So I just wanted to spend a few minutes with you. I know it's a huge topic and really hard to boil down in such a small amount of time, but if you could just sort of give me an overview of how is history in a nutshell formed how I think about my faith and how I live it out. Wow, obviously huge questions. And actually for a British person to be talking to an American person about this is already a little tricky because quite a large swathe of American culture back in the 17th and 18th century consisted of disaffected Brits who had been fed up here, gone to the New World to say now at last we can practice our faith properly. So there's always that sort of sense of don't you Brits come over here and tell us how to do it because we got rid of you some while ago. And there was this funny thing called a war of independence. If I remember right. I've heard of it. 230 years ago whenever it was 40. And so already we have shared history which warps our sense of perceptions. And I've been aware of that once or twice when I've been in America one time when I was a visiting professor at Harvard. I had to preach in Harvard Memorial Chapel and I've been doing some homework and discovered that a great great great great uncle of mine had been the first chaplain of Harvard University which I've never known before and that he was a royalist. He was in favor of King George. And then when the glorious revolution happened he was on the boat back home finished his days as a canon of St. Paul's Cathedral. And I thought yeah this is kind of funny and here am I now. So let's just sort of name all that right off the top because nothing that I say is intended to be a criticism of one particular nation or culture. And I do want to say as well God moves in many mysterious ways and if God was waiting for us to get all the answers right before God could ever live within our lives and work through us and establish a relationship with us. God would be waiting a long time and we'd all be in a big mess. So that everything that any of us say however well-tuned and accurate and biblically shrewd et cetera is still some way down the mountain from where say the Archangel Gabriel sees things. So some of us say this to students when they say how can I ever get my head around this and I say well look here is this vast mountain. I may be a little bit further up than you simply because I'm older and have studied a few more texts but we're all climbers and let's just agree we're on a shared journey. Having said that I don't know very much about Eastern Orthodox Christianity I know a bit but most of what I know is about the Western tradition which is that after the split roughly a thousand years ago of Eastern West then what we now think of as the Roman Catholic Church became the dominant force and in Western Europe that was so until the Reformation of the 16th century and which was a hugely turbulent thing. Throughout that middle age period there were various theological streams but among the great influences on them were the great Greek philosophers Plato and Aristotle and there's an awful lot of Plato in Western medieval thought which is still in Western thought to this day. Now Plato the great Greek philosopher roughly 400 years before Jesus Plato believed that though the material world wasn't exactly a bad and dark and terrible place it wasn't the reality. It was just a shadow of the reality and really we humans had souls which were something not a bodily thing but which belonged to us as it were or at least we had them on temporary loan until they then wanted to go back home where they'd come from namely to heaven and that's an idea that's deep in the Platonic tradition both in Plato himself in the middle Platonism of the 1st century in the Neo-Platonism of the 4th, 5th centuries and to this day many if not most Western Christians assume that the purpose of religion of whatever sort is quote to go to heaven when you die and indeed to challenge that rather as you said makes people think oh dear this person's a heretic it's terrible. All the alarms start going out. Yeah exactly well I know that I know that perfectly well but that's the funny thing right off the top I want to say that the great story of the Bible is about God making a world where God wants to come and live with his human creatures and he makes us in his image so that it's appropriate for him to come and share our life and that is still mind-blowing to me I've been thinking about this for a long time because it demands that we think differently about God, about who God is but that leads to the next thing along because from about the 14th century that is the, no sorry, the 15th century that's the 1400s as opposed to the Reformation period which is the 16th century, the 1500s you get a revival of the ancient philosophy of Epicureanism and for Epicurus unlike most other people in the ancient world because he wasn't the most popular philosopher by any means if the gods exist, gods plural they're a long, long way away from us they have nothing to do with us we have nothing to do with them so that instead of gods having a finger in every pie which was what ancient paganism seemed to think no, we don't need to worry about that they're a long way away nothing we can do affects them so the world just makes itself under its own steam it's all a matter of atoms bumping into each other and doing new things and so this is quite a convenient philosophy for the rich and well-to-do which it was in the ancient world and it's interesting that it becomes popular in Europe just when Europe is becoming what we now call the first world when through its exploration, through its culture, through its science and technology it as it were elevates itself or if it is an elevation above the rest of the world and guess what we become Epicurean and so we tend to favor theories about the world making itself in other words evolution is that evolutionism starts way before Charles Darwin and all Charles Darwin does is he goes on a boat and he finds some finches and tortoises and goodness knows what else to provide some sharp examples of the way in which species seem to have evolved according to their conditions and I know this is hugely controversial in America but I want to say as far as I can see biological evolution is a fact evolutionism is a philosophical theory which actually goes with the ancient Epicureanism you know this was not a new idea in the 19th century and it's all to do then with whether the being we call God if we do call a being God has any part to play in the system or not and one of the things that was going on in Epicureanism was we don't actually want God on site because we are strong now we are independent so you get this thing called the Enlightenment in the 18th century which is a way of saying we're going to kick God upstairs you can go and visit him if you want like a nice old elderly relative go and see him on Sundays he'll be glad about that but then come back to the real world and where we all live and so that goes with historical skepticism particularly in the 18th century which then affects how many in Europe and America read their Bibles oh we can't believe that sort of thing anymore can't believe that Jesus walked on water can't believe that a human being could be divine or that God would become human we now know that that's impossible which means with our newly enlightened version of Epicureanism we've ruled it out before we even start investigating so what then happens alas is that instead of saying wait a minute the Bible has a much better metaphysic than that a much better idea of how heaven and earth would go together than that many many devout Christians in the 19th century the Victorian period in Britain and America and elsewhere went back to Plato and talked in terms of the soul and actually we do have a soul that is in touch with even if but often they kept the distant God either an Epicurean God but he shouldn't really be having anything to do with this or perhaps a Daist God because Daism is like a slightly more friendly version of Epicureanism you've got a God probably just one God who is quite a way away who doesn't normally interfere but probably is looking down and checking us out and wondering if we'll ever make it and that's the model that split level model which so many Christians have to this day and they fill in the gaps with Plato that we have this soul we're gonna have them sooner or later and then you get different theories about who gets to go and why and the different theologies of salvation are really worked out within that frame of reference the Enlightenment produces what is known in the trade as modernism since then really most of the 20th century but it's only really burst on the scene in the last 40 years we've had what's called post-modernism which is a way of saying all those big stories about how great we are and how special we are and how our knowledge is pure and complete and entire that's just a power grab and instead we have a confused world where all sorts of things are going on and this too becomes a power grab actually because it's a way of saying we don't like rulers, we don't like systems we're just gonna do our own thing with all sorts of spin-offs of that that means it's been very very confusing as that has struck the mainstream cultural life I think particularly in America and an awful lot of people who were brought up with a sort of conservative modernism because if you take Plato he will help you to be a conservative within a modernist framework and so we can believe in a God and he did give us a Bible and he did send Jesus, et cetera, et cetera and then we sort of keep the heretics at bay but then post-modernity comes along and says hang on, all this stuff seems to be in the interests of the powerful in the interests of the Western world in the interests of business, whatever it is and maybe Jesus himself might have some rebuke to give us on that and so right now I think we have a lot of people in the younger generation who live in that post-modern world which says a plague on all your big dreams and they're reading the Bible and something hugely attractive about Jesus but the frameworks that they're being given are not helpful as a place to live and I think it's more or less where we are Now, how was that? The five minute version of modern European intellectuals No, you nailed it, yeah The, these are the two red flags that went off as you were talking One, how could God let that happen? You know, how could, how could as far as I understand, like pretty early on there were significant shifts in understanding of what the soul is and what happens so that's one red flag that like how, how could God let that happen? And the other red flag is are you telling me that I can't just sit here and open my Bible and read in English completely perfectly understand everything that God was saying Well, if you could, please let the rest of us know because I was quite muddled about things I'll email you So those are the two things that I find unsettling as a very individualistic American I want to just be able to open my Bible in English and understand it for all it's worth and I don't like the fact that that someone is telling me that things happened long time ago that affected, drastically affected how I live out my faith that feels uncomfortable to me Right, right Well, I mean I think it's very interesting probably only in the last two or three hundred years would people perceive this as odd because in the early centuries the early Christians were fighting so many battles and there were so many different ideas flying around and different groups of Christians would embrace some of them and what we now look back and call the early heresies like Marcionism or indeed Arianism and so on these are things which a lot of people really did believe and I think in retrospect the people who were arguing about the might have said to us that God allowed that in order to stimulate his people to a deeper grasp of the truth you know, if you hadn't had Arianism you wouldn't have had Athanasius articulating the theology which became what we now say in the great creeds the Nicene and Constantinopolitan creeds God of God, light of light very God of very God, etc. and I would say of anything like that it is perfectly possible that in the providence of God wrong ideas are allowed to come up precisely in order that people can say hang on, no we need to do some more work on that because this is one of the things I've found about the Bible throughout my life that the Bible is never a static book it's never simply oh wouldn't just go and check out this answer and then go back to sleep the Bible is always stimulating us and if it isn't then something's wrong you know, when you read the Psalms or the book of Job or Jeremiah or let alone Paul or Revelation or whatever it may be if you think that this will all just go straight in and it's all plain sailing well, I'm sorry you know, you're not taking it seriously and I think in the modern period in the Western world we've been greatly infected by a philosopher I didn't mention before called Hegel and Hegel believed in this developmental scheme that the world was actually progressing in fact, the word progress means what it means for us because of Him and I think a lot of Christians imagine as many did in the 19th century that actually in the purposes of God the world is just getting better and better and better and the Kingdom of God will arrive now the 20th century put a big explosion against that and I wanna do the same with any idea that in terms of belief that we all just believe the right stuff and that's what it should be and I don't want to say that in the way that says everything we believed is wrong because grasping onto Jesus and being grasped by Him remains constant and that's so for many people in many traditions and we are all to a lesser or greater extent muddled but Paul says again and again be transformed by the renewing of your mind and that wonderful line in the middle of 1 Corinthians 14 where he says when it comes to evil I want you just to be little babies just don't need to know about that stuff but in your thinking I want you to be grown-ups I want you to be mature and I think that's a word for Western Christianity now don't remain at Sunday school level there is such a thing as grown-up Christian thinking and it's good for you and it's part of loving God with your mind Yeah, yeah Thank you sir Thank you, bless you Thank you very much


Hi, I'm Zor. Welcome to Indizora Education. I would like to do some calculations related to launching satellites today. Very, very simple, very basic calculations. We are talking only about the speed of the satellite, which is rotating around the planet. And I need that speed, basically, based on certain parameters. So, we have a few laws, basically two laws, and both are related to Sir Isaac Newton. Okay, one law is the gravitational law. If you have two objects, now we are talking about ideal situations when both objects are either point masses or spherical, with the center of the gravity in the center of the sphere. Now, Newton's gravitational law sends the following. Hope is familiar to you. So, this is the gravitational constant, universal constant. This is the mass of the planet. This is the mass of satellite. And this is the radius from a center to a center, center of the planet to center of the satellite. The radius of orbit, we want that satellite to be rotating around the planet. So, it includes, actually, the size of the planet. So, it's from a center of the sphere of the planet to a center of the satellite. So, we know this. Great. This is the force which acts on the satellite when it's rotating. Now, if that would be the only force, then the satellite would just fall on the planet. Now, we have to launch it so it goes around the planet with a certain speed. And considering this is a circular orbit, there is a centripetal acceleration. And if there is a centripetal acceleration, it must be centripetal force, which is basically equal to this one. So, these are two different kind of tendencies which are acting on the same object. And it's just two different ways of calculating this. Because if you would like to, if this is the planet and this is the orbit, if there is no centripetal force, the satellite would go along the tangential line. So, there might be a force which pulls it in. And that's a centripetal force. And since this is actually the source of this force, we are equalizing centripetal force which can be calculated as m times a where a is centripetal acceleration. And this one, these are the same forces just calculated from two different viewpoints. This is from the viewpoint of the gravitation law and this is from the viewpoint of pure movement laws. And this is kinematics, if you wish, because acceleration is a kinematic characteristic. Okay, so what is A? We are talking about the speed, linear speed, the satellite is supposed to be circulating the planet. So, how the speed is related to acceleration. So, we are talking about linear speed. We did calculate it a few times, but in any case. Basically, let me just write it down. A is equal to b squared divided by r. Now, how to obtain this formula is very easy. If you have a circular motion, the best and probably easier way is to describe x and y characteristics of this. It's r cosine omega t and this is r sine omega t. Now, the speed is the first derivative, right? So, the first derivative is, I'm using something from the calculus, but basically that's something which people did many, many times before. The first derivative is what from cosine is minus r omega sine omega t from y is cosine, so it's r internal cosine omega t. The second derivative which gives me the acceleration, it's minus r omega square cosine omega t and y is equal to minus r omega square sine omega t. Acceleration is equal to the length of this vector, vector of acceleration by coordinates which gives me r omega square and linear speed is equal to radius times angular speed, right? So, from this, acceleration is equal to r omega square omega is equal to v divided by r, so it's v square divided by r square and we have formula as I said. Now, it's a very, very quick derivation in any case that's supposed to be addressed in kinematics of rotation which we already covered it before. So, this is equal to m v square divided by r, okay? Now, this is the same force, so I'm just equalizing that and that's where we are getting the speed. Now, what's absolutely amazing, at least for me, is this. So, it doesn't depend on the mass of the satellite, it depends only on the radius. v square is equal to g times m divided by r and v is equal to square root of gm divided by r. So, g is gravitational constant, m is the planet mass and r is the radius distance between the center of the planet and the center of satellite. So, this is the speed which we have to really give to a satellite like a push, so whenever the engine of a rocket brings the satellite to a proper distance from the planet, then it should turn and push it with this speed. As soon as the speed is sufficient, you can turn off the engine. Now, this is a very complicated process because first you have to really bring the satellite up. Now, that actually depends on the mass. I mean, the heavier the satellite, the more difficult it is to bring it up to the orbit. The engine must be much stronger. And then you have to really turn it in such a way that it retains the distance needed for you and then goes. Okay, what else can be derived from this? Well, actually we can derive the period.  So, what is the period? If we have the speed, now the distance we also have, the distance is 2 pi r, right? So, we divide 2 pi r, t is equal by speed, and what do we have? We have 2 pi r, and t goes another way around, r divided by gm. Or we can put r inside the square root. It would be square root of r to the third degree divided by gm. Okay, now gm has nothing to do with general motors. It's gravitational constant in the mass. The greater the mass with the same radius, the faster it should actually rotate, obviously, because the mass is pulling the satellite stronger if it has a bigger mass. So, that's basically it. That's all I wanted to say about the speed and the period of a satellite which is freely without any engine working. Freely rotating around the Earth. It's supposed to be somehow calculated if you want to launch a satellite on a specific orbit. Okay, I suggest you to read the notes for this lecture, which is presented on Unisor.com. The course is called Physics for Chains, and it's mechanics about gravitation. You will find this lecture. Thank you very much and good luck.


I don't know, I don't know when the stream actually starts, it seems to be about 5-10 second delay, or longer, sometimes, it should be live now, we can do some live music while we wait 30 seconds, here, I forgot the link, link again, yeah, this is about 5-6, 5-10, maybe 10 second delay, not great, posting this should be post, just leave it as it is for now, okay, so we have this tool, we were developing last couple of streams, it has this input way from the chicken select, it started quickly, it might be redoing the whole lot, this is interesting, so when you hit F5, that kind of makes sense, but yeah, this chat doesn't clear the data, which is okay, except, yeah, controller 5 should clear it, okay, where is that data stored? Okay, now I'm confused, this is how little I know about the HTML and JavaScript, I thought if controller 5 should clear, I don't quite understand where is that data being stored, and there's obviously something wrong with that, so we are plotting the activation level on top of the membership function, that seems to be okay, same activation of 0, yeah, we somehow need to change this, yeah, there could be a lot of improvements, I'm thinking starting from scratch instead of quickly, yeah, normally starting from scratch is better, okay, I want to develop a new flask application, we are already hosting a few flask applications, so this will be an additional one, more instructions are coming, yep. So, how to use fuzzy logic, it should be an interactive tool, teaching how to use fuzzy logic, the specific application we have in mind is determining the level of noise in an EEG signal, particularly thinking EMG chewing artifacts detection, got it, Dr Beno, for the flask application focused on teaching fuzzy logic with a specific use case of detecting EMG chewing artifacts in EEG signals, front end interface, interactive UI to upload EEG data and visualize the signal, fuzzy logic module, implement a fuzzy logic system to analyze the EEG data, identifying EMG chewing artifacts based on predefined fuzzy rules, educational component, include explanations and resources about fuzzy logic principles and how they apply to EEG signal analysis, results visualization, display the analysis results, highlighting the detected noise levels and corresponding areas in the EEG data, feel free to elaborate or add more specifics. Okay, regards the front end interface, we do want an interactive UI, we do not want to upload EEG at this stage, for testing we would like to use synthetic EEG, we would like to have some sort of scroller that moves through synthetic EEG data, the data should have baseline EEG and periodically have an EMG chewing artifact. Understood, Dr Beno, for the flask application with a focus on fuzzy logic and EEG signal analysis, front end interface, instead of uploading data, implement an interactive UI with a scroller to navigate through synthetic EEG data, this data will have a baseline EEG signal with periodic EMG chewing artifacts, synthetic EEG data generation, integrator feature to generate synthetic EEG data, simulating both normal brain activity and EMG chewing artifacts at intervals, fuzzy logic analysis, the system will apply fuzzy logic to this synthetic data to identify and highlight the EMG artifacts, visualization and interaction, users can interactively scroll through the EEG data, observe the fuzzy logic analysis in action and see how the system detects the chewing artifacts, this setup should allow for a hands-on learning experience without the need for real data uploads in the initial stages. Okay, this sounds great, yep. Fantastic, Dr Beno, if you need further assistance or specific details regarding the implementation, feel free to ask, good luck with your project. Yes, I need you to make the flask application, yep. Creating the flask application requires several steps and I'll guide you through the process. Since I can't code the entire application for you, I'll outline the key components you'll need to implement. Set up your flask environment, initialize. Initialize a new flask project. Install necessary libraries like flask, numpy, for data handling, and any specific library for fuzzy logic implementation. Create HTML templates for your user interface. Include elements like a scroller for navigating the synthetic EEG data. Use JavaScript and Ajax for dynamic content loading and interaction without needing to refresh the page. Implement a Python function to generate synthetic EEG data with baseline signals and artificial EMG chewing artifacts. This function can be triggered when the user interacts with the scroller. Fuzzy logic module. Develop or integrate a fuzzy logic system capable of analyzing the EEG data. Define the fuzzy sets and rules that correspond to normal EEG signals and EMG artifacts. Utilize libraries like plotly or d3, js to visualize EEG data and the results of the fuzzy logic analysis. Update the visualization as the user scrolls through the data. Flask routes and logic. Define flask routes for handling user requests, generating synthetic data, and performing the fuzzy logic analysis. Ensure the back-end processes and front-end interface are well integrated. Test the application thoroughly to ensure it works as intended. Debug any issues that arise during development. Documentation and comments. Document your code and provide clear instructions on how to use the application. This will be particularly useful for the educational aspect of your project. Since this is a complex project, it's crucial to break it down into manageable parts and tackle them one at a time. If you need more detailed guidance on any specific part of this process, feel free to ask. Given the complexity and specificity of your flask application, utilizing GitHub Copilot could be highly beneficial. It's an iPair programmer that can assist in writing code faster and more efficiently. Here's how you can proceed. Set up your development environment. Ensure you. Ensure you have flask and other necessary libraries installed. Set up a GitHub repository for your project if you haven't already. Using GitHub Copilot. Install GitHub Copilot in your code editor, like Visual Studio Code. Start coding your flask application, and Copilot will suggest code snippets and complete lines of code. Begin with the flask app setup, app.py, and basic routes. Use Copilot to help generate the synthetic EEG data generation logic. Progress to developing the fuzzy logic module, where Copilot can assist in writing the algorithm based on your specifications. For the front end, write HTML, CSS with JavaScript, and let Copilot suggest efficient ways to implement the interactive elements. Testing and iteration. Regularly test your application to ensure everything works as expected. Use Copilot to suggest fixes and improvements. Document your code and the usage of the application. GitHub Copilot can also assist in writing clear and concise documentation. Given your project is open source, engage with the community for feedback and contributions, which can be facilitated through GitHub. Remember, while GitHub Copilot is a powerful tool, it's essential to review and understand the code it generates, ensuring it meets your project's needs and attires to best practices. If you encounter specific issues or need guidance on particular aspects of your flask application, I'm here to help. Can you start writing the code? Certainly, Dr. Beno. I'll provide you with a basic structure for your flask application. This code will include the initial setup and a simple route to get you started. For the more complex parts, like fuzzy logic implementation and synthetic EEG data generation, I'll provide a conceptual outline, as these require more detail, project-specific coding. First, ensure you have flask installed. You can install it via pip if you haven't already. Now, let's start with a basic flask application setup. For the index, HTML, create a basic HTML file with a placeholder for your content. Next steps to consider. Synthetic EEG data generation. Write a Python function that generates synthetic EEG data with periodic EMG artifacts. This will require understanding of EEG data structures and how to simulate artifacts. Fuzzy logic module. Implement your fuzzy logic analysis. You might need a library like SKFuzzy for this. Define rules to analyze the EEG data to identify EMG artifacts. Front-end interaction. Use JavaScript to make the scroller interactive. This will involve updating the EEG display as the user scrolls. Visualization. Integrate a library for visualizing the EEG data and analysis results. Please note, this is a basic starting point. Your application's complexity will grow as you add more features like fuzzy logic analysis and data visualization. If you need more detailed guidance on any specific part of this process, feel free to ask. Continue with the code. Yep. Absolutely. Dr. Beno. Let's expand the code to include a basic structure for generating synthetic EEG data and setting up a route in flask. This example will be quite simplified and won't yet include the actual fuzzy logic implementation or sophisticated EEG data simulation.  First, let's enhance the flask application with a route for generating synthetic EEG data. This code includes a function generate underscore synthetic underscore EEG, which, for now, generates random data to mimic EEG signals. The route generate underscore EEG calls this function and returns the synthetic data as JSON. Next, let's create a basic HTML template, template slash index dot HTML, dintract for this route. Improve EEG data generation. Modify generate underscore synthetic underscore EEG to create more realistic EEG data with distinguishable EMG artifacts. Fuzzy logic analysis. Implement the fuzzy logic module to analyze the synthetic EEG data. Visualization and front-end interaction. Integrate a JavaScript library to visualize the EEG data and allow the user to interact with it. This basic setup will get your flask out running. The actual implementation of the EEG data generation and fuzzy logic analysis will be more complex and specific to your project's needs. Let me know if you require further details on any of these components. Continue with the code generation. Yep. Certainly, Dr. Beno. We'll advance the code to include a more structured approach for generating synthetic EEG data, which will be a crucial part of your flask application. This example will focus on structuring the synthetic data generation and creating a basic template for displaying the data. Let's enhance the generate underscore synthetic underscore EEG function to create more structured synthetic data. This example will still be quite basic, but we'll give you an idea of how to proceed. In this function, artifact underscore frequency controls how frequently artifacts are introduced into the baseline EEG data. Now, let's modify the flask app to utilize this function. For the HTML template, template slash index dot HTML, let's add a symbol visualization using JavaScript. This basic visualization represents EEG data points as vertical bars. The height of each bar corresponds to the EEG signal value. Refine synthetic EEG generation. Further refine the EEG data generation to more closely mimic real EEG signals and artifacts. Fuzzy logic implementation. Integrate a fuzzy logic system to analyze the EEG data. Enhance visualization. Use a more sophisticated charting library like chart. JS or D3. JS for better visualization of EEG data. Interactive UI elements. Implement more interactive features like a scroller to navigate through EEG data. Remember, this is a foundational setup. Your project's requirements will necessitate more detailed and specific development, especially for accurate EEG data simulation and effective fuzzy logic analysis. If you need further assistance with these aspects, feel free to reach out. Why the EEG data points represented as vertical? Why is EEG data points represented as vertical bars? Please correct and continue generating the code. You're right, Dr. Beno. Representing EEG data as vertical bars isn't the most appropriate way to visualize it. A more suitable representation would be a line graph, which better reflects the continuous nature of EEG signals. Let's revise the code to use a line chart for visualization. We'll use a simple JavaScript library, like chart. JS, for this purpose. First, ensure you have chart. JS included in your HTML. You can include it via CDN. Now, let's modify the HTML template to include a canvas for chart. JS graph. This code will create a line chart displaying the EEG data points. The fetch EEG data function retrieves the EEG data from your flask root and then calls display data to render the line chart. For further development, focus on refining EEG data generation. Continue enhancing the synthetic EEG data generation for more realistic simulations. Fuzzy logic analysis. Integrate your fuzzy logic analysis to interpret the EEG data. Additional features and testing. Add more features like user interaction with the graph and thoroughly test your application. GUI, UX enhancements, improve the user interface and experience for better usability and learning. Remember, the effectiveness of the visualization and analysis will highly depend on the accuracy of your synthetic data generation and the robustness of your fuzzy logic implementation. If you need assistance with specific aspects of these developments, feel free to ask. I want to continue developing the code. Make sure we have a scroller for moving through the EEG signal. The EEG signal should have EMG chewing artifacts presented periodically. We also would like to display how the fuzzy logic is making decisions about the probability of the signal being clean EEG or contaminated with EMG artifacts. To continue developing your flask application, we'll focus on implementing a scrollable EEG signal display, incorporating periodic EMG chewing artifacts in the synthetic EEG data and visualizing how the fuzzy logic system assesses the probability of the signal being clean or contaminated with EMG artifacts. Let's refine the synthetic EEG data generation to include periodic EMG chewing artifacts. This requires adjusting the generate underscore synthetic underscore EEG function. We'll use a combination of HTML, CSS, and JavaScript to create a scrollable visualization. First, add a scrollable container in your HTML. Then, adjust your JavaScript to handle the scrolling and update the chart. To visualize the fuzzy logic analysis, you can modify the EEG data generation to include a probability of contamination value. This requires back-end changes and additional front-end logic to display these probabilities. Back-end example, placeholder logic. Front-end changes. Fuzzy logic implementation. Integrate a proper fuzzy logic system for the analysis of EEG data. The placeholder logic should be replaced with actual fuzzy logic analysis. Enhance visualization, develop a more sophisticated visualization that effectively displays both the EEG data and the analysis results. User interaction, improve the interactivity of the UI, including better handling of the scrollable EEG data. This framework provides a starting point. The actual implementation, especially for the fuzzy logic analysis, will require more detailed programming and an understanding of both EEG data characteristics and fuzzy logic principles. Let me know if you need further assistance or specific details on any of these components. Okay, can we continue with code development? Specifically, the fuzzy logic implementation. Specifically, the fuzzy logic implementation. Yes, we like to integrate a proper fuzzy logic system for the analysis of EEG data. We would like to look at features like amplitude and frequency in the first stage. We would like to set membership functions using trapezoid shapes between 0 and 1 with 3 trapezoid for each, low, medium and high. So we should have low frequency, medium frequency, high frequency. Then the same for amplitude, low amplitude, medium amplitude, high amplitude. Next, we'll design the rule activation functions and aggregate the output using a centroid method. Modify the code to include these. Yep. To integrate a fuzzy logic system into your flask application for EEG data analysis, we'll focus on two key aspects, one, defining the fuzzy sets for amplitude and frequency using trapezoidal membership functions, and two, designing rule activation functions and aggregating outputs using the centroid method. Since actual implementation of a fuzzy logic system can be quite complex and specific to your requirements, I'll provide a conceptual framework using Python's SK Fuzzy Library, which is a robust tool for building fuzzy logic systems. Ensure you have the SK Fuzzy Library installed. You can install it via pip. First, let's define the fuzzy sets for amplitude and frequency. Next, we design the rule activation functions. Create the fuzzy inference system and define a function for analysis. Finally, integrate this logic into your flask application, where EEG data analysis occurs. Data pre-processing, implement pre-processing of EEG data to extract amplitude and frequency features. And integration, update your front end to send amplitude and frequency data to the analyze underscore e-root and display the results. Testing and refinement, test the system with various data sets, refine your fuzzy sets and rules as needed. This framework should give you a solid start on integrating a fuzzy logic system into your flask application for EEG data analysis. Remember, the effectiveness of the system highly depends on the accuracy and relevance of your fuzzy sets and rules. If you need further assistance or specific details on any part of this integration, feel free to ask. And you continue developing the code and focus on the data pre-processing, implement pre-processing of EEG data to extract amplitude and frequency features. Certainly, Dr. Beno. Let's proceed with developing the code to include data pre-processing for extracting amplitude and frequency features from EEG data. This process typically involves signal processing techniques. We'll assume you have raw EEG data in a suitable format for processing. Signal normalization, normalize the EEG data to ensure consistent amplitude range. Amplitude extraction, extract the amplitude information from the EEG signal. Frequency extraction, apply a Fourier transform to extract frequency information. Here's an example in Python. You can integrate this pre-processing step into your flask application, possibly in the root where you analyze the EEG data. EEG data format, ensure the format of EEG data you're receiving matches the expected input format of the pre-processing function. Refinement, you may need to refine the pre-processing steps based on the characteristics of your EEG data. Integration with fuzzy logic, after pre-processing, pass the extracted amplitude and frequency features to your fuzzy logic system for analysis. Testing, test the pre-processing and analysis pipeline with both synthetic and real EEG data to ensure accuracy and reliability. This example provides a basic approach to EEG data pre-processing. The specifics can vary greatly depending on the nature of your EEG data and the details of your analysis requirements. If you need more detailed guidance on any part of this process, feel free to ask. I would like to continue developing the code. This looks pretty good already. We haven't tested it yet though. Can you make sure the fuzzy logic is actually integrated in the code past the extracted amplitude and frequency features to your fuzzy logic system for analysis? Please make sure this is in the code. Absolutely, Dr. Beno. Let's ensure that the fuzzy logic analysis is properly integrated into the flask application, particularly in the root where we analyze the EEG data. We'll connect the pre-processing step with the fuzzy logic system to analyze the extracted amplitude and frequency features. First, ensure you have the necessary components for fuzzy logic, as previously discussed, and the pre-processing function in your flask application. Now, we'll integrate these components. Here's how the flask root can be structured to include both pre-processing and fuzzy logic analysis. Now that the code integrates both the pre-processing and fuzzy logic analysis, the next step is to test the application. Test with synthetic data. Initially, use synthetic EEG data to verify that the system is functioning as expected. Test with real data. Once you're confident with the synthetic data results, test with real EEG data to evaluate the system's effectiveness. Data format and range. Ensure that the EEG data format and value range match what the pre-processing function expects. Fuzzy logic parameters. You might need to adjust the parameters in your fuzzy sets and rules based on the results you get during testing. Front-end integration. Ensure the front-end of your application is set up to send EEG data in the correct format and handle the analysis results appropriately. Testing and refinement are crucial steps. They'll help you fine-tune the system for accuracy and reliability. If you encounter any issues or need further assistance with specific parts of the testing or refinement process, please let me know. Then we make sure that the EEG synthetic data looks realistic and it has all the necessary components. Same for the EMG. At this stage, we'll be only testing synthetic data. We'll test with real data at another time. We need to make sure the front-end is integrated. Could you generate the whole code without any placeholders? Creating realistic synthetic EEG data with EMG artifacts for testing purposes is a nuanced task. I'll provide a more detailed approach to generating such data, considering the typical characteristics of EEG and EMG signals. This will include modifications to both the data generation and the Flask application, ensuring a more integrated and functional codebase. To create more realistic synthetic EEG data, we'll consider typical EEG frequencies and amplitudes. For EMG artifacts, like Turing artifacts, these are usually higher frequency and amplitude signals superimposed on the EEG data. Here's an enhanced version of the synthetic EEG data generation function. Now, let's integrate this into the Flask application, including front-end integration. Testing the system, test the application with the synthetic EEG data to ensure the front-end and back-end are working harmoniously. Visualization and interaction enhance the JavaScript code for better visualization and user interaction. Further development, depending on the results of your initial tests, you may need to refine the EEG data generation, preprocessing, and fuzzy logic analysis. Real data testing, once you're satisfied with the synthetic data results, you can plan for testing with real EEG data. This setup provides a comprehensive starting point for your Flask application. Remember, the effectiveness of your application will depend heavily on the accuracy of your synthetic data and the robustness of your analysis. If you require further, this setup provides a comprehensive starting point for your Flask application. Remember, the effectiveness of your application will depend heavily on the accuracy of your synthetic data and the robustness of your analysis. If you require further assistance or have specific questions about any part of this process, please let me know. Now, let's integrate this into the Flask application, including front-end integration. We need that line. This goes from windows not scaling properly. We have this in the... yeah, doing the dancing. When taking breaks, using chart... Oh, it's using plotly. I don't know what's better. Yeah, before it took quite some time loading it, so let's actually check. If chart.js... Why is this script? Why is this not in ShowerScript? Can you generate? Can you generate the whole HTML code without any placeholders? Yep. Absolutely. Dr. Beno, I'll provide a more complete HTML template for your Flask application. This template will include elements for displaying the EEG data and a section for showing the results of the fuzzy logic analysis. Okay, stop, stop, stop. Generate all HTML in separate files. So it keeps insisting on putting the JavaScript into inside the HTML file. Certainly. Dr. Beno, let's create the complete HTML and JavaScript code for your application. This will include the necessary elements for visualization and interaction with the EEG data. Create an index. HTML file in your templates directory with the following content. Create a script. JS file in your static directory with the following content. File organization. Ensure index. HTML is placed in the templates directory and script. JS in the static directory of your Flask application structure. Data generation button. A button is added to trigger EEG data generation. You can modify this based on how you want users to interact with the application. Chart. JS visualization. The script includes the use of chart. JS to visualize the EEG data as a line chart. The display EEG data function is responsible for rendering the chart. EEG data fetching. The fetch EEG data function requests synthetic EEG data from the Flask back end and updates the chart. This setup should provide a functional front end for your Flask application, allowing users to generate and visualize synthetic EEG data. Remember, you may need to adjust the JavaScript and HTML based on the specific requirements and design of your application. If you have any specific questions or need further assistance with this setup, please let me know. We have the EEG chart and the button. Why do we have a button? Okay, create JavaScript. Okay, in the HTML, can make sure... Generally, make sure we don't need any buttons at this stage. I don't think, unless there is a really good reason for it. I don't think we need one. Just load synthetic data when the page loads. Make sure we have the scroller door. I would like to load a segment of, say, 100 seconds, sampled at 250 Hz. Understood, Dr. Beno. We'll modify the HTML to automatically load the synthetic EEG data when the page loads, without the need for a button. Additionally, we'll ensure that the EEG data for a segment of 100 seconds, sampled at 250 Hz, is appropriately displayed with a scrollable interface. Update your index, HTML in the template's directory. Ensure script, JS is placed in the static directory. Page load trigger, the synthetic EEG data loading is now triggered when the page loads, onload equals, fetch EEG data, in the less than body greater than tag. Scrollable interface, the EEG chart container is set to be horizontally scrollable. The width of the canvas, hashtag EEG chart, might need adjustment based on how the data is displayed. EEG data visualization, the EEG data is visualized as a line chart, with the x-axis representing time in seconds, considering a sampling rate of 250 Hz. This setup will automatically load and display the EEG data when the page is loaded, with a scrollable interface to navigate through the data. If you have any specific requirements or need further adjustments, please feel free to let me know. Okay, let's place it in this panel. Won't work with it. Put that as the style and not in a separate file. This looks messy, display EEG data. What's going on here? Let's do the shell script. We have these functions already generated. Yes, already have. Let's multiply it to the SP2. FFT back SP2. Have an example usage. It's this random. Okay, let's just copy the whole thing. Just so we get rid of this. Don't need example usage. Frequency is not being accessed. Why? Is this meant to be? That's wrong, isn't it? To be average frequency. Okay, that's wrong. That's the other function that's missing. Fix this one. Analyze g, gold. Get rid of that root. Don't get it. Let's do some rubbish. Alpha 3sk. Right, at least. Doesn't have any obvious errors. I'm still fixing HTML. What was the problem before? Alright. Can we regenerate the HTML code without any placeholders and also a separate CSS file? Yep. Certainly, Dr. Beno. I'll provide the complete HTML and CSS code for your application without placeholders. The HTML will include the structure and script references and the CSS will contain the styling for the page in the chart. Create an index, HTML file in your templates directory with this content. Create a style.css file in your static directory with this content. CSS linking. The CSS file is linked in the HTML head. Less than link rel equals, stylesheet, href equals, style.css, greater than. Make sure the path is correct relative to your HTML file. JavaScript file. The JavaScript file, script, js, is included at the end of the body. Ensure it's placed in the static directory of your Flask app. Chart dimensions, the width of hash tag eag chart in the CSS may need to be adjusted based on your data visualization requirements. These files will provide the basic structure and styling for your EEG data visualization page. Feel free to modify them further according to your application's needs. If you have specific requirements or need further assistance, please let me know. Please make sure the CSS file starts and using the following colors throughout Absolutely, Dr. Beno. I'll include the specified color variables in the CSS file and ensure these colors are used throughout the styling. Update your style.css file in a static directory with the following content. Color variables. The color variables are defined at the beginning of the CSS file using root, making them available throughout the entire style sheet. Usage of colors. The colors are used for various elements such as the body background, text, headers, and the EEG chart container. Chart styling, the EEG chart, hash tag eag chart, is given a background color for distinction. You may need to adjust this according to your display preferences. With these updates, the CSS file now incorporates the specified color scheme, enhancing the visual aspect of your EEG data visualization page. If you require further customization or have specific styling preferences, please let me know. Save the head. Update the CSS using project colors. It seems like it did. Make sure it's not using any other colors. It's randomly selected, which color to use where, but we can fix it later. See if it runs at all. That's something. Don't need any of the other stuff anymore. What avocados? Something missing. Something is missing. It's a format document. It's only 80 lines of code. Something is missing. Yeah, before we go into the HTML, show all this container. It can be... How do you comment out in the HTML? Okay, let's get rid of it. Yeah, because there's a comment in the middle, so then you can comment the whole section. The HTML is silly, that way. It's going to be data in there. Let's pop this in. There's no EEG data visible in the chart. Yep, let's see if it can fix this for us. Don't have much time left, we've got like three minutes left. If the chart is not visible, there are a few potential issues to check. If the chart data ensure the data being passed to the chart is correct and structured in the way chart, JS expects. Canvas context, verify that the canvas context is correctly being retrieved and used. CSS, confirm that the CSS is not hiding the chart or rendering it off-screen or in a non-visible color. JavaScript errors, check the browser's developer console, usually accessible by pressing F12, for any JavaScript errors that might prevent the chart from rendering. Chart, JS version, if you're using functionality specific to a certain version of chart, JS, ensure that you're loading the correct version from the CDN. Here is a basic checklist to troubleshoot why the chart might not be displaying. Make sure that the fetch EEG data function is successfully retrieving data from the server. Check if the data received from the server is in the correct format for chart, JS. Ensure that the display EEG data function is being called after data retrieval. Confirm that the chart, JS library is successfully loaded into the page before trying to create a chart. Inspect the HTML and CSS to ensure that the canvas is visible and properly styled. Please verify these points in your application. If the problem persists, I can provide further assistance with additional information or access to the code. And now I have the code, it's okay. Content, the description of the, this is the HTML code. Can you find any problems with it? And also update the description at the bottom of the page. Yep. Looking at the HTML structure you provided, I noticed a few potential issues and areas for improvement. Duplicate less than body greater than tags, there are two less than body greater than tags. There should be only one less than body greater than tag in an HTML document. Relative paths, the paths to images, stylesheets and scripts seem to be relative and assume a certain directory structure. If the files are not accessible at those paths, the resources will not load correctly. Metatags, the OG image content should have a full URL to the image for most social media platforms to recognize it. Link to non-existent CSS, there's a link to styles.css which is outside of the root directory, slash styles.css. If the file is not in a specified directory, it won't be loaded. JavaScript loading, the script, js file is referenced twice, once before the closing less than, header greater than tag and once at the end of the document. It should only be included once. Add script, the add script at the bottom of the page is inserted via JavaScript. Ensure this complies with your advertising network's policies and website performance standards. Page content, your last sentence asks for an update in the description. It would be helpful to know exactly what content needs to be updated or provided. Here's a revised version of your HTML code with some of these issues corrected. Ensure that the paths to the images and JavaScript files are correct. If there's specific content that needs updating in the description at the bottom of the page, please provide the new text. Review any JavaScript and CSS files for proper paths and functionality. This revised code should be placed in a single less than body greater than tag and reference each external script and stylesheet only once. Make sure that all your resources are correctly located as per the paths provided, or update the paths to match your directory structure. Just download like this, no. Let's turn this into a separate section. Turn this into a separate section without using the fetching data, do we? Keep on accepting the file path. It works, but I will continue this one. Next time, unless there's any questions in the chat or something. Yeah, I'll just sum up first. Yeah, originally we had this physiological application that meant to detect an input waveform. It wasn't working quite well, it was generating a lot of false detections of false positives and false negatives. So essentially misclassify the input waveforms. So we started a Flask application. Can you give a summary for the whole Flask application, a quick one? Yep, that's what it says. Certainly, Dr. Beno. The Flask application we've been discussing is designed as an educational tool to demonstrate the principles of fuzzy logic in signal processing, with a focus on EEG data and EMG artifact detection. Here's a quick summary of its components. Frontend interface, an HTML. An HTML page that loads synthetic EEG data upon visiting the site. A chart, JS line chart visualization implemented in JavaScript to display EEG signals. CSS styling. A separate CSS file defines styles and colors for the HTML content, utilizing custom properties for coherent color scheme. Flask routes to handle EEG data generation and fuzzy logic analysis. A synthetic EEG data generator simulates realistic EEG signals with periodic EMG artifacts. Pre-processing functions to normalize the data and extract relevant features like amplitude and frequency. Implementation of fuzzy logic using the SK fuzzy library to analyze EEG data. Functions to process the data and apply fuzzy logic rules, providing a risk assessment of EMG artifact contamination. Initially, testing with synthetic data to ensure the correct functioning of the front-end visualization and back-end analysis. The application is structured for easy expansion and integration with real EEG data for further testing. This Flask application serves as an interactive way to visualize and understand EEG data processing and the application of fuzzy logic to signal analysis. The face recognition is also doing false detections of a hand on top of my face. Yeah, like now, especially when I'm looking at the other screen.  Go figure. There are a couple of things that we need to fix. First, we need to make sure the EEG signal is actually visible. Currently, I only see a red screen in the chart just filled with red. Second, we would like to display the whole fuzzy logic detection decision processing in charts like the membership functions and the rule aggregation. So, classification and the classification in separate charts. To address the issues with the EEG signal visualization and to display the fuzzy logic decision process in separate charts, we need to approach this in two parts. The red screen issue could be due to several reasons. Canvas styling issue. If the canvas background is set to red in the CSS and no line chart is visible, it may be because the data isn't being correctly passed to chart. JS or there is a problem with the chart configuration. Data issue. Ensure the EEG data array passed to chart. JS is populated with the correct numerical values and not an error message or an empty array. Chart. JS configuration. Verify the chart configuration options, particularly the scales and datasets. Incorrect settings might lead to an unrendered chart. Here's a basic template to define a line chart in chart. JS that you can use as a reference. For the fuzzy logic decision process, you'll want to visualize the membership functions, rule activation and the result of the aggregation process. This can be done using additional chart, JS charts or another library like Plotly if you need more specialized charts. Here's an example structure of how you might set this up in your JavaScript. You would create separate canvas elements in your HTML for each fuzzy logic process chart and initialize them in the JavaScript. Make sure each canvas has a unique ID and reference those IDs when creating new chart instances. Notes. Ensure your data generation and processing logic are functioning as expected. Test these thoroughly on the server side. Check the browser's developer console for any errors that might indicate issues with data retrieval or chart rendering. For displaying fuzzy logic processes, you might need to run the fuzzy logic operations on the server, send the results to a client and then plot them. If you can provide the exact sections of code handling the EEG data generation, fuzzy logic and chart rendering, I can offer more targeted advice. The following is the code that you recommended earlier. Can you modify it? To modify the code as per your request, I'll make the following changes. Ensure the data received is an array of numbers. Make sure the chart correctly plots the EEG data. Update the chart. JS syntax to the latest version as the axis configuration has changed since version 3. Here's your updated script, JS. Please note the following. The fetch EEG data function now includes error handling. The display EEG data function has been updated to use the newer chart, JS configuration syntax. The axes options have been updated from x-axis and y-axis to x and y to comply with chart, JS latest version. Line tension has been changed to tension, which is the correct property name in the newer chart, JS versions. Added title configuration for both axes. The function fetch EEG data is now called at the end of the script to automatically load the data. Make sure to use the latest version of chart, JS for this syntax to work properly. If you are using an older version, you may need to adjust the syntax accordingly. It's generating. Generating EEG is not defined, but I think it's the order of this thing. It must be the order. The code you've provided sets up a flask application with routes for serving an HTML page, generating synthetic EEG data and analyzing the data using fuzzy logic. It also includes functions to preprocess EEG data. Below are some modifications and explanations to ensure your application works correctly. Function order, define all functions before they're referenced in the root handler to avoid name error. Error handling, add error handling to your root functions to manage unexpected inputs or processing errors. Fuzzy logic analysis, ensure that the fuzzy logic analysis, analyze underscore EEG, function is implemented correctly. It's referenced in the analyze underscore EEG root, but not shown in the provided code. Here's the modified code with added comments and error handling. Please ensure you have a fuzzy logic analysis function properly defined and that it's called analyze underscore EEG. The actual implementation of such a function would depend on how you set up your fuzzy logic system, which isn't included in the code snippet. You should also have error handling in place for the HTTP requests. As demonstrated in the generate underscore EEG and analyze underscore EEG routes, the catch and respond errors appropriately. With these adjustments, your flask application should be set up to serve the front end, generate synthetic EEG data upon request, and analyze the data using fuzzy logic principles. In the generate EEG, there's an error handling and a site for analyze EEG. What's up with that? That obviously would not... Oops, how do I know about this function? I can go after the prep process here. So we have the root, we have analyze EEG. Analyze EEG is missing, is it? Analyze, generate, add this function again to know why we are missing. The analyze underscore EEG function should implement the fuzzy logic analysis using the amplitude and frequency values extracted from the EEG data. Here's a conceptual implementation using the SK fuzzy library. To use this in the flask application, you would call this function from the root handler passing in the necessary values extracted from the EEG data after preprocessing. This function assumes that the amplitude and frequency inputs are scaled between 0 and 1, as the universe of discourse for the fuzzy variables is defined from 0 to 1. Make sure to test this implementation thoroughly and adjust the fuzzy sets, universe of discourse, and rules according to the actual ranges and requirements of your EEG data and analysis objectives. Right, that goes. That's the sound thinking on the other side. Okay, chokes aside, this one actually returns the output. Yeah, I might finish it. Hi, Rohan. How are you? Have a regular viewer joining in? It's weird that my, ah, right, now that's not a chat in OBS is a bit messed up. Okay, so now we have that function still ever. We're not destroying a chart or something meant to be destroying this chart. The error message you're seeing indicates that window. EEG chart. Destroy is not recognized as a function. This usually happens if window. EEG chart is not correctly initialized as a chart. JS instance or if it is being over at Nelsware in your code with a non-chart, JS object. Let's ensure that window. EEG chart is being properly initialized. Here's a revised version of your display EEG data function that checks if window. EEG chart is an instance of a chart before attempting to call destroy on it. Destroy, destroy the chart. Ensure that you're not reassigning window. EEG chart anywhere else in your code without initializing it as a new chart instance. It's also important to verify that the data being passed to display EEG data is in the expected format and that no other part of your JavaScript is interfering with the chart instance. By adding the instance check, you can prevent the error from occurring if window. EEG chart isn't a chart. If window, EEG chart is undefined or not a chart, it will simply create a new chart instance. If the problem persists, it might be helpful to review the entire main. JS file to ensure there's no conflicting code. That will be good. Let's try this first quickly. Okay, we have the... It's actually surprising that it looks like EEG. It's some frequency in it, but let's just scroll. Scroll is Gonski. Colors are pretty bad to the last... So it's able to... the good thing is the bot is able to fix stuff. And this is the output I get. It looks like a legit EEG. That's good. The scroller is... I think it's visible, but there is nothing to scroll through how to fix. And also, how do we make sure there are EMG chewing artifacts within this synthetic EEG coming in periodically as you scroll through the data? Yep. From your description and the image provided, it looks like the EEG data visualization is working correctly, but the scrolling functionality might not be as expected. Here's how to address the issues. Canvas size for scrolling. Ensure that the canvas element is large enough to require scrolling. You might need to set a specific width on the canvas based on the total duration of your EEG data. Container for scrolling. The container that holds the canvas should allow for scrolling. This is typically controlled with the overflow CSS property. To include EMG chewing artifacts in the synthetic EEG data, you want to modify the generate underscore synthetic underscore EEG function. Here's a conceptual approach. Note, the artifact underscore interval parameter controls how often the EMG artifact appears in the signal. Adjust EMG underscore for Q to set the frequency of the EMG artifact, which should be higher than the EEG frequency. With these adjustments, your application should be able to display a scrollable EEG signal that includes synthetic EMG chewing artifacts. Make sure to test the updated data generation function to see if it produces the expected results. Remember, the width of the canvas in pixels should correspond to the length of the EEG data you want to display. For instance, if you have a 100-second EEG segment sampled at 250 Hz, you will have 25,000 data points. If you want to represent each second with 10 pixels, you will set the canvas width to 1,000 px. Adjust these numbers based on how you want to represent your data visually. It's not quite clear, but okay. Yeah, let's continue this next time.


Hi, I'm Dr. Bronstein, a pediatric infectious disease specialist at Kaiser Permanente. In this time of school closures and other disruptions to everyday life, many of us parents and caretakers may be wondering how to talk with our kids about COVID-19 and what to do to keep them and others healthy. It's natural to be concerned in times of uncertainty, and this can be a stressful time for youngsters. The important thing to know is, based on the most current information about the impact of COVID-19, evidence shows that children who contract the virus recover well and do not appear to have serious complications. The greater risk is in unknowingly passing the virus on to individuals who are considered high risk, such as the elderly or people with underlying health conditions. For example, a grandparent with heart disease would be at higher risk of developing complications from COVID-19. So keeping children safe and unexposed goes a long way to keep everybody safe. If your child does have cold or flu-like symptoms, it's important to keep him or her home away from crowded spaces and vulnerable populations. Keep your child comfortable and be sure to call your doctor for further instructions. Children count on routines, and big changes like school closings could be unsettling to them. Your words and actions can go a long way to reassure them. Talk with children directly about what's going on. Let kids know that children are not getting severely ill from the coronavirus and that they will be okay. The reason that they might have to stay home is because we are all doing our best to protect our friends and neighbors and slow down the spread of the virus so that more people don't get sick. Make sure they know that they can play a helpful role in protecting themselves, their family, and the community. By doing things like washing hands frequently, sneezing or coughing into their elbow, and staying away from others when they're sick, they can help everyone stay healthy. It's best to relay this information in short, brief conversations, and find a time each day to check in and ask what they're hearing and if they have any questions. This will allow you to correct any misinformation they've heard, answer their questions, and offer reassurance. Providing children with daily structure lowers their levels of distress and increases their ability to cope with uncertainty and change. With children home from school, it can be helpful to set a routine for the day. Decide on a schedule that includes a time to get up, a time for schoolwork, lunchtime, and a few structured fun activities. Keep in place any existing routine, such as storytime, evening TV, and bedtime rituals. Modeling healthy habits for children shows them how we can all work together to do the right thing. This includes managing media coverage of COVID-19. Consider limiting news and social media to a specific time each day. Be mindful of news running in the background with your children present or frequently discussing the news when they're in the room. Try to substitute things that support positive coping, playing a game together, watching a funny show, or making a gratitude list before bedtime. Most importantly, don't forget to prioritize your own self-care. Simple things like getting enough rest, eating well, exercising regularly, and seeking support from trusted friends and family can increase your resilience in stressful times. The more you can do to keep yourself healthy and balanced, the more you'll be helping your child feel safe, calm, and worry-free.


Hi everyone, Joe for Jasby's Case of Breaks.com coming at you with break 38. That's actually not our last filler Break 39 is our last filler. There you go. So break 38. Big thanks to this group for making it happen. Appreciate it There are the teams right there. So first dice roll would be for the break Second dice roll would be for the giveaway part. Two and a one three times for names and teams. One two and three and Two and a one three times for the teams. One two and Three we got the pack down to the chiefs Where are the packers gonna get that Aaron Rodgers deal done? I think I saw on some NFL program on ESPN Here's the first half of the list right here And then the second half list right there that I think that they can split a cap hit if they trade him after June 1st so they're so we might not see a deal happen until June which is kind of crazy Would that make the Jets a little nervous? All right, no trade windows. Let's print and rip. I think it was June If they trade him before June, then there's one cap impact at a certain number. I forget the number But if they trade him after a certain date It could be split between two different years the saga continues. We'll see what happens. All right Thanks everyone There's the list hot off the presses Justin Fields rookie card Where's Lamar Jackson gonna end up a lot of questions still out there Greg got randomized the Bears gets the Rookie card Justin Fields rookie card. All right now. Let's flip back over here. Let's gather everybody's names one through 32 Put them into this new list here, and it'll be the top six after Seven we'll get into that hip raid break. We got we got to do one more of these fillers and then we're in breaksville All right, so top six after seven. Good luck everybody one two three four five six and seventh and final time So just the top six so from seven on there'll be a lot of sad faces here, but from seven on down Sorry, James very close. It's not quite seven through thirty two. Thanks for taking the risk That's that times happy times though for the top six Lee is happy So is Eugene's Brian James James you got in there Jamie and Jimmy There you go. Congrats to the top six after seven. We'll see you hopefully a little bit later for that hip raid break To ask these case breaks calm, but I


The construction of vertex operator algebra associated to U1, the algebra, and some generic simple connections for manifold, possibly this boundary, and we consider it what is kind of how those guys behave under gluing, and also what roles they play. Sorry, I also discussed the relation between the ubiquitern environs and what are called equivalent multi-monopole environs of four manifolds, and what kind of role this vertex operator algebra played in this relation, so they were denoted by. So today, first I want to consider a bunch of other examples of the vertex operator algebras associated to some subclasses of manifolds, and so I consider some examples quite briefly, and one particular class of examples I will consider in more detail. So first, consider the case when the group is, the le algebra is U1, and so this is an example essentially due to an encadging. And so four manifolds will be a resolution of AD singularity, so let me label, so this is there is a, so let me denote a gamma divided by gamma H, where gamma H is a, is a finite subgroup of SU2, which, so there is no muck cake correspondence between finite subgroup of SU2's and simply laced, laced the algebras. So for a simple laced algebra which are classified by AD, we can take a certain finite subgroup of SU2 and consider this quotient and then it is a resolution. And then in this case, the vertex operator algebra associated to the four manifolds is, so I will write on this, is affine, so the VOA associated to affine the algebra H at level m, so this is a good level. So since, because of some questions during do stock, seems that not everybody is familiar with this notion, so let me remind you. So first, so here in many cases they're kind of, for vertex operator algebra there are a lot of abuse of notation, so sometimes people write the same notation for vertex operator algebra and for affine the algebra, which corresponds to, it corresponds to, so what exactly this means is that one can see there is a following the algebra, so as a vector space it is, so we start with the usual the algebra H and so we tensor it with this series T inverse, so we can see the loop algebra and we can see the central extension. So let me denote the central element by kappa and then if, so again I will use the similar notation. So the construction is going to be, everything is going to be very similar to the Heisenberg algebra since the corresponding VOAs. So again if H is some element of my ordinary algebra H, then the, by H with index I I will denote H tensor with T i and then the loop bracket is given by the following correlation. It's probably, sorry it was, so let me, so there are different elements, AB, so for any pair AB from H, so this is a key, here I use a killing form, standard killing form and so my, here I want to start with some, let's say reductive, reductive algebra and then there will be a term, another term which is just a commutator of AB and for here I take the index i plus g and here I multiply in the central element cup. So this gives you some infinite dimensional algebra and so the VOA is a corresponding VOA as a vector space is a highest weight model defined with the highest weight vector satisfying the following conditions. So the K, the central element acts on as a highest weight vector which I denote by 0 as n, my level and the i's just all act as 0 for i greater or equal to 0. So again this defines some highest weight model, this highest weight vector is 0, denoted by this 0 with brackets and so this is the representation induced by these relations and then we can equip it with the structure of the vertex operator algebras in a way completely analogous as we did for Heisenberg, Heisenberg V-ray. So I'm not going to go into detail. So this is similar to Heisenberg. So Heisenberg V-ray we had the same thing just without this. The Heisenberg V-ray was essentially the case when this is a billion, a billion realtime and in the work by the regime it was explicitly shown that this is the homology of the instanton model spaces here. They have a structure of a model of this fine algebra. And one can argue from this, the same result one can predict from the, is an agreement with the physics prediction of the computation of 6G theory, 6G SCFTO. This is so wonderful. So one can consider, let me call it example one prime. So it's kind of a small kind of a certain generalization of this. So this is considered in a paper by Gukov himself. So consider, so M4 will be, is a certain, is a bordism S3, the three manifold which is obtained S3 by the quotient, by the gamma related to some group H to S3 quotient by gamma associated to some A D V Algebra F. Such that if I take this bordism and glue it with the manifold which appeared before along the common boundary I should get the manifold from the same class but labelled by F. So you can consider some sort of this picture like this. So this is your bordism M4 and so here is this manifold or some typologically resolution of a certain resolution of singularity of some A D type and once you glue it in we get another manifold of the same class. Then the statement, determines this M4 up to the formacfism and so the statement is that this thing, so one can argue that this thing should be what is called coset VOA. So in physics it's usually denoted by some sort of quotient. I start with VOA associated to a finely algebra corresponding to the original algebra F and this level N and I quotient it with H. So this is coset. So this is notation and it was introduced in physics but it's in a sense it's wrong to write like this because you don't consider you don't quotient this vector space by this vector space. So this actually means is a commutant of H, N so you can see there are all operators in this vector superiod algebra that commute with this well the usual large space when this is of A type is what is called spherical So one of the nice examples when this is H the algebra is E8 then this is a Poincare homologous sphere. Any other questions? Another example which was considered in so let me mention the following example it was considered in Goukow-Pengen paper and I'm not sure if Serge is here if you can correct me if I said something wrong but anyway ok so the the idea is that so consider M4 is a non-compact toric surface so it can be described by the following toric form which looks something like this so the fact that it's non-compact means they all kind of fly behind a certain line and but you can consider kind of topologically it's better to understand it by some sort of dual toric diagram so it's usually you write it like this some sort of open polytope with some vertices and here you have a torus, sorry the T2 so generic point you have torus fiber and this it's degenerate so one of the cycles degenerate once you approach edge and both cycles degenerate when you approach a vertex and not necessarily but we don't want this poly we don't want this polytope to close well at least in this one can try to close this but it's going to be more complicated so let's consider this case so the there is a torus action on this which is the same which is so the idea is that locally around each vertex it looks like C2 and then one can associate something like C2 and glue these things together so first and so we want to construct what actually so we want to construct the VUA which also we will wobble it by SUN and so this will be what one can call T-coarrant so in particular it will depend it will depend a coherent epsilon2 in the notation the usual notation so there are essentially the same parameters that appear the similar parameters appear in the in-class of story, in-class function generators of a grand homogenous point so what it means here depending so if you fix these parameters to be some particular complex numbers this determines certain VUA and then one can consider the VUA of C2 and this is so let me so in general so this is what is called in general WN the VUA associated to WN algebra but not to go in details what are the W algebras so let me consider the case SU2 and this is what is called Virasura V-ray so this is in a sense a minimal VUA which contains a minimal vertex operator algebra which satisfies axioms so as a vector space this is essentially generated by the written like this where is this so again the construction is analogous of how we did, how we constructed so we started as we did in the Heisenberg Algebra or finally Algebra we started some infinite dimensionally Algebra and we constructed the VUA structure on its some high-street model and so this so of course so here when we talk about the vector operator Algebra acting on the space of on the vector space of vector operator Algebra it has a particular center of charge and this particular center of charge will indeed depend on this guy so it will be 1 plus 6 and then you want to define what do you do when you glue stuff so let me consider just the general situation as long as let me consider the case when the diagram has just two corners so the statement I think will be so let me explicitly denote this dependence on the epsilon and epsilon-2 which comes through the center of charge and this will be first well it's just acts by rotating so you one you rotate one you one C and another you one another C copies this is a one you one and another you one yes but of course we have to choose in order to do this to define this action we have to we have to choose a kind of a basis we have to choose what we call we have to choose this splitting okay but of course so here we have to we have to choose so the torus here is so suppose we fix a certain basis or a certain particular splitting of the torus into a product of you once so this you this you one corresponds to correspond to epsilon-1 and the second you one will the corresponding current parameter will be joined by E2 but then we won't so if once we identify this part with C2 and another corner C2 the the standard choices of epsilon-1 epsilon-2 here and here they will be related by some SL2Z transformation so suppose here the choice I choose just my choice is canonical here but here I have some other parameters epsilon epsilon-2 prime and so there will be something else but before I write before I say what is this so they are related by some so this is the corresponding vectors they are related by some SL2Z transformation and so we have so if you start so this the product of vertex-operator algebra gives some new vertex-operator algebra but in this special case when we have a two copies of Virasura vertex-operator algebra such that these epsilons are related by this by some SL2Z transformation this has some modules which can be added up to this vertex-operator so they have what is called non-trivial extension plus certain models so in general we cannot add modules like arbitrary modules we cannot up to the vacuum model which is the vertex-operator algebra itself so it has a non-trivial extension exactly they are related they are related between each other with this kind of formula and well you can consider a certain well this in general you can take complex so you can have 0 here in principle and there is some one can say more explicitly what you add up here what modules but what is important that this non-trivial extension exist exactly due to this relation between epsilon with inquiry parameter for this C2 and this C2 due to gluing okay so I don't want to go into detail but so what I want to consider in a bit more detail is the following class of examples is that m4 is a product of cp1 times Riemann surface with punctures this is genus g Riemann surface these n punctures in principle so you can write you can draw it like this but if you want to actually analyze if you want to analyze if you want to realize your vector space as a vector space on the level of vector space as a cohomology of the modular spaces of warp written equations then you actually need to be more precise you need to kind of you need to interpret these punctures as some sort of infinite tubes and so what is it so let me say some first general properties so the VOA of this thing so it will it will contain n copies n copies of a finely algebra associated to algebra g which I choose here with some levels which I am not going to specify but they can be explicitly written times u1 so in general there is no such for general if I take a closed for manifold of generic of generic homonymy there is no statement there should be always some finely algebra acting on this VOA but first of all in the particular case when the for manifold is scalar then you should have then there is a u1 which you can also interpret some sort of u1 action acting on the model space of warp written of warp written equations and you also have since you have a boundaries here and components for each boundary you have action of the you have action of your gauge group which can be understood as a kind of constant gauge transformations at infinity and they will be so this the ordinary the claim is that the ordinary symmetries of this model spaces they will promote it to a fine symmetries in this vertex operator algebra and how can one make explicit description well it will depend with here I'm just saying that there is this sub VOA here this is not a quality this includes the sub VOA which depends so whenever there are end punctures there will be this affine symmetry included here so and so in particular if I calculate as a trace over this VOA so I insert minus 1 to the f q to the L0 so f was my z2 grading L0 was my z grading and so I can also insert the certain element notation alpha element of an ordinary so end copies of group G such that Li of G is small g and here I take g to be compact and simply connected times u1 which is certainly u1 group corresponding to the ordinary so this is Li group which corresponds to the ordinary Li algebra embedded in this affine algebra and so then this can be understood as an element so this will be series in q this coefficients being elements of the representation ring of this group so if there was no if this was trivial then I just call it a trace of minus 1 to the q to the L0 I just get series with coefficients being integers but here I have series of this type so of course you can write it more explicitly by choosing a particular what is in physics called fugacities and then this will depend the coefficients will be some rational functions of those fugacities corresponding to maximal torque of those guys so this is some general expectation and this should be a modular modular and in a sense it can generalize your copy model form which will if I realize these guys if I go to the kind of maximal torque the corresponding coordinates of the maximal torque they play role of Jacobi like variables in this model form so this is some general expectation and now one can explicitly describe this VOA there are two ways so this can be understood as conjectures on this structure on this VOA structure on the cohomologies of the model spaces of solutions of both written equations so the first description can be given as follows suppose for simplicity so I write the statement in the case when this will be a genus zero surface then the statement that this is the same as the global sections of the shift of chiral differential operators so I will write on what is this shift of chiral differential of chiral differential operators associated to space X zero M which is the Higgs branch of the corresponding class S which is a bit naive because in principle this shift of chiral differential operators is only defined for a smooth manifold but naive if you generalize this you should expect this thing so here I wrote for genus zero if I take non-trivial genus then there will be additional data which I should include there will be a data of holomorphic vector bundle of this X and there is a generalization of this story of chiral differential operators for the case when there is also a holomorphic vector bundle over X so what is actually is I will write in a few minutes and another way to construct this thing construct by gluing basic pieces basic books so any human surface can be split into pair of puns so it should be enough to say what this is for pair of puns times Cp1 and to say how you should glue these things so in a sense you want to review I have this and a rule on the arrays for gluing so let me briefly review what is the shift of chiral differential operators so let X be a smooth so here I am assuming smooth which is not exactly true but let me anyway or give you a general definition just for a smooth case smooth complex analytic manifold so we want to define this the shift of chiral differential is a shift on X valued in vertex operator algebra so for each open subset here one needs to give it to tell you what is the corresponding vertex operator algebra so valued in vertex it would be possible to define for pair of fans for disc so for Cp1 times pair of fans for Cp1 times disc and disc is a bit bad thing to do you need to well kind of you kind of define for cylinder in a sense for cylinder that is the idea of the second approach which I also want to review if I have time but the second approach if you do this you should do not real checks you can decompose it in pair of fans in a different ways so the result should be the same but here you kind of using this approach of chiral differential operators you kind of define it globally I mean suppose you know the Higgs branch ok so so I don't have much time but so first the idea so I don't give I'm not going to go into deep theory but the idea that suppose first X take X to be just a fine space Cn and consider just a global sections what is the global sections of the shift on N the statement this is what is called N copies so this is VoA which is called N copies of the gamma system so what is this so this is very similar again to Heisenberg so what is this a single copy of so what is this VoA exactly is so as a vector space it so I start as in Heisenberg where I start with the Lie algebra given by the following relations so there will be generators beta and gamma labeled by ij going from 1 to N and as in Heisenberg VoA this would be the lower indices would be just value 10z and they will satisfy this relation times C which is central and again we can start VoA as some folk space obtained by these guys but to me more precise so we consider all possible so we start with some highest weight vector and we connect on it by all possible modes beta and gamma with a certain condition where here I allow so Ni should be strictly positive and this should be just non-negative so you have gamma 0's but you don't have beta 0's and this is a so what's important this is and again everything the structure of VoA just analogous completely analogous to the Heisenberg VoA how you construct an operator the series in operators from this guy the beta themselves they are commute and gammas they are commute this is the only material and so one can notice that this is a module over polynomial ring in gamma 0's because I can always any element of this ring I can multiply I earn some gamma 0's here and they all commute gamma 0's they all commute then for example if I now still working in Cn but if I if I want to define what happens if I remove so you can see the certain the risk open subset which is given by this so it's a complement of a set of solutions of a certain equation and I understand as a spec of C with variables X1 and Xn so this will be coordinates on the space then f is a certain element it's a certain polynomial here and I want to impose a condition that f of 0 is not 0 and then this thing will be so let me denote this in order to not carry all this heavy notation so this will be some sort of standard thing, let me denote it by just Vn, this is a Vui labeled by N so this will be Vn tensor it with the ring of normals and X where I localize with respect to 1 over f and here I tensor with itself, sorry what I mean here I need to replace this by gammas gamma 0 of gamma essentially what I, here what this means here so the space, the vector space can be understood as a space of polynomials in all these biters and gammas with different indices and here what I this was just a polynomial and here what I, if I want to go to this subset I allow to divide by 1 over f and so what I do formally is a, what I actually do is I can expand this 1 over f in 1 over f of gamma 0 in variables gamma 0 and I can do this I always do this expansion at 0 because of this condition and this will produce me a series a series in gamma 0s, sorry now I will allow a certain type of series in gamma 0s not just polynomials so this so this procedure allows you to define this on the risk open subsets of Cn and now, so here I'm kind of skipping details do a huge jump but essentially what you want to do is so you want to see some more general space X you can cover it with some patches where each patch is locally as a morphic to Cn and there will be some transition functions which I can so this will be Cn minus something Cn minus something and then so for each of these patches I have some VOA defined by this construction and then I should define a certain transition functions and this transition function should be morphisms between VOAs so the transition functions VOAs associated to different open and this morphisms defined as follows so the morphisms between VOAs so suppose here I have some coordinates X and coordinates here I will denote by X tilde so if I as usual I denote by this thing as gamma n by beta so this will have index i i minus 1 i and for example if my coordinates are related like this X i is given by some functions gi of X and then this means that gamma tilde so this is a series in that where the coefficients will be operators acting in the VOA here associated to this subset is just related to gammas in another patch by the use of this function for beta so if you have if you denote by inverse functions by F's beta tilde i is given by d tilde where you replace it by some tilde and you multiply it by you want to do the sum gi anyway you can write explicit relation between how you map operators here how you map the operator between these VOAs and so you need actually some condition on the topology of X in order for this to be in order for this shift to be globally defined and this condition is c1 equals 0 mod 2 and that the second part of TX is 0 how much time do I have so now you want to plug in this construction of the Higgs branch of classes here and you want to obtain some shift and you consider the global sections of the shift this produces some vector superior algebra and so let me mention briefly the approach with gluing so I don't have so let me so to talk about the gluing of vector superior algebra itself so you can do this but this is a bit involved so let me just mention this on the level of on the level of what happens on the level of characters so let me first consider the case SU2 well maybe I can mention so I have well let me just say some words but don't write explicit formulas so the idea is that so the general idea is that for general co-homology so if I want to calculate so suppose I start I want to start with some Riemann surface and I want to split it into two pieces so they are connected to the piece A and piece B and they are connected by some tube which I want to cut so the statement will be a certain co-homology which is known as BRST co-homology so in this particular case is what is called quantum drainfield circle of reduction with respect to this will be a reduction with respect to diagonal affine the algebra associated to the punctures the puncture this puncture in this piece and this puncture in this piece so namely this will be certain co-homology of the following tensor product so I take a vertex operator algebra associated to this piece A so now I once I cut I have here puncture tensor the vertex operator algebra associated to this piece and tensor so I need to take a tensor of two copies what is called BC system valued in adjoint representation of G so the BC system is an odd odd parity means the generator has parity 1 odd analog of beta gamma system which I described before so anyway there is some procedure but let me tell you something about the basic building block for example for SU2 this is the Riemann surface times so this will be just 8 copies so this is a combination of the beta gamma system valued C8 so there are 8 copies here there is this as promised they are indeed SU2 times SU2 times SU2 and times U1 action and for example the corresponding character here is very simple all this thing is just one of our product C to function where I take a product of all signs so C to function of any product so B is fugacity associated to U1 symmetry and X, Y, Z as fugacity associated to this SU2 and for example for SU3 you can understand this as a one way to understand this is the global sections of the shift of carol differential operators where X is E6 instanton centred E6 instanton model space and the corresponding character for example it can be explicit so here so naively on this VOA there is there are 3 punctures there is SU3 cube symmetry acts but actually this SU3 cube symmetry is actually as natural embedded in E6 and it happens that this affine symmetry, SU3 affine symmetry enhances to E6 and for example so this is for example in the work by myself, Song and Yan so this is some non Lagrangian theory but if you can still calculate it like physically the carol 2 dimensional theory doesn't have any Lagrangian but you still can calculate its elliptic genus which is a character of this VOA you can calculate which can be interpreted as a generating function for electric characteristics of wafovitum model spaces here so in particular you can explicitly see that this is indeed an element so there is explicit formula which I'm not going to write and you can indeed check that this is can be interpreted as a series it has a form of series in cure where the coefficients are elements of the representation of K6 times u1 and so for example on the level of character there is explicit integral formula how you do this okay I should stop here