there should be no cascading, you know And each at each level so suppose I'm a say suppose suppose I'm making saris in in say surat So so the power loom guy, you know, he makes the he buys the yarn. He pays the tax Then he makes the the the say the the the the the the the the the the white cloth, you know And then he pays tax on it He claims credit and then that goes next to the the guy who's dying it and then and then that fellow then pays tax He then got this thing So the entire thing was based on an assumption that you know, there'll be a fantastic system where immediately you will have You know all these things. I mean, you will have tax Whatever this thing at each point, you know your your input tax credits You will get and it'll be a seamless kind of a system. Whereas what has happened is your entire Probably we are having one of the greatest de-industrialization maybe since the British times, you know What what we are seeing today, you know industries are closing like, you know, like Almost by the minute, you know, I mean and and and everywhere and jobs are disappearing like, you know Like I don't know flies and mosquitoes kind of a thing. So in such a scenario, nobody is spending There is no spending when there is no spending. There is no revenue generation, right? And and and initially everybody thought, you know that the formal sector will benefit Whereas without realizing that even ultimately a Hindustan liver and all is ultimately selling to somebody who's Who may know who may have been earning his money earlier in cash, you know Who would have been and and there was a lot of cash which was rotating within the economy today Now there is no circulation of cash. There is no spending and this is a classic recession, you know And and which India has never seen, you know a demand constrained This has never been a demand constrained economy for the first time We are seeing real estate prices falling again again now we have to see, you know What is the proportion of, you know, stamp revenue and these kind of things? How much is Is the earnings to the state? All these are being squeezed, you know And and on the other hand, they are trying to raise Revenues by all other kind of things like like for example now in UP now They've just raised power tariffs by about 12 percent at this time, you know I think I think the minimum power charge now in in UP is I think now seven rupees now, you know Which is which is unimaginable. So you will find all these new kinds of It's not only the center which is going to try to to protect its revenue turf through all these new surcharges I'm sure even states will try and work out some ways of You know raising revenues and all and these are going to happen at a time when you are going to have Continuing to have and a spending compression, you know So so so they will be a private so the private spending compression is already happening, you know And on top of that you are going to have even even even the governments sort of compressing their revenues So I think this entire this Finance Commission terms of reference all these things have lost complete relevance today, you know Because we are in a completely new kind of a thing The GST the compensation was supposed to be it assumed a 14 percent revenue growth What is the revenue growth now 4 percent 5 percent? Where is the money going to come from? So I think this is a very serious Thing you need to go as I think TK was saying you need to think beyond just whatever whether this one particular You know surcharge it has to do with a whole lot of things. What is going to happen spending? What is going to happen in the next two years? I think I think we need to look at the short term this long term and all is not going to work What is going to happen? You know, so this goes much beyond the Finance Commission. Thank you


Yeah, I showed some of this yesterday in the privacy talk on LinkedIn. They are focusing on the why you're doing this, this topic, or the technical requirement of how we're doing this. So, yes, I think that's really the competition of what we're sort of saying is the existing services around the digital driver system. And just starting to further improve it. And being more problematic with this community. We're going to trust the audience there to expect there's an innovation. And what does that expect the others? They expect the driver of booking for hotels, for planes, for trains. And so we're going to be able to get that to a couple of people. We're going to be able to get that to a couple of people. And integrate with the digital services on the phone. For example, so we're going to be trying to be, if you want to take it at all, if you want to turn it into digital services or something like that. So if you're trying to look at it, this is actually an innovation. So far, I just want to give you a price for that, which is the new idea. So obviously, the solution is this, we need to go out. So what would be the requirements for this? And first of all, a price difference. So that's the thing that depends on this. This audience of mine don't need all of this actually in the world. Not when I went out of here or leaving the US. And, well, here it is. So it's out there on the US and also in the US. The last constraint, yeah, is compared to Google. We need to do this with a spare time. So a sustainable approach would be good. So, yeah, how do we do this? First of all, it depends on, it's actually less of a code problem than more of a data problem. There's some hard problems in code too, but most of this exists for ladies, it's not very difficult. When you need it, for example, you can model it and it won't speak and it won't have that power, but it's just a metal integrated network. But for the data, there's still some actual gaps. And as a data, that basically goes to three different areas. The first one is your personal experience.  Is that the least helpful when it's just access? Because that data is given to you. You have to do that for two months, essentially. The problem isn't more of an inspection slide. That thing is also not more of a data problem, so we don't want this to be the case. The second problem of the data is what's standing data. So this is an information line, where it's the output of the data which turns out there's not really any secure coordinates which you need to identify as that kind of information. That isn't technically stated. A lot of these people have managed to do to me at once, but they don't have a problem. Unlike a lot of these sites, if one of you, within three or four months, you should be able to start a change. So shipping displays aren't going to be much. And finally, the data. So this is, like, the ACH changes. It's kind of a premature incident of information that usually only takes a couple of minutes before you have a project. There's no way you can ship that, for example, so this needs to be looked at for a while. Yes, look for those three sources of data that you need to look at. So those are the local data. So it's going to kind of as the same problem where they use, like, the data market position that we have to look at the kind of scan of the list. That's the schema law, which is actually a free and old standard by first kind of sort of computing to that. But we're still pushing that because it has gained, for example, some traction. And that contains, like, a lot of stuff, basically the data volume for the wall, and we have a lot of trouble with this stuff. It's one of those connected, like, pathology things, so, like, the inheritance, all the money, like, you know, all the money. But yeah, it's something that needs to be looked at. As you find out, in the book, he has a form of S&M or chasing spectral limitations, which makes it very easy to expect that even your passport form actually includes both the question which is part of the answer. If you don't need to, you still have to regularize questions for the text in there, as a form language, but that doesn't give us much space in standard form, of course. Then there's another connected standard for what he asks us, that's the editable list. That's essentially the file containing some chasing of data, that shows that you have a lot of stuff, and so that's something that also works. And finally, there's the barcode for your typical morning master. They also have kind of standardized VPN program. Yeah, then you have standard data. There's some specialised data source, like the studio, and then you can have what was written out of the data that you called anything you want. And yes, very, through the license, very actively developed very easy to edit. I mean, this is work, right? Is that the format side of your computer card? And then you have the most problematic part, and that's the dynamic data. It's basically no free data source source. And another possible thing is that there's no idea that this is ever going to change. Because this relies on, for example, the feedback information of the training hardware way. And I think I really want to look at data and data and be able to publish it. I don't see people picking up a lot of free data and be able to see the data and make some sense. So, then we go into what is, I don't know, APIs to your particular use. Those APIs actually exist. Many of them need to go beyond cost, but that's not really standardised. The problem there is more of a good model, I think, because they require APIs, which are, of course, the hardware for your piece of work. And they have interesting types of conditions. My model always be compatible with what we want to do. And this is one of the aspects I'm hoping we can get from it. So, I guess we're going to put it here. Is there enough to, you know, privacy indications to look at? And if you decide to look at it, and you have operational things to look at, the approaches might be on a server-side, server-complete, or you might want to do most of those things to manage the APIs and do a program for the data that has a wide, unified interface to our applications. But then the nice, kind of collective interface, and we have people actually who already serve as a data structure for that. So, I haven't found anything that we really want to implement, so that's something to discuss. In terms of existing standards or existing data formats, the Apple bullet class is just a very good update mechanism but with that, the only thing that I would actually not take was the standard age change or any kind of that. This is why we use this system. And then there's the old public transport applet, a platform, probably four times, one of those things that are lost will be in transition. As David mentioned, that's using another public transport which can be TTFS, which can live updates, but it's designed to live updates for the entire transport platform. So this is not something you can directly use for all applications. So this is going to be a really good way to say this, and allow us to subscribe, just for the one thing or the basic, or the four things. So there's a few building blocks, but this is certainly the more challenging program. So that's the theory. What do we actually have for now? There's the definition that I doubt what is it all about next week. There's two new libraries included. First one is the TTFS. That's essentially just a small paper for the use of the public transport applet system, including the format and the specifications of the applet that can be consumed by the applet. The more interesting one is the TTFS framework. That contains the data model and that contains the extraction code. So you feed that in text file, HTML file, TTF file and the initial reporting parts whatever, and it applies to this fact that you're looking for that's going to be the structure of the patient present and otherwise having tasks for the extractors or individual providers. And then the post-process data that I'll mention in this data or the hashtag that I'm looking for is data. That's part of it, so you'll have access to that. And that, for example, includes the information of the patient and that also. So you have geocomments and also more of that. Correct. And then you have two places where the extraction code is not ready and you have the type of extraction plan in the carrier and showing my platform into the carrier and which allows you to look back to your current, for example or show you the distribution of the map. Or you can actually check the connection that or you can see the map, sorry, so so you can find the workflow. The look started although it was used to be my feedback protocol and I don't start. So help is very welcome actually making this more pretty. So you need to change that statement. And then the second thing is the type of connection to the carrier which was also more of a bandwidth. And that has a finite view of what all the data that we managed to extract. It can have a lot of tasks for the location you are going to be in. That feedback is a little extra, so you can see a lot of data about it. Because the carrier needs to send out the locations, so it's also quite a sneak. That's of course the feature that I wanted to do before giving culture. I need to know what it was going to be so I can go and start. And that was actually a lot of beautiful information on how you need to have a communication with the carrier before. So I'm going to like be a core. This is how you get to do your type of stuff. I'm getting to that. The middle part is very really important tasks. And this is actually good enough to pass visual and reporting class inspection at the airport. So I have to imply business or almost more, at least with this student. And it has to be the background that's been passed to me. And this is not images, but this is actually evaluating the raw data that's been there. It's the person that wrote it. So we actually know what was being there. And finally the travel information extracted from the data mainly from the comal pack over the day this morning. So the first example is Switzerland and half of my car was from the FJS office. So it turns me up. And then you can see of course with the UK that it is probably not all the other versions of the UK as you know, the comal pack is the right side of it. It's correct. Yeah, you're going to change that in the final weeks. Those pictures are in other words so it's perfect as well. And I respect you guys. So, yeah, it's definitely possible to build something like that to the government and these girls. At least to the point where it's practically the sort of constantly certified users pay for these work flows so that's good. I think it's next year, which will be yesterday the information that came in just in the morning when we were asked to build a perfect car for all of that and so start by trying it. Yeah, but let's forget about that for a second. We need more test data. So far this is very biased to what's been said in the business channel. But since you're full of your particular life you can watch this channel if you have tickets for that booking emails anything related to works. I don't know if you're interested in that. We can, of course, look into that together just to show you how to spread our sense of information. This is not always me because of memorabilia and it's true all the way. We can't really test the past against the direction of the war but you've changed the attitude of the business or something. So I'm asking if you can actually send me more data if you want to just travel around trying to make it better. And another aspect is this is essentially just 30% because it's one of the people in that solution. There's a whole bunch of stuff there that needs to be integrated. My trust is mine. There is public transport. That's more than the model. That's why this is my reason to be building more stuff that can combine with your location. And that's definitely more important. But you know that's the fun of it. Can I ask also part of my business which I don't have in all things for example I have a criminal for certain part and I just took up the public transport cycle and edit. We have some basic editing that is to say welcome but it's coming out anyway and the integration of the this type of transport is not specific but it's working also especially between the different steps to do it. Between the writing of the app and how it goes and the schedule. That's the studio. Second question is part of the process which is the same package that requires similar stuff. What would it be made possible? The structural applications that Jean has brought into management and planning and orders as well. The expansion system for the structural data and the data model should be included as well. I haven't seen a studio actually having that kind of publication so I don't know what happened but you could build that essentially in a very simple way and it would be really nice. Thank you very much for your presentation and for the strange work that's actually done there. And you will be able to see the facilities by the right before and scrapping airport as you call it. It's okay. The other one needs scrapping but for OEM it's fine. The problem is the size of the data that you would want but the conditions you would need to make work. How many years do you have to go straight and work on that? The solution that if you actually are providing the data you get the clear coming. Okay. Here I need to look into that. If you have any needs for services that have any legal advice from my way to get to it, sure. That would be perfect. I don't want to know when you are going to make that suggestion myself by the way but if you are interested very much let's see, this is my the case of I'm your I need one to comment on the same. I have an app called CDIAPS which is about the public banks that are already in Europe and I mentioned that they have a single server that they work in the next two so the other company is the only one you have to trust which is them and they also they do web-strapping for most of the banks because CDIAPS and in fact CDIAPS I don't think it's terrible we could ask a different problem like how does it work and so on it's possible to the things that don't really work in all of the best way to do it which is it doesn't really work so we need to do this kind of analysis data analysis so so if you can actually I don't think it would work that would be something like this and it's not provided by Japan for some of the we have the policy so they are moving in the right direction but I think that's something like this we probably need to make some plans in the long run for example integrating this K-Ether's book for example for example the second question would be during all the situations of open APIs from web-strapping APIs for booking so that would be possible for example going to K-Ether's book the sender says come visit me next week and I will connect with the right and send booking booking so far is possible because when I travel I rarely post stuff myself so I don't know which description but yeah I have to be able to test another device there's probably some there must be some use of translation to use that as well for example in K-Ether's book there's a 50-shot of the K-Ether money and it allows you to get the extract from K-Ether you need to do an explicit team but you need to go to K-Ether's book and it's the method of K-Ether that also attaches to the the specification of K-Ether so I hope this video was helpful and if you have any questions please leave a comment I think K-Ether knows we are doing a great job and that's probably still a good service but I don't know if it will make sense but I think it will actually be very good I think it will be useful for most of us for most of us


Bemidji girls also in action Saturday hosting Cloak a second half Jack's down eight Laura Beberdorf finds the cutting Lexi Wade on the inbounds for two of her nine lead cut to six later in the half Jack's down double digits now rumor flatness drives and finishes through the contact to cut the lead back to single digits the Carmen Faust and Cloak a would be just too much for Bemidji Faust delivered a game high 18 for the Lumberjacks and Cloak a win 71 62 if you've enjoyed this segment of Lakeland news please consider making a tax deductible contribution to Lakeland public television


The University of Seville, working in collaboration with the Andalusian Institute of Historical Heritage, has conducted an intensive Lidar survey in a historically compelling area between the Spanish coastal towns of Capasoto and Sancti Petri. Their goal was to discover the remnants of a long-written-of temple, one dedicated to ancient deities. However, what they discovered instead was an incredibly ancient once enormous mass-dwelling complex, yet intelligently laid out as if almost akin to modern-day standards of care in regard to sanitation management, food production, and quality of dwelling for its massive population's well-being. A mega-metropolis that predictably the academics responsible for its discovery have only attempted to downplay the find, but also tried to claim it as merely proof of their original temple assertion. Clearly, they are merely backing the tale of events put forth by whomever funded said expedition. From the researchers themselves, the survey area consisted of submerged landscape, seemingly dominated by a series of ancient marches. Everything we feel was most probably intelligently managed farmlands prior to the Great Deluge, which eventually drowned this entire mega-metropolis, yet I digress.  By combining data from previous anomalous discoveries, the team created a cross-section of findings, and by a process of elimination, they pinpointed an area in which to scan. Yet interestingly, after said discoveries of the structures, they quickly and simply delimited the entire area without any further field study or investigation whatsoever. Did this rapid delimitation of the area, in regards to the lidar scanning, possibly be in an attempt to obscure the true enormity of this pre-flood ruin? During their focused investigation, they found rectangular structures some 300 x 150 meters in size. However, these discoveries contradicted their own strictly followed academic accounts of this supposedly legendary temple's whereabouts. This discovery being the mission's objective all along, yet curiously, as mentioned, any further expansion of the lidar investigations, academic funding, has been stonewalled. Could their reluctance to continue further investigations on a mission which has already clearly cost a lot of funding due to them actually having discovered yet another complexly intelligently clearly advanced pre-flood mega-metropolis? Well, we find said possibilities and the rapid growth of independently owned lidar technology incredibly exciting. An unexpected discovery was recently made by a group of scientists. While exploring an as-yet unmapped section of the Pacific Ocean, just off the coast of Hawaii, they stumbled upon something incredibly intriguing. During the exploration of the summit of an undersea mountain around an area known as the Papahanao Mo Kuakea Marine National Monument, a protected conservation area encompassing some 580,000 square miles northwest of Hawaii, researchers stumbled upon and briefly along a possibly incredibly ancient yellow brick road. It's the road to Atlantis, when scientist has quip to the press jovially, not realizing how accurate he may one day be found to be. Quote, our exploration of this never-before-surveyed area is helping researchers take a deeper look at life on and within the rocky slopes of these deep ancient seamounts. Previous expeditions aboard the Nautilus Research Vessel have unearthed the plethora of eerie aquatic anomalies. What makes the discovery interesting is its seemingly artificial nature, appearing to indeed be the legendary yellow brick road to Atlantis. The mission, made of bricks, laid next to each other in a near-perfect fashion, many of which exhibiting 90-degree angles. Others involved in the mission have also been quick to discredit the discovery, however, claiming it is nothing other than a natural formation. Quote, at the summit of Newt Kasimaut, the team spotted a dry lakebed formation, now identified as a fractured flow of high-yellow class-tight rock. The remarkable brick-like divisions between the rocks are likely the coincidental result of heating and cooling stresses from multiple volcanic eruptions over millions of years. End quote. There are many ancient antediluvian ruins which have been discovered and indeed shared here upon our channel. Many so undeniably artificial that their sheer existence due to the geological data and thusly the dating of their submersion continue to pose historical chronology a real problem and we feel if further investigation of this site could possibly be undertaken in the future, this explanation of it being a natural formation could one day be perceived as a dismissal of a truly ancient yet also clearly yellow brick road. Could the yellow brick road to Atlantis, just like that of the Bimini Road, one day be found to be a true road? Well, we find such possibilities highly compelling. Discovered in 1860 within the astounding valley of the Kings, the Atlantis Ring has since proven to have been a most incredible of finds, not only for the sacred, sacred geometry that was found to have been inscribed upon this seemingly insignificant clay ring, but also for the strange, seemingly reoccurring pattern of curses or good luck talismans wrapped around the entire magic of this once incredible yet now lost civilization. Once discovered it was said to cast a protective spell upon those who wore it, a supposed positive energy force that although as strange as that of the Curse of Tutankhamun, is one that is far less mentioned within the career and discoveries of Howard Carter himself. Regardless of the fact that it has since gone on to be an incredibly popular mass produced product, once kept secret for many years by Carter himself. Also now sold under the claim that it does indeed emit a powerful energy field around the wearer. The science behind these claims we cannot claim to understand. However, the Ring's modern popularity, along with a lack of coverage regarding this possible legend within the discussion of Howard Carter's career, we have found peculiar. Featuring two triangles, six small and three larger rectangles, with a semi-cylindrical form, it was originally found by Marquis de Grain, a blueprint of the ring was soon sent to Carter himself, who made and wore a secret replica which he kept himself until his death in 1939. In 1922, Carter would discover King Tut's tomb. Before opening the tomb, hieroglyphics above the tomb's unbroken seal were read. It said, the wings of death shall touch all who violates the pharaoh's eternal rest. Unperturbed, they opened the tomb, discovering treasures beyond all of their wildest imaginations, yet, as warned, all who were involved in this discovery eventually met curious fates, with just Carter himself left, the one person who was undeniably the most guilty party in the entire excavation. He would not die until 17 years later, at the reasonably young age of 66. During these 17 years, however, the flurry of media attention around the claimed curse persisted. Interestingly, whenever asked how he had seemingly escaped the curse for so long, he would always reply that he had a secret talisman, a good luck charm, that protected him from the curse. This initial cast of the ring Carter had made, it turns out, he seemingly knew of its incredibly important geometric significance. Yet it was not until 1940, while going through his documents, that his studies, and indeed rules of wearing the ring, were revealed to the world. His talisman, a replica of the Atlantis Ring. A relic many thousands of years old, originally made from S1 and clay, like something out of a holy grail story. It seems the least valuable, seemingly most conspicuous of finds, turned out to be one of the most, if not the most valuable, to Howard himself. Out of all the golden wonders he had ever unearthed, this one, one which he didn't even discover himself, he kept closest to his heart. It is because of this, that we find the Atlantis Ring highly compelling.


The ability to look at things differently is kind of what the Air Force is really pushing for. Doing business the old way, the same way we've been trying to do it, and the methodology that we've sort of pigeonholed ourselves into is no longer the case. It's hard to do that anymore. With rapidly changing technology, adversaries who are barking down our door, we have to be the agile force that the Air Force needs us to be. That the DoD needs us to be. And sometimes the best way to do that is to be educated. Understanding that there are different perspectives that everybody brings. It really does give us the ability as an Air Force to adapt appropriately to that ever-changing environment. Education is always a piece of it. Experience is also another piece of it. But being willing to break down those barriers and sit across the table from someone who has a different perspective than what we have. That's Air University.


Now, now, is it over? I'll wait one more minute and start again. OK, first I want to apologize at the end. I rushed a little bit through Freeness. Freeness is a very complicated concept, but I think there'll be a lot of talk about Freeness in the school. I think Camille, for instance, will talk about it. I'll also talk again about Freeness today. So today I want to talk about three things. So this is the kind of the second introductory lecture. And I want to talk about sample covariance matrices, so estimating covariances from real data, but often from a theoretical point of view. And this was actually studied in the large N limit. Well, it was studied in a small N limit. And for finite side matrices by Wishart, this is why the matrices will be at the beginning of the 20th century, I think, 1920, just something that I don't know the date exactly. So Wishart studied small sample covariance matrices. And then Marchenko and Pasteur in 67 studied the large N limit of these matrices. And then the more modern formulation is using multiplicative free convolution. So I'll explain what that is. Just a little note, Marchenko and Pasteur, which I'm going to talk about their work today, their Ukrainian mathematician. Pasteur is about 80 years old. He just moved to a cold normal because of the war. And miraculously, Marchenko is still alive. He's like 99 years old. I've heard he's now in Canada safe from the war. So I was always wondering if Marchenko was still alive because he was born in 1922. Anyway, but he is. Well, I don't think he's very active anymore. Okay, so sample covariance matrices. So I wanna tell you how large sample covariance matrices are interesting. So what's the, well, first, maybe let's assume that have some data drawn from a matrix from covariance C. Maybe to make things simpler, you can think of Gaussian IID data drawn from a covariance matrix, but you don't have access to this matrix where you have access to is a sample. So the sample, let me call it H. So H would be a rectangular matrix, which sometimes I will deny XIT, okay? So it's a variable I at time T. So I have multiple times, so I'll have T. So I have T slices of my data, which I assume to be each column each time is IID. And then what I'm, my data is actually a vector and the vector XI has actually a covariance, true covariance C that I typically don't know, okay? Or, and I'm gonna, so this data XIT, I'm gonna put in the matrix H, which is gonna be N by T, okay? So I have N variables and T observation. Be careful, often mathematician will use P variables and little N observation, okay? But my notation is N. So my matrices are always capital N by capital N, okay? But very often, if you look at sample covariance matrices, they'll be P by P matrices, because it's also to the number of degrees of freedom and so on, they use P. But I'll be using T for the observations and N for the variables, okay? So what is, and I'll use this E for empirical. So I'll define the matrix just if you wanted to compute a covariance matrix from data, you would say one over the number of samples, some T goes from one to big T of XI at time T, XJ at time T. This is how you build a covariance matrix and here I assume that either you've already subtracted the mean or the mean don't matter or you don't know the mean. So I'll never worry about the expectation of the variable X. So let's assume that you know a priori that have zero expectation for instance, okay? And this you can write as a matrix product. So it's easier to write as H H transpose over T, okay? So here T is transpose and here T is the number of observation, okay? So this is an N by T matrix. So this is a rectangular matrix. So it's very important. So this is a rectangular matrix N by T. The transpose is T by N. So this is the result, the sample covariance matrix E and it's actually a matrix element. So the matrix E itself, all right, as this product, okay? So what can we say about this matrix E? Well, one thing that if T is finite, no, sorry. If N is finite, let's say you have three variables, okay? And T goes to infinity. Well, then E converges to C and there's nothing more to say. The class is over, okay? But this is not the limit that interests us, okay? So this is what I would call classical statistics. In classical statistics, you don't work if you have thousands of observation and three by three or five by five matrices, you don't worry about estimation error of your covariance and all I'm gonna say is irrelevant. The interesting limit is when the number of variables is large and by large, I mean large compared to the observations. So I was interested in this problem because in finance, especially in quantitative finance, you often have very large portfolios, say hundreds or like 500 stocks in the S&P 500 or 3000 stocks in the Russell index. So typical people deal with portfolios with thousands of stocks and they need to measure covariance matrices using daily data and say 1000 business days is four years of data. So if you use eight years of data, you have 2000 business days and if you have 2000 stocks, you really have about the same, well, you literally have about the same number of observation as variables. And then we're very, very far from this limit of n finite t goes to infinity. So saying that e converges to c is very, very wrong. So this is one I'm gonna try to convince you today that in this limit, e does not converge to c. E is something else has interesting properties and we're gonna study the properties of the sample covariance matrix, e, okay? So what can we say? So let's, before having a model, let's just say that we have some data h. So h could be anything. It could be non-stationary. It could be random. It could be all sorts of randomness that I don't care about. It's just some rectangular matrix of data as long as the label, the rows, the rows make sense. Then I can compute a sample covariance matrix of the rows. And so, which would be e equals one over t, h, h transpose, okay? And some basic things I can say about this. Well, first of all, it might have zero eigenvalues, okay? And it often has zero eigenvalues. And to see this, I'm gonna consider, actually I'm gonna forget for a moment because if I only consider zero eigenvalues, the normalization one over t doesn't matter. And it's simpler to ignore it. I'm gonna consider matrix h, h transpose, and h transpose h, okay? So these look very similar matrices, but they're completely different object. This is an n by n matrix, and this is t by t. But you can show, I won't do it here. It takes three minutes to show that the, if this matrix has a non-zero eigenvalue, then this one will have the same non-zero eigenvalue. They share the same non-zero eigenvalue, okay? And so, given that they're not the same size, and by the way, they're symmetric and positive definite. So they can be diagonalized and all the eigenvalues are positive or zero, okay? So if you have two matrices that are not the same size, and they share the same non-zero eigenvalues, it means that the only difference could be in the zero eigenvalues. So for instance, typically we'll be dealing with a case where t is greater than n, okay? And in that case, you know that at least t minus n eigenvalues are zero in this case, okay? But you could have cases where n is greater than t and then it's on this side, okay? So if t is greater than n, I have the same non-zero, therefore I need to have quite a few zero eigenvalue. And for instance, yeah, maybe that's an interesting case. Already, okay, now I go back to sort of a sample covariance matrix that I'm trying to estimate from real data, that if I'm in the case where n is smaller than t, then my e must have zero eigenvalues, eigenvalue is equal to zero, okay? And then the number is at least t minus n, okay? So my matrix C, I could assume it full rank as non-zero and I cannot, so already you see that the matrix E is not a faithful representation of C because if I'm in this limit, which is pretty sick, I have, sorry, sorry, sorry, sorry, sorry, sorry. The limit where I have more variables than observation, if I have more variable, there are many ways of seeing it. I like to see this way, but there are many ways you could also see that the system of linear equation is incomplete and therefore they must have zero eigenvalues. Anyway, so if n is greater than t, if t is too small, then definitely e has zero eigenvalues where I could postulate C doesn't have zero eigenvalues. And so hints as a fact that the matrix E is not a faithful, doesn't converge to C. Another thing I could do that's also fairly easy where I don't really need a random matrix theory is to compute the moments. So remember the moment operator, which is one over n trace of a, so T of some matrix M is one over n trace of the matrix. And this typically, in most cases, becomes self averaging. And but I could add an expectation value, okay? So in expectation value, actually in this setup, the expectation value of E is indeed C. And so this trace operator is linear. So I do have that the trace of E is equal to the normalized trace of C. So the first moment match, but it's a relatively easy computation. You see that already the second moment they don't match anymore. So that I have that trace of, this is, I'm taking here, maybe I should be more precise. I'm taking the n goes to infinity limit with a number of Q, which is n over T fixed. Okay, so I'm taking a limit where both n and T go to infinity, but the ratio is fixed. So again, my setup for stocks, suppose that I have twice as many days that I have stocks, okay? So Q equals a half, but then I let the number of days go to infinity and the number of stocks goes to infinity and I study the properties of these matrices. And then in that limit, you can compute the second moment. Okay, so basically I'm dropping terms that are negligible as n goes to infinity. And I get that T of E square, the second moment is equal to the second moment of C plus an extra term Q trace of C, what now, normalized trace of C squared, okay? So remember that this limit here and finite goes to infinity, T goes to infinity is since Q is n over T is the limit Q goes to zero. So the limit Q goes to zero, you get normal statistics and you can show actually that in this limit, the moments match. So when Q goes to zero, when n is fixed and T goes to infinity, this term disappears and you have that the second moment of the distribution match and actually all moments of the distribution match. And again, we're back to this, that E has actually converged to C and there's really nothing interesting to say about the matrix E. But in the general case, and this limit here, when n is greater than T is when Q is greater than one. Okay, so because Q again is n over T. So if n is greater than T, that's greater than, okay. So we'll have essentially, we'll have Q equals zero, which is the sort of classical statistics. And then we'll have an interesting regime from Q between zero and one. And then Q greater than or equal to one, we will have zero eigenvalues. You can still say, you can still quantify what happens, but in the Q greater than one, the E will sort of have zero eigenvalues. And somebody asked me in the still just transform when you have a finite number of eigenvalues with certain values, in this case, we'll have a finite fraction of zero eigenvalues. We'll have to have a pole in the still just transform or a Dirac delta in the density, okay. So, but I mostly concentrate on, in this case, that's more typical where Q is where we have enough data. We have more data than variables, but not that much more. So Q is between zero and one, okay. Okay, so can I say more things about the matrix E? Well, first, before doing that, I need a model of my data. So how do I model data with a fixed covariance matrix? Well, if you were to make a computer program to generate correlated data, in many ways you could do it, it's easy to generate IID data. So you generate IID columns and then you correlate the columns. And one way to do that is you could say, work in the eigenbase, for instance, and multiply and then the variance if you're in the eigenbase, the variance is the standard deviation is the square root of the eigenvalues. And so you can generate data in the eigenbase with standard deviation equals the square root of lambda and then go back to the physical base. That's one way of doing it. There are many ways of doing it, but they all amount essentially to doing a square root of my covariance matrix C. So I have my covariance matrix C.  If you look at this combination. So H zero is IID data. So H zero is N by T, IID, normal zero one for instance. So you first generate a white data and then you multiply to the left by square root of C and then this will give you correlated data. So I'm saying that I'm a model, this is a model for correlated data. And again, in real life, there are many, many complicated things that can happen. But if I want to have multivariate stationary, by stationary, I mean the covariance is the same for all the columns. And then multivariate Gaussian, it's not necessary, but it just makes life easier to, at this introductory level, just think of everything as multivariate Gaussian. It doesn't need to be, because in large N limit, as long as the variance exists, it's enough. But anyway, in this case, we'll think of a multivariate Gaussian with a covariance C, then you can build it this way. And there are many ways to prove that this is the case. But just if you look at expectation value of one over T, H, H transpose, you can quickly convince yourself that this is C. Okay, so that your data, and this is true for every column. So this is a multiplication to the left, so multiply every column. So every column of H as covariance C, and it's IID on the time axis. So again, I like the finance analogy. It's like saying that every day you get a different sample, but of correlated variable. And this is what, okay. Okay, so now I'm building, so now I can say that E is really the same thing as square root of C, H0, H0 transpose square root of C, and then I need a over T for normalization. Okay, so this is my model of the data. And I could try to study the eigenvalue distribution of this, okay. Now remember that. Mark, sorry to interrupt your question on the chat. So on a physical note, why are we actually interested by the eigenvalues of covariance matrices and applications? I'll give examples on Wednesday. On Wednesday I'll show financial applications. Well, but we actually not necessarily interested in the eigenvalues per se, but we need to characterize this matrix and the eigenvalue gives us a lot of information. And for instance, I also mean this, my series of lectures about eigenvectors as well. So I'll also, but I need to start with the eigenvalues. First I understand the eigenvalues and then I can understand the eigenvectors. And then when I want to build, the whole point, and then there will be the lectures on, the two lectures on Wednesday will be estimating C given E. But today we're doing the forward problem. We're given C, what's the consequence for E, but the inference problem is more interesting. The inference problem will be, we're given E and we want to infer C. And essentially if we can infer the eigenvalues and the eigenvectors, we can reconstruct the matrix. So that's kind of the argument. And another reason you want to know about eigenvalues because when you invert, very often you need to invert a matrix. And if it has small noisy eigenvalues, inverting a matrix with small noisy eigenvalues is super dangerous. So knowing that there are small noisy eigenvalues is important. Okay. So again, so this I can do. Yes. So this I can do with free probability theory, but I won't use free probability right now. And therefore I'll use, I'll compute something slightly different, which is equivalent, but it's a bit cumbersome to go from one to the other. As I told you H, H transpose and H transpose H have the same eigenvalues except that different size matrices. And so, so this is an N by N, this is T by T and the normalization are slightly different. But anyway, let me compute. Just this could be slightly easier is to do this object. Let me define this object H, a zero track. Well, let me define. Let me just this object. So, so this object is a bit different where it sees on in the inside or see here is on the outside. In terms of eigenvalue, as I said, it really doesn't matter. It's just a question of keeping track of the zeroes eigenvalues and the proper normalization. But this, this, this is this computation is easier to do. And this is actually what March and go to our study. Okay. And if you think, well, since H is rotation invariant, you can actually, it doesn't matter. You can choose C to be diagonal. If you choose C to be diagonal, then it's like studying data where the variant changes every day. You have IID vector, but the scale fluctuates. So it's something that happens in finance. It's called volatility. You have on different days. You might have days where things move a lot. It's a big correspond to a big value for C. And days where things don't move much for the small value for C. So think of measuring IID vectors in a fluctuating variance way. Okay. So, and this I'll write actually as a sum. So I have one over T sum over T of X, I T J T where X or IID, but then I have this C, which I'll say that the eigenvalues of C are sigma square at time T. Okay. And I, and the order doesn't matter. So I can even rank them. Okay. So the matrix see I can diagonalize it because this is rotation invariant that could also rank. So, so a sigma square of zero with a sigma square of one would be the smallest eigenvalue of C and sigma square of big T would be the largest eigenvalue of C. And this is equivalent to some and here the either IID variables. Okay. What's nice about this form that this here, I might put the one over T here. Okay. This object is a rank one matrix. And so it has a single eigenvalue non zero and all the other eigenvalues are zero. So I can really write it as some over T as some projector. Okay. And the projector tease was just redefine projector T as X was basically vector X. T X T transpose and then some normalization in the square over T. Okay. So I have a projector. Well, and this is a this is a vector of size N. Okay. And in my normalization given the, the, that the X is our IID with variance one, this, this object is variance N. Okay. So, and so you can convince themselves that this has two, two, I can, as one eigenvalue. And in large and limit, this is the, the, the, the normal sum of the squares of this is N, N component. So it's a sum of N positive number. It doesn't work with large number. This doesn't fluctuate. So I have one eigenvalue equals to N over T. Sigma squared T. And I have N minus one. Eigenvalue. They're all equal to zero. Okay. So this is a, this is why I call it a projector projector. This is a projector in one dimensional space. There's a single eigenvalue. And on top of that, not only it's a projector, it's rotation invariant. So here I've written my matrix E as a sum of rotation invariant matrices. And so I can use the freeness that I sort of rushed. At the last lecture. To say that I can compute the spectrum of E, because I can compute the R transform of E. The R transform. If they evaluate at some point G will be equal to the sum over T of the R transform of each of these, these matrices. Okay. So I have a sum of matrices. They're rotation invariant. So I have this property that the R transform is additive. It's additive two by two. But since each of these is rotation invariant, I can add another one, add another one, add another one. And so it's additive all the way for, so I have, I'm adding. I'm adding T large capital large T. Rotation invariant matrices. So I can, so if I can compute the R transform of this object, I'll be able to compute the R transform of, of the sample covariance matrix. And again, the R transform is related to the steel just transform. So I can invert the steel just transform and get, and take the imaginary part on the real axis and get the density. So this is, this is how we go. This is not how much you're supposed to work. Did it because they didn't know about the R transform, but I'll get the same result as they did. Okay. So what, so to get the R transform of this object. I need to, to. Basically, our trend. I need to do the steel just transform. So again, I'm going to put a little T because this explicitly depends on this variance sigma T. Okay. And what is it? Well, I have, it's one over N. And then I have one over this eigenvalue Z minus. Well, this is Q by the way. Okay. So I will cue Sigma squared Sigma T squared. And then I have N minus one other eigenvalues. They're all equal to zero. Okay. So this is a, this is the, this is a serious transform of a projector. Exactly. So normally, I'm sort of cheating here because normally, the R transform is only defined defined in the large and limit. So I should only keep the terms that are finite as N goes to infinity. So as N goes to infinity, the, the, the serious transform of a projector. Is just one over Z. Okay. Which is the same as the previous transform of the zero matrix. Okay. And the R transform associated with this. Okay. So I can. So this is G. So again, if I only keep the terms that are. So this, this disappears one over N. And this minus one also disappears as one over N. The only thing that matters is one over Z. I can invert this relationship. I get Z of G. Equals one over G. And the R transform is Z of G. Minus one over G. So the R transform is zero. Okay. So I've lost everything. I get, I get a sum of zeros. Okay. So I'm going to cheat. Because I'm not a mathematician. I'm allowed to cheat. I'm going to say, well, because I have a large sum here, maybe I should keep my R transform to first order in one over N. Because T is large. So I'll have N terms. So if I compute the R transform to order one over N. Then. Then the R transform won't be zero. It'll be, it'll be something. And then I can sum. I can sum T of these things. And get the, the correct result. Okay. So. So I see time is going by. So I'm just going to state the result. Okay. So it's fairly easy. Just to give you just a bit. So basically I'm going to do it iteratively. So I'm going to write G of Z. As a term to first or to a zero order plus a correction in one over N. And then I'm going to invert. I'm going to invert this. To first order in one over N. And then remove the polar one over D. So I see time is going by some just going to state the result. Okay. So it's fairly easy. So I'm going to put the R transform. And then I'm going to put the R transform. And then remove the polar one over G that's all there. And get this, the, the R transform. And then I'm going to sum over T. So if I'm not mistaken, I get something like this. Are. You have G equals some. Okay. One over NB. T equals one to T. And then. Right. Otherwise I'll get. There's. Hugh Sigma doesn't really matter exactly what it is, but one minus. G. Okay. And, and in the larger end limit. I could I could I could sort the eigenvalues of this matrix C and and they become continuous and and sort of say that sigma square t becomes a function sigma square of t between zero and one. Okay so and replace this sum by an integral this is a sum over t I have a one over n so there's a factor of q that will appear with cancel this factor of q and trust me the answer would be zero to one dt of sigma square now of t of a function one minus g q sigma square of t okay and this is the r transform okay so two things you can jump out well maybe I was too ambitious to to deal with the case where does the matrix C okay so if C is the identity if C is the entity all this eigenvalues are one these sigma squares they're all one this integral of one just simplifies tremendously and this is called the white case it's called a white wishart so the sample covariance matrix is a wishart matrix wishart actually considered the matrix C so if you don't have a matrix C then it's called it's a wishart matrix with the identity true covariance and then I call that a white wishart and then you have that the r transform is very simple evaluated point g is equal to one over one minus q g okay so that's one result that we get here it was just it's like doing the same computation without bothering with the sigma square terms okay and then another thing you could do is rewrite because this is the r transform but the r transform is directly related to the steel just the inverse steel just transform uh minus one over g and if you write it like this and and you say this is an implicit equation for g okay because uh and and you can just write like that instead g of z g of z okay so this equation here written like that this is essentially what marching point pastor got in their paper in 67 okay they related the steel just transform of a matrix of that type to an implicit equation that that's that's the marching point pastor equation that's a bit hard to solve but you could solve it for them the methods to solve it numerically and it relates the steel just transform uh with itself with this integral that depends on the on the density uh yeah um okay and yeah and and so this is a bit cumbersome and and it's particular to um to sample covariance matrices and so I just want to finish the last five minutes um with something a bit more general we in this uh having to do with because um really these these objects go I'll go back to the previous object e equals square root of c h0 h0 transpose over t square root of c this is really a product of the matrix w okay so I'm going to find a white way short the mu zero if you want is just this matrix okay this this is this is if you want this is a sample covariance matrix of of white noise the sample covariance matrix of data that uncorrelated okay and it has the r transformed equal to this okay by the way I um I won't have time you can invert this you get a quadratic equation for g you can easily solve the quadratic equation you get a branch cut and just want to write it at least that the density of eigenvalues that you get for something like this which is going to write it's called the it's also called the martian copeture density again martian copeture density is for the white wishart okay for the if you want the colored wishart the one with a matrix c in the middle of a matrix c on the side uh is is an integral equation but for a white wishart it's a simple equation and its row of lambda is going to be a square root of lambda plus minus lambda lambda minus lambda minus over two pi lambda and with lambda plus or minus that depend on q by this formula and where it looks like a very small graph it looks something like this okay it goes from lambda minus to lambda plus and so if if q is between zero and one this is between zero and four okay so lambda minus is between between zero and one and then the plus is between one and four okay so and and it depends on q okay so this is the martian copeture density for the for the white wishart so so this matrix here we know how to characterize very well and the matrix we're interested in here is actually the product and it's a rotation invariant it's also an invariant it's a rotation invariant product of it's a product of rotation there matrix with some other matrix well i mean i write it this way um it's it's but yeah maybe i think that's important that most people would say the product of a matrix would be like c times w but c times w is not symmetric symmetrical so for positive definite matrices i prefer to write square root of c w square root of c okay and for the eigenvalues it doesn't matter well this is a non-symmetric matrix but it has the same eigenvalues as this guy but for the eigenvectors it will actually matter quite a bit whether um the the c is on the outside or in the inside for instance this is a rotation invariant matrix this is not this depends on the eigenvectors of c okay and i'm really rushed for time so remember i told you that well we we worked a little bit with the r transform that that sort is additive for a product for sums of free matrices well there's something called the s transform and what you would have is a s so it's evaluated say at point zeta you know at point x would be sc so there's a there's a transform that for an object like this for an object that's a product of a random rotation very large matrices and some other matrix there is there exists a function that depends on the spectrum it's called the s transform if you know the s transform of c and you know the s transform of w zero then you know the the s transform of the product the free product and once you know the s transform you can go from the s transform to to the to the the seal just transform and to the density and i think i should stop here and when i'll need to use this i'll explain a bit better how to compute this s transform this transform is again related to some inverse of seal just transform it's a bit just slightly more complicated but but we'll see that next time okay thank you ranch and by the way i'll go slower the next time this is this is background material let me recall the program who's next so okay someone who's next should know who's next so let me just distribute