As we discussed in the past module, analytics is all about using data to answer questions. But how we approach doing this is very much dependent upon the complexity of the system we're dealing with and the kind of questions we want to ask. Analytics has been used in organizations in a formal way for over a century now being pioneered by the work of Frederick Taylor in his analysis of work processes and Henry Ford's measuring of his newly established assembly line. This is a relatively basic form of analytics where we're studying a very limited number of components and processes in a somewhat linear fashion. This linear approach has largely dominated business intelligence until quite recently but as we'll discuss in this module, things have just got a lot more complex and our approach to analysis is likewise changing to become a lot more sophisticated. This is now what we call advanced analytics or complex analytics. Whereas with the more basic approach to analytics, we're asking relatively straightforward questions about a relatively simple system that is limited in scope. With complex analytics, we're trying to answer complex questions or another way of saying it is that we're doing analytics for complex systems. To give this context and relevance, we can note how our world has just got greatly more complex along almost every dimension over the past decades. Whether we're talking about telecommunications, transport, international politics, supply chain management or the media landscape, the number of nodes and the degree of connectivity has greatly increased. In many cases, such as in financial markets, it is an order of magnitude greater than it was prior to the 90s. This new level of complexity that has emerged within virtually all of our systems of organization has major implications for how we should approach analytics. Living in a small town, you can simply walk around and talk to people to find out what was going on. As we form larger organizations during the industrial age, new tools of communications emerged. The telegraph, telephone and postal system enable people to communicate effectively within these large organizations. Television and the newspaper inform people of what was going on in their region, city or nation. But today, we find ourselves embedded within vast complex systems, networks that often span around the planet. Corporate supply chains, huge social networks, sprawling metropolitan areas, the global air transport system, the global biosphere, financial markets, these are things that shape all of our lives. But somehow, we don't have the means, the vocabulary or the methods that actually grasp them in their complexity to see them or to really know what is going on in the system. As a consequence of not being able to see the workings of these systems and thus in some way manage them, we get financial crisis, we get environmental crisis, we get violent social outbursts because we can't see the mounting tensions. Large corporations drop off the S&P 500 faster and faster because they can't see through the complexity and respond fast enough. In these increasingly complex environments that organizations operate in today, traditional conceptions of linear cause and effect breakdown, things become ambiguous and simply left without interpretation. We find ourselves in a reactionary state, continuously surprised and shocked, volatility increases, we start to see only some of the trees and no longer the whole forest. As a consequence, our organizations become incapable of acting decisively, knowing what to do and making important long-term decisions and investments. As this complexity proliferates, we are burying the proverbial needle in the haystack. More data means more noise. We stop being able to hear the things that we need to be able to hear. This is the same problem for businesses, for individuals, for researchers, for policymakers, for anyone living in this world of globalization and information technology. So how do we make sense of a complex world? We need new models and new ways of looking at the world, but just as importantly, we need new tools and methods for amassing and processing data and information. And this is what this course is all about, these new data sources and tools to support a more comprehensive understanding of the complex systems that we are now challenged to try and understand and manage. Whereas the traditional business analytics of the past has been based upon well-defined and well-structured data sets that were limited in size and complexity. Today, we have a wealth of new data coming from a myriad of new sources and we call this big data. Whereas the data of the past was structured into specific vertical categories being used to answer specific questions. This stream of unstructured data from a multiplicity of sources enables us to create context by making connections between a diversity of data. We no longer just have data about the products we sold and look to see how changes in the price changed the sales. But we now have a massive amount of data from different sources that can be used to find much more complex patterns and correlations. Data about customers, about location, about all the other products available. Specificities about the store where an item was sold or the time of day, the weather, etc. and all of this can be put together in new ways to find new patterns that were previously hidden. Whereas in the past, if we wanted to know where a fire might break out in a city or an accident on a highway happened, we were inclined to look at the phenomena itself. But with complex analytics, insight may come from a completely different realm that has nothing to do with that actual activity. With analytics, we look simply at the event. With complex analytics, we can now look at a network of data points to create some kind of context to the phenomenon so that we're no longer dependent upon simplified mechanistic cause and effect descriptions but can begin to look at things in a more realistic fashion as a network of interacting factors. John Kelly of IBM talks about this change as such. What is different now and has changed is that it's no longer about taking this data, putting it into a computer, running a calculation and getting a balance sheet answer. What's important now is what is the context of the data? What is it connected to? What effect is it having on data around it? It's basically a network of data. It's no longer sort of tabular columns, a rows of data, it's interconnected systems. Just as data is no longer a single thing, so to the means with which we process it is changing, in the past we used mechanistic rules like formulas in a spreadsheet that were dependent upon strict well-defined data sets as input. Today we're moving from rule-based mechanistic algorithms where all components are pre-specified and well-defined to computational graphs, which are networks of nodes that learn through self-organization. Complex analytics gives computers the capacity to understand data in new ways like humans do. This means that computation can now act on data derived directly from unstructured contexts and real-world environments. One of the best examples of complex data analytics is WebSearch. WebSearch was one of the first widely used applications of big data and advanced analytics. A search engine like that of Google or Baudu looks through massive amounts of data and within seconds analyzes it in a multiplicity of different ways. WebSearch has given us the capacity to look into big data, to look into all of this information we have and we can think about the effects of that on transport, on research, on almost every area that now depends upon this big data of the internet and complex analytics in the form of search engines. In this respect, people often equate our newly found technological capacities of complex data analytics to that of the microscope or telescope. Jay Walker of Ted Med describes this revolution well when he says the microscope in the 1650s and 60s opened up the invisible worlds and we for the first time were seeing cells and bacteria and creatures that we couldn't imagine were there. It then happened again when we revealed the atomic worlds but now there's actually a super visible world coming into play. Ironically, big data is a microscope. We're now collecting exabytes and petabytes of data and we're looking through this microscope using incredibly powerful algorithms to see what we could never see. With these new technologies that we'll be talking about in this course it's like we're building a new kind of instrument like we're building the telescope for looking into complex networks. For the first time, we're able to look at these complex systems that are all around us which have a structure, a pattern and even a beauty that are invisible without the right instruments. The implications of this are huge in terms of how we understand the world and our place within it and of course how we make decisions and act on them.


But I wanted to go ahead and introduce, I'm not sure which one of you guys is speaking first, but we have, okay. Emily Ellingson. She's a Northern transplant that we're loving having here. She has training in horticulture and she's been working at the University of Kentucky's arboretum in charge of their native plants. They're more the wild areas, right? I'm not sure. I have a terrible memory. And then probably Emily will clarify during her talk. And then we also have Heidi Brown writer, another Northern transplants loving it, one from Wisconsin, one from Minnesota here in Kentucky with us. And she's working for the Office of Kentucky Nature Preserves and they're both going to speak to us about native plant propagation projects. Okay. And everyone see that. Great. Hi, I'm Emily. I'm the one from Minnesota. And I'm the curator and native plants collection manager at the arboretum state botanical garden of Kentucky. So I managed the walk across Kentucky native plant collection, which I'm going to talk about a little bit. But I, I'm going to switch gears a little bit, or I'm not going to go into a lot of projects. I'm sort of setting the stage for Heidi to talk about more projects in Kentucky. I'm going to talk about something I'm really interested in, which is conservation horticulture and how native plant propagation can enhance conservation goals. So I'm going to start with some definitions, which may seem kind of obvious, but setting the stage for what I'm going to talk about so horticulture is the art and science of developing producing commercializing and using high value cultivated crops so think medicinal food crops ornamental plants that you'll find in a nursery. This is a post, you know, botany, which is the academic study of plants and doesn't often have to do with improvement in marketing of plants. Plant propagation encompasses how we develop and produce these plants. And there are just a million ways and unique and creative ways to propagate plants. I've built on this, I'm also not going to go into that. But I will say that there's some common methods, especially if you want to increase genetic diversity or maintain genetic diversity in a conservation collection seed collecting or propagating plants from seed cuttings, layering grafting, micro propagation and tissue culture from small vegetative parts of plants. It's really neat, but any method that you're propagating plants with you, you'll select that based on goals of the species that you're working with. So, every species is different. Some require more treatment and more care than others and you really need to know the requirements and life history traits of those species. My very dictionary definition of conservation is the prevention and wasteful use of a resource. So in environmental and plant conservation, we aim to protect plants from extinction, maintain and restore habitats and plant communities, enhance ecosystem services and protect biological, biocultural diversity. And so conservation horticulture sort of brings all of these three things together and these these concepts together. It's horticulture that is concerned with integrated conservation and environmental awareness. What do I mean when I say integrated conservation and environmental awareness, I found this graphic that would be really helpful to look at we, when we say when I say integrated conservation. We describe the vast array of tools in our conservation toolkit. So, this graphic broadly defines these as research, for example, reproductive research and reproductive biology, genetic diversity studies, germination, phenology, interpretation, which is interpretation perhaps in botanical gardens, but also just what all conservation plant oriented groups doing outreach and like like this symposium. And then two main avenues of conservation, which is XC2 conservation and NC2 conservation, which I am going to go through in this next slide. XC2 conservation is onsite conservation, and this is conserving species in a habitat in which they are found. Examples of this would be preserving tracks of land and doing restoration, habitat restoration activities on the site. So the Rose Pagonia has another highlight here. This is that photo under the NC2. One is, it is endangered in Kentucky and that's growing in a bog in Letcher County. XC2 conservation is offsite conservation. So this is conserving species outside their natural habitat, perhaps in a botanical garden as an educational and research focused display. Perhaps in a seed bank, a pollen bank, or even employing more modern methods like cryopreservation, the deep freezing of plant tissues. And this, this photo shows false grama on his modium hispidysimum, which is also endangered in Kentucky and this is growing in a bed in the blue grass region of the walk across Kentucky at the arboretum, which I'm going to go into a little bit more later. The goal of conservation horticulture is to maintain live plant plant collections that are genetically representative of natural populations and this is going to be really important if the plants that we propagate are actually going to be used in restoration activities. So I managed the native plant collection at the arboretum and it's called the Walk Across Kentucky and it is called that because it represents the seven physiographic regions of Kentucky, which you can see on that, that Kentucky map down there. The colors actually correspond to each region that is in the Walk Across Kentucky. It's really cool about this and what, what makes the arboretum and XC2 plant collection is that all of the plants are wild collected. So we go out collect seed, maybe collect plants depending on the propagation method we're using. We grow them at the, at the university. So we're affiliated with the University of Kentucky. So this, this photo is here there's a magnolia macrophila big leaf magnolia seedling and hydrangea. It's an arborescent the wild hydrangea. And then we actually put those in the landscape. And this is conserving local genotypes, and it's a conservation collection that safeguard species so we're not we may not necessarily then be propagating plants from the arboretum and growing in the ground. But we are sort of just keeping them for future reference and for research that can be done easily at the arboretum. A conservation collection like a really true conservation collection is an XC2 collection that supports species survival and reduces the extinction risk of globally and regionally rare species. This has to have depth and breadth so when collecting plants you need to have try to capture the diversity of the population range and also have enough plants to be able to to keep that going in a in a closed setting like a greenhouse. So I really enjoyed this quote and one plant in one pot is a certain rather limited challenge which I can definitely attest to just trying to propagate a very wide range of plants at the arboretum to grow 200 plants for an indefinite period and maintain the genetic diversity among them it's not the same challenge 200 times over. It is a quantitatively and qualitatively different challenge and a difficult one. The picture on the right there is the conservation collection of fissure plants from the Atlanta Botanical Garden which was somewhere that we visited in March with the Plant Conservation Conference, the Southeast Plant Conservation Partners in Plant Conservation Project. I want to go through the just to give everyone an idea of the sort of things that you have to think about when propagating plants for conservation and the challenges that you know this quote sort of highlights. So this is from the Center for Plant Conservation, which is a really amazing organization.  You also can't collect from more than 10% of a seed crop in any year and no more than five out of 10 years. So I wanted to talk about this because it's really important that we are collecting in a sustainable way, and we're capturing the diversity of species so that it can be, we can better put plants into the, maybe back into the wild that will survive and flourish. This no more than 10% of a seed crop thing kind of goes out the window when you're talking about plant rescues so if you're a spot is slated for development and you need to actually rescue all those plants or if there's a very very small population you might change some of these parameters but this is a general rule. You have to propagate and maintain this material. So we always want to seed bank things to keep XC2 collections in multiple places. We do have excellent record keeping. And something that is really interesting to me is that when propagating and growing plants. And something that's pretty different from the horticulture industry, you actually don't want to do artificial selection. So, whereas in the horticulture industry you might select for something that's the most floriferous or the most vigorous when you're collecting plants for conservation, you want to avoid favoring large seeds or vigorous plants and you want to collect from the short plants the tall plants all sample from the whole range of genetic diversity, allow time for all seeds to germinate and how it's in monetary for for health and that's that's something that's just really interesting to me. And it's going to be more useful in your conservation collection. And the last step and arguably one of the most important is using the material. We the the final goal of a conservation collection is to be useful and that can mean a number of things. It can mean placing whole plants and XC2 collections, for example in Botanic Gardens and seed banks. It can mean reintroducing plants. So this is when plants are grown and then transplant into a habitat and location where they've been found perhaps supplementing populations are placed in an extirpated population can mean trans locating plants. So when plants are transplanted to habitats where they are found but perhaps not a location where they've been found. And then the other more the last more contentious item is assisted migration which is the human assisted movement of species in response to climate change so this is actually involving moving species outside of their recorded range in order to prepare for the changing climate. A whole seminar I think could be or day could be devoted to talking about assisted migration. So conservation horticulture and the propagation of native plants where otherwise is directly related to conservation target goals from the global strategy for plant conservation. So these goals these goals claim to are aimed to have 75% of known threatened plant species conserved in C2 and XC2. And then importantly, their target 16 advocates for regional, national and international levels of cooperation. So examples of this would be the Center for Plant Conservation. The Botanical Gardens Conservation International and various plant conservation alliances, known as PCAs. So PCAs encourage partnerships among many different institutions use botanic gardens, plant societies, universities, federal and state agencies. And this is an order to coordinate and coordinate plant conservation by sharing expertise and resources. What's really exciting is that Kentucky is starting a plant conservation alliance and you can see there's a lot of work going to going on in Kentucky. And so now I'm going to hand it over to Heidi Bronrider, who's the botanist for Office of Kentucky Nature Preserves and the TNPS vice president to talk about some of these, some of these projects. Can you all see my screen. So, yeah, I am Heidi Bronrider. My talk today is going to focus on seed collection and propagation projects that we are currently working on in Kentucky. But first I wanted to touch base a little on how we've actually been able to accomplish these projects through our Kentucky Plant Conservation Alliance that Emily just mentioned, as well as Kentucky Nature Preserves Conservation Section. The focus of the past several years has been to build a larger botanical community in Kentucky, and trying to bring that community together in order to more effectively deal with some of the conservation issues we have going on in our state. State Plant Conservation Alliance started in 2016 as a committee of the Kentucky Native Plant Society, and then it took a step further in 2019 with the creation of our Plant Conservation Section within Kentucky Nature Preserves. So now the Plant Conservation Section acts more formally as the KPCA with each of our botanists being a coordinator of the Alliance. Since 2018, we've hired on six new staff members into that state program, which is a huge milestone for Kentucky Plant Conservation efforts. These steps have allowed us to increase our coordination among Kentucky Plant Conservationists, as well as increase the number of Plant Conservation projects that we're actually able to accomplish. And I would be remiss if I didn't acknowledge all of the work that's been accomplished by Tara Littlefield, who has literally been the backbone to all of this progress that's been done in recent years for Kentucky Botany. Here she is presenting at the 2020 Southeastern Partners in Plant Conservation Conference, also known as SEPCOM, at the Atlanta Botanical Garden. And this was actually a really great opportunity for us to formally present on some of our current projects, as well as building new partnerships with organizations that are working towards similar goals. So on to some of the projects that we're working on. As Emily already went over the different types of projects, I will describe some of the examples of the projects that we've actually done. So we have an orchid conservation project. And you can see why orchids are so easily loved. They are very charismatic in a diverse group of plants. But unfortunately, we have a lot of orchid species in the state that need our help. So we partnered with North American Orchid Conservation Center to do research on some of our rarest orchids. So in 2019 and 2020, we worked on the Rose Pagonia, the Small White Lady Slipper, the Kentucky Lady Slipper, and the White Fringeless Orchid. Some of the aspects of this project included seed banking, all four species, a genetic analysis, as well as mycorrhizal research and banking of the mycorrhizae that are associated with these orchids. And on the slide is a photograph of a root crypt clipping of an orchid. And this is part of the research being conducted to determine the associated mycorrhizal relationships with each of these orchid species. But so far, we've only been successful in determining the associated mycorrhizal fungi with the White Fringeless Orchid. An important long-term goal of this project is the propagation of these orchids so we can restore them into suitable habitats in some of our natural areas. And you can see in one of the photos is actually a baby White Fringeless Orchid that is currently being propagated at Atlanta Botanical Garden. So listed here are just some of the rare plant species that we have collected seeds of in 2019 and 2020. It's not completely up to date, but there are over 30 plant species on this list that we will send off to get propagated and hopefully get back on the landscape one day to boost their current populations. Some of our partners for propagation include drop seed nursery, native plant seed nursery, ironweed native plant nursery, Cincinnati Zoo and Botanical Gardens, Round Stone Native Seed and Atlanta Botanical Garden. One of the nice things about our seed collecting project is it can be easily incorporated into many of the other ongoing projects we have at Nature Preserves. For instance, our roadside pollinator project that Tony discussed earlier, with roadside providing such an important habitat for remnant grassland communities, we have been able to collect many of our rare plant seeds while doing this project. For example, Wild Blue and Nego, Royal Catchfly and Purple Milkweed are all seeds that we were able to collect this year while surveying Kentucky road sites. So of the seeds that I've mentioned so far, they target specific rare plants, but this year we also started to target several rare plant communities. And this whole plant project stemmed out of the lack of a local seed supply for some of our restoration projects at Nature Preserves. It's very important to use seeds collected locally rather than bringing them in from outside of the state because local seeds will maintain the genetic diversity within a population, as well as increase the long term success rate of these restoration projects. Currently, we are targeting various grassland communities across Kentucky. These habitats have become increasingly degraded and mostly lost due to human activities. And now mostly, they only exist as unsustainably small habitats. So we intend to collect seeds from numerous plant species that are associated with these communities simply in order to create a seed stock that can be used to restore degraded sites in the future. The three grasslands that we are targeting include the Bairns of the Penny Royal Plains, which are a mosaic of glades, tall grass prairies and oak savannas. They support species like the Carolina Lexper and the Glade Violet and Limestone Painflower, but they have been largely lost due to agriculture and pastureland and fire suppression. The Bluegrass Limestone Glades and Barrens are naturally open grasslands and savannas on dry rocky slopes. They support species like the Indian Paintbrush that you see here, the small white lady slipper and the federally endangered Shorts Goldenrod. The Outer Bluegrass Glades support our federally listed and endemic species Kentucky Gladecrest, but these landscapes have been lost due to development as well as agriculture and pasture. And then the last grassland that we're targeting is the Southern Cumberland Plateau Grasslands, which consist of deep soil prairies. They have a lot of sun loving fire dependent plants. And historically they consisted of a complex of pine oak savannas, sandstone prairies and barrens and glades, but today they're mostly restricted to roadsides and power line corridors. The long term goal of this plant community seed collection project would be that once degraded sites have been restored using these seed stocks, we can then introduce some of the rare plants that we've propagated back onto the landscape along with their associated species. Another important project is seed banking. As it provides the insurance against the extinction of these species, we've partnered with Missouri Botanical Garden and Atlanta Botanical Garden to seed bank several of our federally listed plants, including the globe ladder pod, the white frung just orchid and the Kentucky Gladecrest. And most of our propagation and reintroductions we've worked on up to this point have been federally listed plants, but as part of the Plant Conservation Alliance, we have been able to broaden our scope to include state listed plants and endemic species such as the Woodlilies and the Kentucky Clover. Woodlilies occur in the southern Cumberland Plateaus and their habitat is restricted to the power lines and roadsides of the Daniel Boone National Forest. Its populations in Kentucky have declined by more than 90% in the past 40 years, and this is due to habitat loss, lack of fire, mowing as well as excessive herbivory. So we've been working with the Forest Service to restore populations of the Woodlilies as well as its habitat. So we have more than 200 seedlings currently growing in a greenhouse that drops seed native plant nursery. And our hope is to transplant these this coming spring. But that's dependent on if we can get a prescribed burden on the nature preserve where we'd like to put them. Getting prescribed burn in prescribed burns in can be tricky. It's very weather dependent and also trickier with COVID as it requires large groups of people to conduct the burn. But we are hopeful that we can get this happening in spring. We are currently working on several projects related to the Kentucky Clover, which is an extremely rare endemic species to Kentucky. It has been seed-banked. Genetical analysis is currently being conducted at EKU, and research is being conducted to determine the best propagation methods for this species. Currently, it is being propagated at Cincinnati Zoo and Botanical Garden, and these plants will hopefully be used to boost population numbers in the future. Shorts Goldenrod is a federally endangered plant that occurs around Blue Lick State Park area. Cincinnati Zoo and Botanical Gardens propagated plants for us from seed, and this past fall we were able to put over 100 plants at Clay WMA in collaboration with KDFWR. Clay WMA is close to Blue Licks, and it has similar soils and habitats for Shorts. And we also collected more seeds this year to get propagated, and we hope these plants will go into areas that are actively being restored right now near Blue Licks on nature preserves properties. A globe bladder hot pod is another federally endangered plant we've worked with. At Cove Springs Park in Frankfurt, Kentucky, seeds were dispersed to create new populations of this plant. And it took several years, but population numbers are reaching sustainable levels, and successful new populations like this are a great pathway towards the recovery of this species. Running Buffalo Clovers, another federally endangered species we're working with. It was proposed for delisting in 2019 by US Fish and Wildlife Service, but that hasn't happened just yet. From 2008 to 2010, there were several introductions of this plant in Madison County in partnership with EKU and Blue Grass Army Depot. And there were also introductions at Shaker Town and on a few private farms. We're currently, we currently have plants growing at Cincinnati Zoo and Botanical Garden, that we hope to transplant to Lower Hards Creek State Nature Preserve in Clark County this coming spring. And in the last couple months, we've sent off cream-junctioned seeds to Cincinnati Zoo and Botanical Garden to try to propagate. We are hoping to reintroduce these at a few sites around Blue Licks State Park that are currently being restored by nature preserves. So, looking forward, we still have a lot of work to do to further our state alliance. Several steps need to be taken, including formalizing the process in which someone actually becomes a KPCA member. We also need to create foundational documents that state our missions and what projects we're currently undertaking. We need to recruit a larger volunteer base as well as building more partnerships. Partnerships are really the key to our success right now. And for propagations, we want to reach out to more local seed exchange groups in hopes of perhaps getting volunteers to propagate species for us, as well as we also want to develop more guidance on the proper collection of rare seeds. And here are some of the dozens of partners we have collaborated with. I just want to thank all of them for working with us on our plant conservation projects here in Kentucky. We really wouldn't be able to do it without them. And thank you for listening to my presentation. I see a few questions came through on the chat window. However, I can only speak for myself to say that I really, really want to eat lunch right now. So, perhaps we can address some of those questions in the chat window. And because we have our keynote speaker, Ellen weekly at 1230. So we have a very short break.


I met, I saw, I never met him actually, but I saw good more only once in my life in a lecture when he was sitting in front and I was sitting far back. But I think over the year, I can say that over the years I at some or other point I read every line of his book on sheaves that for many years this was a very useful source for me. On the other hand, I have learned a lot from French mathematicians, some of them being here. So it's an honor for me to be being invited to speak here. Thank you very much to the organizers. Let me maybe put here the very basic notations. F is the local field, that's the new characteristic P, positive P. Then G is the F points of a connected reductive group over F. Little K is my coefficient field, an arbitrary field of characteristic P. So everything in this talk will be representation theory in characteristic P. And so correspondingly by mod G, I mean the abelian category of smooth G representations in K vector spaces. And then D of G, as you can guess from the title, I will derive something at some point. So D of G will be the unbounded derived category of mod G. So complex is unbounded in both directions of smooth G representations up to quasi-isomorphism. So these are the basic notations.  Most of this will be known to you, but I also have to set up the notations, further notations. So I is any, for now, I in G, any compact open subgroup. And then we can form x, the compact deduction from I to G of the trivial representation. So of course, all these coefficients in K, I won't mention this again. Which here, of course, is simply free vector space over the corsets. G acting by left translations. And then once we have that, that is a smooth, of course, smooth G representation. And then we can, it's a very big one. And then we can pass to its Hecker algebra, which is just the endomorphism ring. I think I just call it H, which is the endomorphism ring, G endomorphism ring of X, but with the opposite ring structure. So to make X a left, so a right H module. And then, as you know, there is a pair of, you have a pair of joint functors between, so mod H is simply, of course, the category of, let's say, left H modules. And on one side and on the other, we have our category of smooth G representations. And maybe I denote this by T for tensor and this for homology or comology. So if you have a module, we tensor it over H with our module X, which is a right H module, and then G acts on this, why it's actual X. And on the other hand, if we start with a representation, we just take its i-fix vectors and to see the action immediately, we rewrite this by Frobenius' reciprocity as the G homomorphism from X into V. And then, of course, the action, right action on X, it uses a left action on this home space. Now, unfortunately, these functors are very badly behaved. Certainly in characters Dp, for example, they are not exact. And if they are not exact, of course, it's not a particularly clever idea to think we should derive them, say, this way past the derived picture. But this does not mean that we simply derive them. It means more than that. So the first thing we do is we pick a, I mean, this category mod G, I mean, of course, the modules of a ring anyway have projective and injective objects. The category of smooth G representations is known and easy to show that it has enough injective objects. So pick an injective resolution of our X i dot. So these are complex, of course, one-sided to the right, unbounded to the right complex, exact complex apart from X, of course, of injective smooth G representations. So we pick such a resolution and let me write to be clear in mod G. And again form the endomorphism algebra. And again form its endomorphism algebra. But this is now a more complicated object. So we take the endomorphisms. So this is a differential graded algebra. Because by an endomorphism I do not just mean the endomorphisms of this complex, G endomorphisms of this complex, the usual ones, but the ones of every degree. We also allow endomorphisms which raise the degree, which do not go from ij to ij, but from ij to ij plus a certain degree. And this degree is encoded here. So that gives degrading. So this gives a graded object. And then the differential of i on both sides induce a differential between the endomorphisms. And of course the algebra structure is the opposite of composition. So this gives a differential graded algebra. Maybe let me say right away, so maybe I say up to quasi-isomorphism H dot does not depend. Because it seems I have made a choice here, right? I choose the, there's no preferred injective resolution. But if I choose a different one, I get a quasi-isomorphic algebra. It does not depend on the choice of the injective resolution. I get a quasi-isomorphic algebra. And since I, in a moment, I mean, we are only interested in the derived category of this one, then quasi-isomorphic algebras have isomorphic equivalent derived categories. So this is not really a choice. And then secondly, of course the old algebra degree zero comology of this one. Because the usual endomorphisms of an injective resolution up to homotopy correspond exactly to the endomorphisms of the resolved object. And I mean degree zero, somehow the kernel of the differential here, degree zero, these are the usual endomorphisms of this. And then H zero is quotient out by the image of the differential. This kills all the homotopies. Okay, and then there's the following theorem. So now I have to impose an assumption on I. Suppose that I is for P and torsion free. Then, now in this context, we derive the above functors. So on the left side, we have now the derived category of this DGA algebra. And here we still have our DG. And then I can, so the tensor product is right exact. So I have to derive it from the left. And on the other hand, the home is left exact. So I have to derive it to the right. These then are quasi-inverse equivalences of triangulated categories. Okay, so that's the motivation for what I want to talk about today. The assumption as such in this generality, the assumption is not particularly strong because you can always make I a little bit smaller to achieve these two additional properties in any pietic group. On the other hand, since I will, I mean for the following, it is an assumption because I think more or less right now in a moment I will specialize to particular I's which do not in general satisfy this assumption. Let me maybe first, I can still put this here. So this H dot of course is a very complicated object obviously because it's a differential integrating. So to simplify things, we can pass to its homology algebra. So maybe I put this here. So the homology algebra of H dot is the same as the X. So because here we can get rid of this injective resolution, this is just the X algebra of our original big smooth representation in this category. And then again because this was a compact induction by Frobenius reciprocity, this is the same as the homology algebra of our compact open subgroup with coefficients in this representation. So this is already a much more familiar expression. It has one, at first one big disadvantage and most of what I will be saying later is somehow to make this useful thing anyway. I mean here of course the multiplication H dot induces a multiplication on the graded object. So we have here the intrinsic multiplication and here this turns into the opposite of the Yoneda product. The concatenation of extensions but it's not visible. I mean because right axis only once here it's no longer visible, directly visible on the homology of I. So that's what I want to talk about mostly. Certain structural properties of the homology algebra. So the Rachele Olivier. But from now on I make, from now on I is one particular group. From now on I always, also in further sections, always is the pro-P Ivohoi subgroup of G. So I mean the Ivohoi subgroup was occurred already and pro-P means just it's the pro-P Siudo subgroup of the Ivohoi subgroup, which actually is a normal, I mean because of the structure this is a normal subgroup of the Ivohoi subgroup. It's a very simple quotient. And then in this section here also let G be F split. So these are the assumptions for this section. I do not for now, when I will then I will specifically say I make no assumptions about, I mean it's pro-P anyway by definition but I make, for now I make no assumption about torsion freeness. I mean since the, really in some sense the only thing one can explicitly work with is these homology groups. We have to use them to study the multiplication. And so let me introduce a little bit further standard terminology of course. So in G I pick a maximal split torus. In there I have the maximal compact subgroup and in there I have T1, which is the pro-P Siudo here. And what else? So then the corresponding, let's see, it goes the wrong way. So we have of course the extended affine y-group. It's the normalizer modulo T0 but we work for the pro-P we have to work with in larger quotient v tilde which is the normalizer modulo T1. So this is the important group here. And then we have the Brouillatitz decomposition. G is the disjoint union of these double cosets. And so you see this allows us immediately to write our x, right, which was the vector space over the coset g mod i. We can decompose it into xw where xw, let me use this suggestive notation. It's the induction only to this double coset. So it's the vector space over the Iwi modulo i. In particular, it's an i-equivariant. This is i-equivariant. And so the homology of profiler groups commutes with arbitrary direct sum. So it's the direct sum. And let me abbreviate this by h star w where maybe I put this, save some time. So this is just the homology of i coefficients in xw. But what is this? So now we use Shapiro, right? I mean, this is this here. And of course, before Shapiro, we can, I mean, this is a homogeneous space under i. So I can rewrite this as the h star i induction from i in xw to i where iw is the intersection of i and w is conjugate. And now I can use Shapiro, Shapiro's lemma, which says that this is the homology of iw with trivial coefficients. And actually, I mean, this is all very simple. If you go both things at once, then this is just on the coefficients, the evaluation map in w. So this is setting up the technical tool for the following. And so the basic, maybe the first basic result about multiplication is the following, which looks, I mean, I think you will be, in some sense, it reflects something which in the class in the undirected algebra is very well known in its description by generators and relations. Namely, if you multiply two of these pieces here, so hj, different degrees possibly, and w and w tilde, then you end up in a finite direct sum of all u, of course in, maybe I already did this way, iui is contained in the product of these two double cosets, hj and then the degrees add up, of course, u. So that's good, at least, for the beginning. And now let me go through three structural results. So the first one is the anti... I mean, the usual vahori, or propi vahori hj is known to have an anti-involution. And so is the, so has the homology algebra. And the definition looks, the definition is very elementary, maybe at first it doesn't look like it should be anything interesting, but let me do, okay, will I ever get this back down again? Anyway, I have one in this, and actually this is the principle in all three cases. Yeah, right. In all three cases is that when we do something which does not, which kind of looks kind of trivial, but it turns out to be relevant for the multiplication. So here we define this, make this following very elementary definition, define the K-linear automorphism J. So in the, in the, here, in this picture, I-comology picture A of h star x in the following way. So we do this on each piece, h star w, right? I use, we use, where is it? Up there, we use this Shapiro. This is the same as h star Iwk. And then we just conjugate this by w, by w inverse, in fact. And we end up in h star, the conjugate of Iw, I mean you can do this in two seconds, by w inverse is Iw inverse.  And then the theorem says that J is an anti, anti-automorphism of the commodity algebra. Anti means, maybe I write it down because this is meant in the graded sense now, of course. So J of the product of two elements, there is a sign, right? Minus one to the product of the degrees of the two elements, J beta times J alpha. And the proof, I mean, I will not go in any, any proofs, but I will tell you in the, in the second part, somehow the technical instrument, so that the proof comes from the second section here. So again, let me do something very naive. So the G-equivariant map. I have a map from x, tensor x, back to x. Extremely simple. I have two functions, f, tensor f prime. And I just map them to their point wise product. I view the induction as the elements here as functions with finite supports, point wise product. That's, of course, G-equivariant. And this then gives me, together with the usual cup product, right? The cup product on group combo G goes, I mean, it goes into the new coefficients of the tensor product of the old coefficients and then we can use this map to go on. So it uses what I call here the cup product, h i, h i, i x, tensor h j, i x to h i plus j, i of the tensor product, but I immediately, sorry, I compose it with this map. It goes back to h i, h some degree i of x.  This thing and this cup product under Shapiro corresponds to the usual cup product on the homology groups of these I w with red. If you have trivial coefficients, you have the usual cup product. That's very easy to see. But it has, of course, the immediate consequence that this cup product is, I mean, right? It's completely component wise. If I have h i, v, cup, h j, w, this is always zero if v is different from w. So why should this be helpful at all? But in some sense, the second main technical statement so in some sense maybe the key technical proposition is the following. And I formulated it somehow vaguely because this is in formulas, this would be complicated. But I give you as a corollary one very nice and simple formula in a special case. OK, so maybe I can put this here. I need some notation. I mean, we do know, let's say we have an alpha in h i, v, and beta in h j, w. Then by the, is it still somewhere? Should be still somewhere. By the first technical proposition here, we know that the product alpha times beta is the sum over this u in the product double coset, certain elements gamma u. And now the technical thing says that the gamma u can explicitly be expressed in terms of the cup product, this cup product, and homological restriction and co-restriction maps. So this is really the tool which allows to compute the product. Let me give you, I find very nice instance of this, in general this is a very complicated formula. But let's suppose that the two elements, L and V, that their lengths add up so that the product element, the length of the product element is the sum of the individual length. Then actually we only have, then the only possible u is actually the product element. We have only one term here. And for this, so then the product alpha beta, so the nice way to write this is the following. Alpha times tau of w, cup tau of V times beta, where this is the standard notation here for the usual hacker operators, tau of something is the characteristic function of this double coset of something in the usual hacker algebra. So this reduces the product here to the cup product and the modules only the multiplication of the degree zero part on everything which is, I mean this is easy to describe. What is true is that if the lengths do not add up then this is still for the highest term in here, one still has this formula, but there are many complicated other terms then. So then let me see is equality. So now I have to assume for the last two points here in this section, I do assume that i is torsion free. The reason for this is that the consequence of this here by Lazar, an old result of Lazar, that all these subgroups, all these open subgroups Iw are Poincare groups of dimension d which is the dimension of g over qp. You can view perhaps g, either you take the dimension as an algebraic group and multiply it by the extension degree or, I mean I should say that this torsion free enforces that the field has to be of characteristic zero at the local field. Or you view it as a periodic league group and take its dimension as a periodic league group. So this means they have homology only up to degree d. So the immediate consequence in particular or homology algebra sits in degree zero to d. So it's zero for star degree bigger than d. And we will use this later. In the highest degree d, all this, the homology of all these groups is one dimensional. Plus the cap product pairing is non-degenerate. I don't, for each of those, I don't write this down. So now we use another map. It's a very simple map. Have g equivalent from x to k. We just, I call it sigma. If you have a function here, I just add up all the values. It has finite support so I can add up all its values. And this induces together with the cap product for the first, our cap product. And then we take this map on the coefficients. And let me, so this is, let me this, you know this for later use, capital sigma h d i little sigma. Ah, actually I don't want to do this in general, right? I mean we want about duality. So I take your d minus i, then I have here h d d d. i with trivial coefficients. And this I identify once and for all. I told you this is one dimensional. Identify this once and for all with k. And then I can use this, I can use this for duality, this induces a duality map. Right? So get k linear x d minus i x linear dual. So I check for linear dual. So it's easy. Let's take for a moment to this, this homology picture. So these are, what is not difficult to see is these are injective, injective with image. It's of course not surjective with image. All what we call finite linear forms. I mean since this is the cup product which was on each IWP is the usual cup product which is non-degenerate. This gives of course immediately the injectivity and it also gives, so finite just means the linear form is finite. If it's non-zero on at most, finitely many of these summands h d minus i v. So this is all on the I picture but then the proposition is the following. So this map, so I'm going back now to the x picture. The above map is an isomorphism of h comma h bimodules. So this is x i, x comma x and this here before the dualizing is x d minus i. If I leave a little space I have to put some decoration here in a moment, x comma x and of course here the dual, linear dual and then let me write simply indicate this finite. So in the moment I only have rewritten these two terms in the x language and I consider the above map. This is of course also a bijective by what we know already so the statement here is that the h bimodule action which comes from the h action on these two terms is reflected here by the h action on these two terms but changed by the anti-involution where j on the left x denotes x into a, x was originally a right h module so I make it now into a left, into a left, no I always mix up and it was a left module, h was acting from the right so I make it into a, what is the usual convention about left and right? I think now it's a left h module via j, via the anti-automorphism. I mean more should be true but we can prove this here the whole, not only the h, the degree zero action on this from the left and from the right it should be something like this should be true for the, I mean the same statement in some sense should be true for the whole algebra structure but this we can't prove yet. But this allows us and I will show you in the last point d I will show you this, the consequence right, I mean this will allow put here d then this is zero here it's the usual Hecker algebra but with some twisted action and since the usual Hecker algebra we know very well and then we also know the twisted action very well we can explore this to get some information about the structure of the top degree piece. So this is the, in this section the last subsection the top homology hd, hd of h. And again here of course if I want to apply this I have to assume that I is torsion free. Maybe I abbreviate this because I want to, I have a still in the last section so maybe I do only the last fact. So let me write down one but maybe I don't have the space here. Let me only write down the cleanest proposition I have to make. So assume that g is semi-simple, simply connected with irreducible root system then. So for the first part I could, some of this is true in more generality but for time reasons let me put this all together. So then the top homology, right we have this map, we have this map to the 2k actually this splits so this is the die sum of hd ik and let me put here trivial plus of course then the kernel of this map sigma where the drift stands, maybe this I put here right away here. This means as h bimod, this is the trivial h, I mean the h structure on here is the trivial one, trivial h bimod but maybe I put here this separately so this here is super singular, it's a huge super singular from the left and from as h module from the left and the right so super singular here is somehow the analog of super cuspital in the characteristic theory maybe. Anyway it is to formulate the last maybe really more structural fact is I need, I mean super singular, there is a certain ideal in the center of the propi hivorik algebra, a specific idea and super singular means that a module is torsion for this, for this, no I should, I think the other J I used for the convolution so super singular means the module is torsion for this ideal and then the last fact is that this super singular, very big super singular module, so then an obvious super singular module, five dimensional one is I just divide h by the ideal which this central ideal generates in h and then the statement is, so I have this finite dimension super singular module and I take its injective hull of h mod jh, again from the left end and from the right. Okay, so far our structural results about the algebra now I want to talk about at the end in the last brief last section, a little bit what I strangely maybe call derived parabolic induction. So let us pick a parabolic subgroup and of course I think it occurs to me I forgot to say this and I introduced the torus, of course there always has to be a relation between the torus, my Ivorori has to lie so to speak in the apartment of the torus and also yet now of course with the p there has to be a relation to the chosen Ivorori subgroup. And then I mean it's a very easy fact that the usual parabolic induction from mod g to mod g is exact, right, so there's nothing to derive, I mean it's on the nose it extends to a functor on the derived category. Sorry, of course, yeah. So what I mean here is of course using the previous theorem how do we describe this on the side of the derived Hecker algebra. So I will now because I have to distinguish right so far my objects had no subscript usually of course when I will right now maybe h dot m or g I mean and so on I indicate by a subscript whether I'm over m or over g. Now let me first reformulate some known thing so define the h which is hg, hm, so usual Ivorori algebraic bimodule which I call x index g comma p and it's just I take the parabolic induction of xm and I take the i g invariance and then maybe I can put this here I have no space then there is this lemma which is just the reformulation of a result of Olivier and Vigneras. The diagram maybe these are two diagrams made into one mod g mod m sorry mod hg and here mod hm m here we have parabolic induction so here we had this pair in each case this pair of a joint functors tg, hg and similarly here tm, hm and here we have just the tensor product by this bimodule and moreover I think this is so far I cannot yet explore this for the derived picture but I think this is something probably very important and moreover this bimodule xg comma p is finally generated projective over I mean only on one side on the hm side over hm. Okay so that's the picture the undefined picture and so let me finish with the derived picture which looks like a kind of a formal consequence so now define right now we need an h dot g h dot m bimodule which I then of course call i dot subscript gp and let's at first let's just imitate what we did above I mean right there was the the invariance taking invariance is the same as home g equivalent home and here from the universal thing so which is here the injective it's injective resolution into here a little leave a little space the parabolic induction of the universal thing over m the injective resolution there so I mean that was actually my first attempt which turned out to be completely wrong so that but also has to resolve this first injectively so this is right I mean the the the parabolic induction does not preserve injectivity so although this is an injective complex it's a parabolic induction is no longer so I take take an injective resolution but the problem lies there let me come back to this later in my last sentence and then maybe I actually yeah then the theorem is that we have diagrams completely analogous to this one so d h dot g g d m h m dot right I mean where the left right let me maybe only repeat it here this where the left derive this was the right derived of the of this one and correspondingly here we here we have the trivial derivation of parabolic induction and we here we have the derived tensor product with this by model this commutative didn't write it there sorry is commutative now as I said this looks as if would be a completely formal consequence but there is a problem there's a huge problem here namely this is so this means passing to an injective resolution as g representation so in mod g I want a bimodule right from the right I want the action of h m dot so it acts on here and then by functoriality it acts on the parabolic induction but if I take now injective some injective resolution in mod g I completely use this lose this action there's no reason why I should preserve it and so that's the huge problem one has to find so one has to take specific so I mean one needs specific or a specific injective resolution functor in the framework in the framework of differential graded categories it has to lift this whole thing I mean the derived categories in some sense a the homotopic category of a differential graded category which takes the all these gradings into account and one has to do this injective resolution business on the level of DG derived categories DG categories and I mean that this is possible is a is a theorem by Schnürer Olaf Schnürer really non-trivial thing so once you have this then the thing becomes a formality but without it it's it would be hopeless okay thank you very much I mean excuse me I probably should know the answer to this but I mean does this thing exist for characteristic zero representations of groups with the regular periodic groups yes but it's nothing additional because there these functors are exact right the the Ivorori propi groups have no comology in characteristic zero so the whole thing is just the usual HEC algebra there's nothing new happening there I mean did you discuss such things in that paper 2007 or is that no I mean I made I made comments yeah I mean the surprising thing is of course there in characteristic zero as you I'm sure you know you do get say for the propi Ivorori you do get a equivalence of categories but not with the full category of smooth representations only those which are generated by its Ivorori in propi Ivorori events whereas here I mean the surprising thing is that under these assumptions of course the higher come on even even right I mean you may have a representation of course in characteristic p every representation has a non-zero Ivorori fix propi Ivorori fix vector but they don't have to generate the representation nevertheless somehow the higher comology sees sees the representation whether it's generated by its Ivorori fix vectors or not this is in the characteristic p case yeah I mean certainly so for completely formal reasons the the right adjoint right once you have because of the equivalence I mean the usual parabolic induction as a rider joint which is left exact and therefore you can derive it so you have a rider joint for this on the derive category and since these are equivalences you have a rider joint here and you can compute it it's the home from this bimodule the left home the problem is with the left adjoint this usual shakifangta is right exact but it's not clear whether one can derive it because for that you would need projective objects in in in the g-re representations which do not exist in characteristic p so I think that's where this I mean probably this fineness property reflects some fineness property of this year which allows us to see that this is also has a left adjoint so you mentioned that the formula gets very complicated when you suppose for example the length of v is one the length of v is one and you have some formula? Yeah but don't ask me to write it down right now I would have to get up because you get then right I mean if you have let's say this is this is s here right but the lengths do not add up then the possible use are I think s w and omega w where omega is of length 0 and you get terms I mean this this one of these terms I think this one is still kind of I'm not sure which one but you have all the terms occur and they are complicated I mean at least so complicated that I don't know them right now without looking up in the paper. Even for v is equal to w is equal to s? Yeah I mean what? No no no you have every omega even in that case. v is equal to w is of length one. Yeah yeah sure and you have you have s squared here and you have omega s here so you still have many terms. No but you think omega is equal to s? No no omega is of length 0 in this case I mean right I mean I was just describing if this is of length one here a reflection what the possible use are and there are there is one which s times w and then there are q minus one omega times times w and so you have them even if w is s as well.


Welcome to Jalassette News, take a top stories and cryptocurrency Jalassettes and bring them down to bite-sized pieces today. It's really one big story and there's a lot of different multifaceted aspects of it, but it's titled Cardano reports a new major upgrade as ADA posts an inspired rally. This is really all it has to do with moving forward with the road map as far as Cardano and moving into the Gogan era as far as smart contracts. And there's a a lot of different minutiae that we have to take a look at and really disseminate to find out exactly what's going on. And hopefully I'll get a little help from my friend Hashoshi, another YouTuber to explain some more of the technical side. So we'll go over all that and there's a lot of information to go over. But first let's take a look at what is going on in the market. So today it is February 17th, 1140 a.m. on Paso, Texas time. So here's what we got. Again, I think that Bitcoin went above 50,000 for a very short amount of time. But like I've always said, when there are round numbers people are going to take profits. So just expect a retracement. That's just how it is. But I'm happy for that because, you know, if you would dollar cost average, this would be a great time for you. Bitcoin, I have stopped purchasing. I have my limit and I already have my positions and I've already talked about how I believe it's going to go to 150,000 and then it's going to retrace to around 30, 40,000. So anything over that, I don't see a point in actually purchasing anything else. I'm trying to get more into the DeFi space because I think that is the biggest opportunity for growth. And I look at places like Ave and Synthetix, which I'll be doing more of a video on later. Anyhow, Ethereum down to 1744 after getting to 1800. So that's good. Tether, sure. Polkadot and again in that fourth spot and up 3% for almost 30 bucks. That's amazing. The kind of run that Polkadot has had. And again, if you're going to bet on anything, you're going to invest in anything, invest in people. So if you take a look at what I call the Ethereum mafia, kind of like the pay to call mafia, you got Gavin Wood, Dr. Gavin Wood, who created Ethereum alongside Vitalik Buterin, Charles Hoskinson for Cardano.  So that's why you see Cardano Polkadot and Ethereum pretty much in the same place. XRP is down a bunch and that is because there was a article which talked about how Ripple and the SEC looks like they're not going to be able to come to an agreement. And if you know anything about cases and lawsuits, you know, this could drag out for quite a long time. I'm not here to bust anybody's bubble, but I've been through a lawsuit and I can tell you right now it is long, it is expensive, and there's a lot of different circumstances to really get out of it. And there's a lot of factors in play. So if you think it's going to happen anytime soon, it'll think it's happening. So sorry. Anyhow, Binance Coin down 3%. Like Coin, what else we got? Anything up majorly? Not really. Oh, 16% for Cosmos. I don't have Cosmos, so I don't really care. And again, on my channel, just so you know, I'm super biased towards all the things that I own and just how it is.  Ave, I'm down 12%. Hey, what are you going to do? Data token down 6%. Everything's down right now. And again, once we hit these highs, we're going to see your retracement. Let's take a look at, first of all, let me blow this up so somebody can see it. Sorry about that. And what I want to take a look at is what is going on as far as the sentiment of the market. So let me just click on this projected range. Okay, so business from trade the chain, and you can take a look at what the sentiment is as far as like tweets and all the things that are going on in the different websites and blogs and Twitterverse. So I don't know any of these. I don't know, Telos, Cream Finance, Mainframe Horizon, Blockstack, but apparently, hey, Telos, Telos is going to go up 16%, maybe down 13 in the next hour. That's kind of a crappy range. Trust swap, negative four to plus four, Grim, whatever, Maker, Celsius, that's pretty interesting. Bill Barish, I see it going down, but if you want to check that out, there's a link in the description. Let's just jump into today's top story because this, to me, really is the big thing. And Cardano is just one of those projects that takes a long time. They've done a lot of different, I mean, it's really just a creep into things, but I think it's going to be big. Look, we're almost hitting its all-time high of like $1.13, $1.18 somewhere around there. We were at, I think, 93 cents at one point. We'll take it. So what's going on? What is the catalyst for what's happening? So there's been a major upgrade, and this is from all the ADA posts. So just to go back in time, this article was written on February 14th, but it states here on February 3rd, Cardano's development firm IOHK successfully connected the hard fork and applied the Gogan native token upgrade, known as the merry upgrade to the Cardano's test net, which transforms the blockchain into a multi-asset network similar to Ethereum. And the things that really vary as far as Ethereum is fees, gas fees. And there was a tweet from Ray Youssef. He is the owner of Paxful. He talked about how great non-fungible tokens are, if it wasn't for the fact that it just costs like 170 bucks just to get it up and going if you want to do a non-fungible token. And we all see these with like the fees for ERC 20. And we'll get into that, but this upgrade, we'll talk about in a bit, is really going to decrease almost nothing, fees. And it's pretty amazing how they do it. So the team expects to have launched the main net by the end of February. So let's back up. First of all, let's take a look what they're talking about as far as the Gogan roadmap and Cardano. I will link this in the description. It's just the roadmap.Cardano.org. And what it talks about here is actually let me blow this up so everybody can see it. It makes a lot more sense if I can actually show you what you're looking at. So Gogan itself has the ability to build dApps, the essentialized apps on Cardano's fellow foundation of peer-reviewed research and high assurance development. So that was the big thing because when people always talk to me they're like, well, what has it done? Who is building on it? What is going on? Which I understand you couldn't really build too much on it because they need a Gogan to come into play. So now that Gogan is here, now you can start to have dApps. And they've built their own language, Plutus. They've done a lot of things as far as making it very easy to build on it. So I expect things to take off. And the real question was always like, well, why the heck does it take so long? This part right here where it says peer-reviewed research and people are like, what are they talking about? And all this means, let me come back here. All this means for this peer-reviewed research is that they actually put these papers out and they don't have people inside their team go, yeah, looks good. What they do is they send it out and they say, we want you any kind of academic different properties or different schools or different people to actually take a look at that know about blockchain. Take a look at what we are proposing. Would this actually work or is this just not a really good thing? And it's always done, well, it's done a lot. As far as medicine, as far as pharmaceuticals, they want to do peer-reviewed research. They take a look and say, this is what we have. Tell us if this is total bunk or if this is actually going to work. And these are the only ones that actually do this. So I understand now why they do it, just because the same thing as far as medicine and medications go, or the medical field, they can take a look at this and go, hey, tell us what you think. And so far it has come back very positive. And this is the thing as far as taking these small incremental steps to make sure it's done right. Think about some v5 products that you know about right now. How many of those have crashed and burned just because they're trying to throw things out there? And I got to look, I got to tell you, for what I do as far as entrepreneur, I'm the same way. I just throw stuff out until it breaks. Like, well, that didn't work out, we'll do something else. Well, let's do this, let's do that. But when you're playing around with people's money, it's a little bit different than an actual product. Like if a product comes out and rolls out and like, oh, it didn't work out, so we'll just change it. But when you're talking about people's money and life savings, you can't do that. When you're talking about going into like Sub-Saharan Africa and making a payment system, you can't really do that. When you're talking about, you know, bringing in these like Fortune 500 companies and then just think just screw up left and right, you can't do that. And I get now why they have done all these things and it makes a lot of sense. Anyhow, let's, let's move back here. So this is one of the goals for the golden era has been the creation of Clutus, a purpose built, smart contract development language, an execution platform using the functional program Haskell. This allows one code base to support both on and off chain components, improving the coherency and usability of the development experience, compared with existing smart contract implementations. So jumping back to finish up this article, it talks about for the first time users on the Cardinal blockchain will be able to create their own tokens, be it fungible tokens or NFTs. And if you've been aware of what is going on, I think NFTs are going to be the next big thing. I have not kept up to date with it, but I will be delving into that a lot deeper moving forward. And then this was the interesting part. And we'll get into this with hash in a bit, but Cardinals token design. So the first major difference following the upgrade is that there will be no execution fees, none. So in Ethereum, we can call those gas fees, but on the Cardinal native blockchain, there's going to be no execution fees. This is from Heinrich Pfeiffer, General Secretary of the Cardinal Foundation. He states native tokens on Cardinal are forged on chain with no need for a smart contract and therefore no execution fees required to transact native tokens on Cardinal. Instead, sending tokens requires a nominal fee called the minimal aid of value. And he talks about how you can actually model these together and it'll increase the fee just a little bit, but not too much. So again, when we take a look at what's going on with Ethereum, it's a great platform and everybody's building on it. But the reason is because you really couldn't do too much with Cardinal. Now that the Gogan era is here, people can start to create dapps and then those fees are going to go down. I see a pretty good market niche for Ethereum to really plug into. Will they be the dominating force? Who knows? But I think, again, that there is enough room for two major players. So let me skip this part and just go to the last piece. So the big thing for me is about usability because I'm not a programmer, but when it states here, it says the fact that Cardinal has been implemented in Haskell, a functional programming language that is known for its high liability apps, could open up different business use cases involving large enterprises and even governments. And Pfeiffer finally states Cardinal may stand up or may stand to capture an altogether different share of the market than Ethereum at a national level, identity solutions, back and eventual infrastructure, and powerful enterprise use cases. So what is so important about Haskell and Plutus? And it really comes down to that Gogan road map. So let's jump over there. I'm going to show you exactly what I'm talking about. And the Gogan era also encompasses work to make Cardinal accessible to wider audiences via Marlowe, which is good for me. This allows financial and business experts with a no previous technical knowledge such as myself to create smart contracts. So Marlowe and the Marlowe playground simplify the process for creating smart contracts for financial applications, finding subject matter experts to directly contribute without requiring deep programming skills. This could be a big boom for potentially DeFi decentralized finance. So remember what I want to know, we talked about this in the past, we say, if you don't know what to pick as far as DeFi, you don't really know what Ave, you only know about Compile, you only know about Synthetics or Wi-Fi, just buy Ethereum because everything's built in Ethereum. However, I think that may change. So for all this stuff, I mean, even for me, like I'm looking at this and I'm like, what the heck, it's kind of confusing what they're talking about.  That's why I brought in my friend Heshoshi. So let's jump over to the Zoom meeting and let me have Heshoshi actually explain what the heck is going on. All right, everybody. So welcome here. We've got Heshoshi from the Heshoshi YouTube video and our YouTube channel. And he is one of the few people that I watch almost on a daily basis, along with a couple of different YouTubers.  So the first one I have is when I was, when we were reading this hash, we were talking about how with the Gogan era coming in, that now that people are actually able to create dapps on the Cardano network. First of all, have you done anything with the Cardano network and how easy is it to actually build a dapp on Cardano as opposed to whatever else you might have done in the past? Yeah, sure. I think that from a perspective of, I guess, experience building things, I think the most experience anyone would have at this juncture is working on sort of a test nets or playgrounds, right? Because the major updates are going to come to the Cardano main net, maybe people might know it by the name Gogan, will bring eventually the ability to build smart contracts on main net, which then subsequently enables decentralized applications at large. So what I've done to date is I've tinkered with the two language playgrounds. You have on one side, you have Plutus, which is the really formally verified functional programming language based on Haskell. And then you have Marla, which is basically an abstraction of Plutus. Marla was intended for people that might not be programmer-programmers, right? It gives you a graphical user interface to drag and drop logical components. If you can build a workflow and you understand business process flows, you can make then a functional Plutus smart contract that's deployable to main net. And that's using Marla, which is more specifically a domain specific language. Got you. So I've worked on both. Perfect. So Hash, could you see Marla being used for any kind of financial industry where they're like, you know, we want to build kind of like decentralized finance, we want to cut out the middleman, and we want to make this flow, we have no coding ability.  Yeah, I think that's exactly the target. And I would see, you know, business process managers, some, you know, I guess people who manage financial transactions and even enterprises that want to enter into contractual agreements for which payment is processed between the two, they can do that using literally a drag and drop interface. And I can send you a link and you can click and you can go to the playground. You can see it in action and actually build out something on Marla now in a test net environment, which is really cool. Send it to me and then I'll put it in the description so people can play around with that. That's pretty awesome. So that will make a lot of sense because I know with the different heads of the organizations for IOHK and IGO and whatever else, it seems like they're really focusing on the Fortune 500 companies, like the big enterprise type of levels. So I can kind of, now I can put the pieces together about why they want to do it like that because not everybody has developers and they kind of make it like that. Got you. So talk to me real quick about the fees because I mean to transfer everything on Ethereum is crazy, ridiculous right now. Even NFTs and things like that. How can you drop the fees to where these Fortune 500 companies be like, you know what, we don't know what's going on over there, but we like what we see here. Let's go this route. Yeah. And so I talked about this recently on one of my videos where there are a lot of people now calling for no fees. Let's just eliminate fees from blockchains. It's a barrier to entry. I vehemently disagree with that idea because fees are very important in terms of the security model for most decentralized networks to be what they are. First and foremost, it prevents people from malicious actors from just sending thousands and thousands or millions of empty transactions to the network to DDoS it, to denial of service attack it. So when we move past the no fee idea, really the biggest thing that drives fees in most of these types of networks is laws of supply and demand. There's a limited amount of block space. There's a limited amount of processing power and storage space. Those are the big three and the miners or the block makers, they have to process smart contract transactions in the map to store the data, if there's state changing information, etc. That's the main driver for fees. And Ethereum, the reason why the fees are so high is because of supply and demand. There's just not enough space in blocks and enough room in blocks to process enough transactions. So that's where we're at now. And did you have something to add? Sorry. No, no, it wasn't about that. So talk to us real quick about block space, Ethereum versus Cardano because Ethereum was created what, 2014, 15? 15, yeah. Yeah. And then we talk about the second generation blockchain. Now we're looking at Cardano for the third generation. So how does that blockchain size differentiate? So now we can have those fees, not so much because, like you said, there is supply and demand. We have more of a supply over here. Yeah, I think it's just architectural decisions that were made in the development of Cardano. Understanding that when Cardano really, really kicked off, let's say, ages ago. It's been a long time since Cardano started building. They were taking lessons learned from Ethereum back then and have continued to do so. And so you have architectural decisions like the modified UTXO model that they use, plus the proof-of-state, the Orboros protocol for consensus that's been developed voraciously over the last several years. And so those are some of the things that help with scalability, right? You can process transactions faster. You don't just have one parameter to pull on, which is just block size. So it's part of the mix is how fast transactions can be validated securely. Gotcha. Okay. So first of all, Hash, thanks. I appreciate you coming on. So lastly, I'm going to ask you a bigger type of question. Where do you see Cardano and Ethereum at the end of this bull run, which, oh, no, we'll say the end of this year, 2021, as far as market cap. Where do you see it in the next five years? Interesting. I think if you look at Cardano and what they have planned, right, the master plan, quote-unquote, starts to come together this year with Gogan and then subsequently Bosho and Voltaire, some of the governance stuff that's coming. I have a feeling likely what that will mean is that Cardano's market cap will at least double this year, in my mind, at least, if not more. I think in the five year time span, a lot of people are looking at Cardano to start challenging the market cap that you see Ethereum has, right? And I think sometimes people talk about Cardano taking the market cap that Bitcoin has, but they're so different. I don't think you can compare the two. You're more likely to be pulling from the money that's already in something like Ethereum. But that being said, all of this is dependent on new money coming into the space. So there's that one caveat. I don't think it's going to be a situation where Cardano just takes all of Ethereum's market share, because there are also other projects that are involved in this fight. And it's not a zero sum game. A lot of these projects will be successful in their own niche. And Ethereum is really going to be hedged on E2.0. It could very well hold on to a large proportion of the market cap it already has, but maybe just add new money more slowly because there's competition. I have a feeling that's really what's going to happen. Yeah, I agree. I agree with that. I think there's room enough for two, but again, we will see. So you heard it here first. Hoshoshi said $10 to Cardano at the end of this year. Great. Thanks. One can only pray. All right, man. I appreciate it. Let's jump back. Okay, so I hope that helps. Now you know Hoshoshi. He's one of those guys that is always in my description of every one of my videos of all the different YouTubers that I watch, almost on a daily basis. So you can check them out along with all the other people that I have down there. So let me just finish up with this. And that is that if we're talking about Cardano, I've got to talk about stake pools because I just want to talk about my own. So just so you know, DNews has its own stake pool. And just so you know, we now have two. And the reason that we have two stake pools, and you can find all this information at pooltool.io, actually an easier way is in the description of every one of my videos, if you just scroll down the Dan Cardano stake pool, there's a link right there. It'll take you to the actual webpage. And if you just scroll down to wallets, it'll tell you everything you need to know about how to stake with DNews. But what I really want to talk about is that two things. Why do we now have two stake pools? Well, first of all, it's easy. If you go to pooltool.io and search for DNews, you can see how much are active stakes, the fees and epoch fees, all those things. But also if you scroll over, you can see this thing called lifetime ROS, return on spend. And usually the industry average for Cardano stake pools is between four and six percent right now. For the first one, we're around 5.35. So we've been up as high as 5.42. And then I think we're down to 5.26. But we're always above average. And the reason is because we use the Microsoft Azure network with Kubernetes and we try to be up as much as humanly possible. 99.9%, if not 100% of time. So we don't miss any rewards. On top of that, the reason why we just started last week, the DNews stake pool number two is because of this. If you go to pool.pm and look for DNews, I'll link that in the description as well. You can see that our saturation point is at 48%. So why would we make a new one? Well, in a couple of weeks, I think in March or so, they're going to set the limit for the maximum to around 32 million, 31.5 million, some around there. So we want to get ahead of this because if you stake to a saturated pool, something like this will happen and we blow this up. So when you have too much saturation, everybody who is delegated to that pool will lose rewards. So in this case, they are oversaturated 70%. So you're losing 70% reward loss. Before that happens, we need to make sure that we get in front of that. So right now, if you want to stake with the DNews stake pool, you can go, first of all, watch that video, which explains how to stake through your deadless Yoll-Roy or 88 light wallet, how to find that second stake pool, which is pretty easy. Just go to DNews and just find the ones that have the very few least amount of delegates and just delegate to that. And watch the video and we explain exactly why. In my opinion, our opinion, Cardano staking is vastly superior to Ethereum staking. There are no slashing rewards. You can move in and out anytime that you want to. And it's just a really simple process and it's just automated. So that is it. That is it for today. So actually, no, that's not it. Excuse me. There's a couple of things I want to talk about. I forgot about this. So as far as Cardano goes, people talk to me and they say, well, you know, Cardano is going to be the greatest thing ever. It could be, but you have to look at what's going on right now. There's a website called crypto fees.info. And we take a look at this. You can see all different crypto projects and what people are actually using right now. So we take a look at Ethereum as a number one. This is as far as fees go, this is where you can see like what is actually being used. So Ethereum is being used massively and people are paying massive fees. Next one is Bitcoin, next one is Uniswap, SushiSwap, Compound. It's a good one to get into. And you can see that the more fees that are added up, the more people are actually using it. So we take a look at this. We're like, well, shoot, we go all the way down. There's not really much anything that is going on as far as Cardano at 5,916, which is right here. Not too much. So people would just assume that, okay, well, Cardano is never going to make it because that's just how it is. But I want you to remember one thing. Now I'm not here to say anything that one person is going to win or one's going to dominate. I think there's room enough for two, just like we talked about in the article. But if we take a look here, I just want to show you Internet browsers. And if you're old like me, you can remember these Internet browsers, but just as a quick refresher, people always talk about, well, this, it's only going to be Ethereum for a while. Remember Netscape Navigator? Well, that dominated in the 90s. And then all of a sudden Internet Explorer came around. Again, people don't know because they've got old, you don't remember this stuff. So then, well, what happened? Well, that would just stay on top, right?  And before you knew it, that started to take over. Well, not really, but it would take a little bit of time. And then all of a sudden, as time went on, 2005, 2006, and 2007, there's going to be this, this web browser, it's going to start to pop up at some point. And it's going to be talking about Google Chrome. Google Chrome wasn't really much of anything. And all of a sudden took a year, a couple of years, really started to really play a part. Firefox was supposed to be the next one, didn't make it. And then Chrome came in. Why did Chrome come in? Well, it was just better, it was stronger, it was faster, and it was backed by a lot of different companies and industries that really put their weight behind it. Of course, Google was the biggest player. So when we started to talk about, well, Cardano will never make it because Ethereum is just so up high. True, could be. As time goes on, we will see who will be the dominating force. Again, I think there's enough room for more than one browser, like right now I'm using the Brave browser. Some people use Google Chrome, and some people use something else, so whatever you want to do. But that is it for today. So if you made it this far, I want to say thanks for watching all the way in. I appreciate it. If you like the video, give it a thumbs up. Also consider subscribing because a lot of things we talk about are time sensitive. And that is it for today. So thanks so much. I'll put two more videos up if you like this one and what YouTube is magic. That is it. Thanks so much for watching. See you on the next one.


Hello everyone, so we'll talk about our third and final abstract data type that uses an array-baseless data structure And that is the deck or double-ended queue. No, it's not DQ. It is a deck and a deck is actually it's It's kind of an esoteric little ADT doesn't get used in a whole bunch of applications But nonetheless, it still exists and it's not too hard to understand what it is A deck is an ADT where addition and removal Happens at both ends right and you can say that it essentially combines the behaviors of a stack and a queue It has a notion of a front and a rear Just like a regular queue does but you are allowed to add to the front Remove from the front add to the rear and remove from the rear and that's it But you know what differentiates this from a list The differentiator is you can only operate at either end You have more flexibility in what you do at either end But the operations all happen at the end. You don't work in the middle You can't get random elements out of the middle of this thing. Okay? there are some Reasons for using this It's because one area where you see it a lot is CPU process scheduling Right, so you have a whole bunch of processes that are running on your computers for all your different apps that you've got running right now and your operating system decides who gets to go, right and Oftentimes the operating system puts those things in a queue all the apps that are running on your computer Demands some processing power from your your computer's brain from the CPU But your computer's brain can only handle one thing at a time. It can handle them very very fast about three billion times per second But it can still only handle one at a time and it's up to your operating system to determine Which one of the hundreds of applications that are currently running right now actually get the that valuable processor? attention and CPU process scheduling usually it happens in a queue first come first serve But every once in a while something really important comes along and it needs to go first it needs to go to the front of the queue And that's where you see a deck show up, right? Like if you hit control I'll delete on Windows and you want that keyboard stuff to go through and The stuff to pop up immediately. Yeah certain things have higher priority. Okay, so decks exist But the good news is if you understand the concept of a queue, it's pretty easy You have a front you have a rear you can add and remove from the rear and you can add and remove from the front That's it the middle. We don't worry about So let's just make sure we understand conceptually what a deck is Let me switch back over here in my way for it Okay So now we're looking at this page of the worksheet the deck page on the worksheet and let's walk through the operations It's going to look like a queue. Okay, the things that we do so step one We initialize kind of an empty deck nothing there, right? Okay, step two add to the rear Line line is going to be the rear of the queue Well, so are the rear of the deck excuse me So just like a queue a deck needs to have a notion of a front and a rear Now when there's only one item in a queue or a deck the front and the rear are both that one single Okay, if the deck or the queue is empty Front and rear don't exist, right? There's there's kind of like an error state there If you try and access the front or the rear of an ID queue Or deck so when we add to the rear here both the front and the rear are pointing to our In reference to this line. Okay, same will be true if we added front here Right. Okay. There's one item in a queue or a deck. It is both the front and the rear Okay. Now deck step two We just did step two step three We are going to add to the front Add front Bear now add rear add front remove rear remove front those are all methods You will write in your deck class How you in you will implement them using a Python array based list So it's going to look a lot like your queue implementation, but with a couple of extra things All right, so we are adding to the front the bear Move my little step indicator a little bit. So let me put the bear in front Okay, and we need to Move the front here Okay So we've got the bear Then the lion And the bear is front Lion is the rear. Okay. Again, think of it Like a line at a grocery store or a line to get on the airplane Some people can go first and they get added to the front. They are specials. Okay All right Step four adding to the rear. Okay, so we're in line at the airport and the bear gets on the plane first Could get on the plane first the lion gets on the plane Next and now comes the hog step four add to the rear the hog The hog goes at the end and now Conceptually the rear of this list Is here All right, we've just done step four All right, step five. We remove from the front Step five you really see this on the screen Step five we remove from the front Okay, who's at the front? Well conceptually We've defined the front to be here. So the bear where you're going to remove and return the bear And when we remove from these data structures, we are usually returning them as well. Okay, so remove and return So the bear goes away Who is now the front? front is now The line step six Remove from the rear. Okay, who is the rear? Conceptually the rear is the hog Okay, so the hog gets removed and Return hog is gone. He got tired of waiting in line. So he left. I can happen, too Want to get a drink who is now the rear of this deck? Well, there's only one element in it and that's the lion. Okay, so the front and the rear You know as you add front as you add rear as you remove from the front remove from the rear You just got to know conceptually where's the front? Where's the rear and add or remove? You know consistently from whatever a location you specify. Okay? That's about it.  Okay So Here's the big O's of these operations and like we had let me get rid of myself Like we had with the queue It when we use an array based list it as our data structure for Implementing our deck data type. We have to make a choice in our list our Python list Where's the front? Where's the rear?  It's up to you. You will pick There's no right or wrong answer for a deck or a queue. You just have to pick one and use it consistently and just like with the queue You some of your operations will be big O of one and some will be big O event Which ones are big O of one or n? Depend on whether you choose the front Index zero or index negative one as the front of the queue and the deck Okay, so what what's important here is that you understand why When you have a data structure, that's a Python array based list You're picking one is the conceptual front or conceptual rear of a deck or a regular queue You need to understand why One of those things working at one of those ends is big O of one versus big O event Okay, so convince yourself of why that is and make sure you understand it because you will definitely get questions about like what's the efficiency of queue dot Anqueue or deck dot remove rear when your data structure treats Index zero and the Python list as the front And what's it going to be as big O once a big O event you got to know it and don't memorize it Be able to figure it out based on what you know about array based lists. That's the key You've got to know the efficiency the big O efficiency of those array based list functions Everything else is going to follow from that. So as I mentioned last time, I'll bring myself back for a minute queue and deck operations We care about adding and removing from these data structure or these data types. Excuse me in These ADT's abstract data types one of these operations adding or removing must be big O event Because we use a Python list as our data structure must be must be the case because that's a limitation of the Python data structure Okay, so We could make adding and removing from a queue from both ends of a queue they go one but We have to change we cannot use a Python list Internally we have to take it up a notch. We got to implement our own data structure and we will next time so Have a good look over these You now hopefully have all the knowledge that you need to work on your next assignment Where you're going to implement the stack the queue and the deck ADT's and then you are going to write a little program that uses your Stack to solve a problem Let me know a questions you have and I will see you next time