This session, a principle-based moodle with Karin Brown from ETH Zuri. Thanks, Karin, over to you. Thank you very much, Helen. And thank you to all of you who have chosen to come and watch this live stream or to attend this session. I'm really looking forward to hopefully having some interaction with you in the form of questions in the forum. So don't wait until the last minute. If you have any questions or comments, please pop them into the forum as we go along. So just a few words about me. I work at ETH Zurich, which I was explaining earlier. Apparently Einstein went there and that's one of our main claims to fame in the middle of Zurich City. And we use moodle as our main, as our strategic learning management system. So I want to talk to you a little bit about this, this topic of a principle-based moodle and what I mean by that. So this project was born out of a desire to make the link between good teaching practices and our particular moodle service explicit and to centralize them in a way that was much stronger than what we currently do. So in this presentation, I've got sort of two sides to it. The one is I'll tell you the why, the what and the how. But then also really if possible to have a conversation and find out if the ideas in this presentation are useful to you and if so in what way, or if they pose any challenges. And if so, what kind of challenges do those pose? So keep those questions in mind as I progress through these slides. So why did I decide to present on this? And the first answer to that is that I'm a systems person and I'm pretty analytical. So when I first joined our moodle team at ETH, I found myself asking the question, why a lot? I'll be sitting in Change Advisory Board meetings where important decisions are made about how moodle will be developed at ETH. And decisions were being made and I'll sit there saying, well, why did you make this decision that way? But this other decision in another way. And sometimes the answers were things like, well, it's the rules around here. There's a policy that dictates that this is how we have to do it. Or sometimes the answer was, well, depends on who asked for this change in moodle. What's their position at the institution? How much political power do they have? Or another answer might be, well, that's just how we've always done it. And to me, that was a little bit dissatisfying because I thought it was important for us to, first of all, internally become really clear about why we are developing moodle the way we're developing it. And also so that we could communicate those decisions externally, which would go a long way to being more transparent with our users. So then that would also hopefully inform the change request that they submit to our service. So what did we do? And how did we move towards a principle-based moodle? And the first thing I have to explain is that I wear several hats at our institution. One hat is in the moodle service team. And the other hat is that I'm a faculty developer, which means I work closely with faculty and individually and in courses to help them improve their teaching practice and to become more innovative in their teaching practice, potentially using moodle. So I was part of a conversation where we asked ourselves the question, what does good teaching practice look like at ETH? And this was something that we wanted to describe so that we could use it as a vision for our work as faculty developers. And we did this by collecting important documents such as the vision of our institution or policy documents about quality teaching at ETH or quality criteria, all those kinds of things. And then we sort of filtered those through our hearts and our eyes, our experience and our own training as faculty developers. And we sort of condensed these down until we had a list of 10 principles of good teaching practice. I always avoid the word best and there isn't one best way to do this, but rather we wanted to have these guiding principles or what I started referring to as North stars to guide us in terms of what good teaching practice, particularly at our institution, looks like because it is different than individual from institution to institution. So what happened next? So I took these 10 principles and I went to our service owner of Moodle at our institution and I said, look, I think this offers something here. Not only do we have some guiding principles for good teaching practice, but actually we could look at this as good online teaching practice. Let's give it a go. So we got together and using these principles, we asked ourselves, well, if these principles are true, what does that mean for us as a Moodle service? And so I'll show you how we did that using my little letters here. The first one is the P for principle. So we started with the principle and said, if this is true, if this principle is true, then what is it that is the student will experience when they're in Moodle. And if this is what the student experiences, then what does T the teacher have to be able to do in Moodle to make better reality. So if you want dialogue, you need dialogue modules, you need the forum, you need messaging, you need, you know, you need the students to be able to communicate with each other and with the teacher. And if this is what we want the teacher to be able to do, well, then what does M Moodle, what does Moodle need to offer? Which settings do we need to enable? Which blocks do we need to offer? Which plugins do we need to install? And so you can see by working backwards from our vision of good online teaching, we were able to start coming up with concrete ideas that will guide our Moodle team in the future. So let's look at one of these examples in detail. So the one principle I've chosen here is participation. Now I am deliberately not giving you my entire list. That's strategic because I don't want you to look at these principles and think, oh yeah, that'll work for me in my context. It may or it may not. The process is just as important as the product. Okay, so if you go to email me later or in the forum asking for the principles, of course I'll send them to you. But keep in mind that it's more valuable for you to identify the values and the principles that are inherent in your context and those are culturally defined. So that's another thing to keep in mind. So participation, which we defined here as students and staff experiencing access to suitable teaching and learning and can have an active role in its development. So we looked at the student experience. Well, what would that look like? And I'll just let you read those four bullet points then. So you can see we looked at it from both access to Moodle, but also removal of barriers, active learning that can participate in active learning, but also active participation in Moodle development. So okay, so that's what we want students to be able to experience. Next, what must teachers be able to do? I'll let you read that. One example there is accessibility. Lecturers or teachers should have easy access to guidelines for maximizing accessibility and removing barriers for learning because these prevent participation. So what does that mean for Moodle then? Let's have a look. So an example here is that Moodle is integrated with our university systems or with other university systems.   Then what was really interesting is we sat down and we thought, okay, this is the world we would like to have. How close are we? And we could give ourselves some ticks, but we also felt that there were some areas where we had work to do and that's what this last column is, our action plan. I'll let you read that. And so what that means is that if you can sort of link these circles, the blue circle is our operations manager. So what he does is he's responsible for ensuring that the system does what we want the system to do, but that the lecturer doesn't do what... I'm just going to stop my webcam because I'm thinking I'm experiencing some lag.  And that was really satisfying and was really different from the daily business of discussing server response time and that kind of thing. So yeah, that's my last slide. I want to move to the slide where I asked you those questions at the beginning, what opportunities might something like this present to you or what challenges does it present to you? How could we overcome these challenges? And I'd love to see some questions from you or some ideas because I don't know anyone else who's doing this right now with Moodle and I'd love to hear from you if it is something that you're doing. Thanks very much. Thanks very much, Karen. Yeah, there was just a short time in the middle where your sound started breaking up and you stopped sharing your webcam. I think that helped but it seems there's no questions or other points in the forum discussion yet. So I don't know whether if you want to go back to a previous slide and talk about it again. Which one was the one where I started breaking up? That's a good question. I think it's the one before this one. It was after that one. Okay. Yeah, so yeah. Yeah, so basically I was just saying that if you compare this to the earlier slide, we were in a position where we were making decisions at Change Advisory Board meetings that were not always consistent or we couldn't always explain the rationale. It felt a bit random at times but now with the principles, what we're hoping is that our conversation will look a lot more like this so that we can say well, so-and-so has requested a plugin. Does this process further participation or does this support student-centered learning? So these are three of our principles and it's gonna help us use a more strategic view of the type of system we want to have and therefore the types of plugins that we will approve or not approve when they come in as change requests. I'm really curious if anyone has something similar to this at their institution or what longer-term principles they use to make decisions at Change Advisory Board meetings. How many stakeholders were involved in the dialogue is a question I just see. So it's working backwards. So when we decided how these principles would apply for Moodle, it was everyone with a decision-making, with an operative decision-making roles as a service owner, IT operations manager, of the course Moodle. We also have an exam Moodle. He was there too and me. So it was four of us thinking about the application of the principles to Moodle. But the principles themselves were the result of our entire faculty development team. And then the documentation that informed the principles went through a massive consultation process. So we have a policy called Quality Criteria for Teaching at ETH, which is a mouthful of the policy. And that one went through an extensive consultation period with lecturers at our university and administrators. But what we're also doing is we're using this as a process to feedback on the principles as well. So as our Moodle team talked about the principles and whether or not they work for our context, we could then give feedback to faculty development and say, look, this definition didn't really work for us, but this bit really did. And so we see the principles as a living document that will and should change over time. And as they change, I feel like they'll sort of balance out and then we'll come to a centralized understanding of what they mean. Does that answer your question, Ian? So I have a little question. Hope you didn't answer it already and I missed it. But I was just wondering, how long did the whole process take that you've described? Well, that's a good question. So what we did is we had about, I want to say about four meetings in the Moodle team, which were an hour long, where we worked through the principles and we went through each column. And then we had sort of one more where we looked at the action plan. So it was maybe five hours, but it was important, I think, to have it rest in between so that we weren't constantly working on it. But to get to the principles did take a lot longer because there were more people involved in the discussions and we're still not quite happy with them. But I suspect that as we use them, we will develop more of like a loyalty towards some principles over others. So for example, participation is one that I'm sure we'll keep coming back to. And Tim, you asked how hard was it to get down to 10? It wasn't that hard, but we actually feel like 10's too many. And the reason why is because, as you know, the human memory doesn't like numbers over seven. So we feel like we should really whittle it down to a small set of numbers that are easy for us to remember. So we can go, oh yeah, our five principles are. And you can list them all for soon as you have a lot more and that becomes harder to remember them. And then you tend to only remember the same five, same days, we'll just use those. So we're still trying to actually get down further to 10. So it seems like the questions are pouring in. Now people have had a few minutes to think about things. We have a question from Jessica, saying, hi, Karen, I love this. We have a very loose version of this, but have such a small group that runs our Moodle that we're finding it difficult. Could you talk about how many people were involved at each step? So when we, so if I'm working backwards again, so our Moodle team is relatively small as well. We have, as I mentioned, the two IT managers or the operations managers, our service owner who I see is in the group here as well and myself. But then we also have developers and system administrators and we didn't involve them in the conversation. So we kept it at a certain tier. So it was the four of us there. And then when it came to actually developing the 10 principles, initially there were about eight of us, but then we developed a working group of three and we sort of really nutted them out. And then we thought the best way to really do this is just to use them and see what works and what doesn't work. So it's all kind of bubbling up to the surface. And it's another way to, because otherwise I think it could feel quite rigid if we now said these are the 10 and this is exactly how we're gonna work together. So it gives us some flexibility to still say, you know, I'm not sure this principle works and there's no hard feelings because we know it's all still in flux. Then I see a question there about making principles, transparent, so we're defining principles to start a process, yeah. I think this is also really important in terms of capturing culture. So one reason why this is so important to me is because when I lived in New Zealand, there was a very strong influence of indigenous culture and everything we did. And they have a very different worldview. And so by defining principles at the beginning of a development service, as you suggest, of a development process, you really are able to give yourself that North Star. So when you start losing your way, you can go, so where are we going again and what are we doing this for? And you can go, yeah, that's the way because that's the way the principles are showing us. So did you answer Silke's questions about how did you get the lecturers and students involved? So the lecturers and students were involved when it came to defining the policies that we mined in order to determine our principles. But we haven't taken our principles back out to the lecturers yet because we're still kind of playing around with them internally. So we are still trying to actually work across the teams in our organization and see if we can get it to really feel useful to us internally and then we plan to make it more transparent externally. And one of the ways we communicate that is through a blog that we use to discuss things like our guiding principles for Moodle. So we use a blog for that communication tool. Right. I also think it would be included in any documentation that guides people around putting in change requests because we would like it that if people, before they put in a change request they ask themselves that question, is the change request going to actually further the principles and if so how? So a comment from Jenny, she writes, I wondered if the TESTA project might be of interest. I think there might be some similarities. Great, I'll look that up. Remember everyone watching on the live stream, you're very welcome to post in the discussion forum afterwards if more things come up or if you have further questions that Karin can answer. We're actually running out of time now. So we'll have to finish there I think. So to say thanks again very much, Karin, for your presentation and thanks to all of you for your interest. Thank you.


All right, welcome back, it's still plus politics. The chairman of the Southern Governors Forum, Rotimiak Keredolou, has reiterated that the next president of the country must come from the South. Akeredolou, who is also the governor of Undo State, won that any political party that failed presidential candidate from the North would lose the presidential election because such candidate would not have the support of the Southern Governors. According to him, those pushing against power rotation in the country are toying with the existence of Nigeria. Joining us to discuss this are Mohamed Abdelay, Chinadu, Ifei Chilobi, and Ayo. They are all the public affairs analysts. Many thanks for joining us, gentlemen. Thank you. All right, I'll start from you, Ayo. You are from the Southwest. You just had my introduction. The governor of Undo State is saying that if any political party present a candidate from the North, they will not get the support of the South. What's your position on that? Are you in agreement with the governor? Ayo. All right, I think we've lost Ayo. De Lettza, let me take it back to Mohamed. Thanks for joining us. I'm sure you can hear us. You've heard the position of the governor of Undo State, and he is saying that... Yo, yo. Mohamed, can you hear me? I can hear you. All right, so you have followed the position of the governor of Undo State. I just want to know your candidate opinion because he's saying that the South would not support any party which failed to govern candidate. First and foremost, thank you for having me. But as it is, all of the parties are shying away from the rotation of power because in less than, say, one year to the post, none of the parties to the best of my knowledge have come out to say we are in our candidate, or this is the particular region where we will be having our presidential candidate come from, whether it is the APC, the GDP, and all others, none of the parties are doing that, are saying that at the moment. So I think it is actually wrong for the Arapa-Umiya Kegyudu, I mean, the governor of Undo State to categorically say that if any party fails in Nodana, the Soudanas won't support. And I must say this. You see, democracy, whether we like it or not, is a government of numbers, is a product of numbers, I mean, to say it. And the fact is that the Northern part of Nigeria still holds swing in terms of voters' power. Or it holds on any candidate whether it's coming, the candidate, particularly candidates coming from the South to romance, excuse my word, to romance the Nodana, like what have Chinubu doing at the moment? For every little thing here and there in the Nodana, he was in Zampara before he traveled to London and so on. And even the vice president, whether he won, he has declared or not, but you see him romanticizing the Nodana, he was in Kano State for a public lecture two days ago, but he used the opportunity to visit the family of Hanifa that was murdered some weeks back. So I think it is very important that any candidate, particularly that wants to win the presidential election, must embrace the Nodana.  And at the moment the Nodana is constituted, I'm sorry to say, the Nodana region has an advantage. All right, thank you, Mohamed. Chinudu, let's talk to you right now. You have heard from Mohamed that he feels politics in Nigeria is a game of number and a search, so the South should romance with the North if they really would hold sway come 2023. But I'll take it further to say that wouldn't there be any issue of a conflict of interest in regards to the North or the South, whether who they are going to feel, shouldn't there be issues like should we field out a candidate from the South-South or the South-East or the Southwest? What's your position, really, Chinudu? Luke, we have to lay down the peanut butter at this point. First of all, the question of leadership should never, never, ever, ever boil down to tribe or tribalism. It should never. That point has to be made that this is the reason why our country is polarized. This is the reason why a lot of things are happening. I can talk about the Southeast when I was here the last time I talked about how this tribal undertone surrounding our politics has caused a lot of issues and there's so much unrest in the Southeast as it is. Of course, that's not what's on the table, but we should never make the issue of leadership tribal, it should never be a question of tribe or whatever. Coming to what the governor has said, well, he's the chairman of the Southern Governors Forum that can decide what they need to do, but Nigerians need to understand that what we need is a leader who will take us from the doldrums because we are the doldrums. I was in the radio program earlier today in Nogu and I told them that he that is down needs Fiannual Hall. Nigeria is on its back. We are falling to our worst. What we need to do is rise and what we need to do is to pinpoint that man who will be able to clear the clutter, who will be able to walk through the maze and get us out of where we are because we are, like I said, we are the worst and if I can find a better word to use, we are our worst right now. Now what we need is someone with the right initiative, the right thinking, the right tactics, to get us out of this nonsense that we are in. It should never be an issue of tribe. If we come to numbers, there are a lot of factors. You can't just say that the North is super when it comes to numbers. I'll just go against my values of not being tribal or following the line of polarization in any way, but if you look at it, the North is mostly made up of Muslims while the South is mostly made up of Christians and if you look at the religious constitution of a country by population, the Christians are more. So you would know that the Christian North will possibly go with a Southern choice. So you can't just sit down and say that the North is superior when it comes to numbers because there are other tiny, tiny factors that you need to look at. But to round this thing up so that other people can't speak, it should never be a question of tribe, which is completely that tribe again. All right, Cheney, do we still have Ayo there with us? All right, Ayo. So let me throw back the same question to you. Yeah, I can hear you. Let me throw back the same Ayo, we can hear you. Ayo, we can hear you. Okay. So I'm trying to back the same question to you now. Would you really say that the issue of ethnicism in Zonin and all of this talk about the North and the Southern dichotomy, you know, they've actually done us more harm than good and they've actually brought more disunity than even pushing Nigeria together as one. I think we lost Ayo. Well, if you can get me Ayo. Ayo, are you still there? Well, let me get back to the frequency. I can hear what you're saying, Ayo. Let me get back to Mohamed. Mohamed, you have followed the conversation. So for Anchi Neidu said it goes beyond numbers. It goes beyond the polarization as ethnic groupings, as the North, the South, the Southwest, the South East, that it's even more to religion and all of that. But as it is right now, shouldn't the conversation be more about who has the best interest of Nigerians at heart, who has the pedigree and who has, you know, all that it takes to bring a better Nigeria? Mohamed. The question should be, I agree with my brother, Mr. Chinin, that he as Nigerians should concentrate on who is best to deliver the dividends of democracy to the country and its citizens at large. But we must also understand that these things doesn't just come in. There must be a process. If you follow our process as a country from 1960, I'm sorry, we are not yet ready to film the very best candidate. It's shocking, but that is just the truth. Because if you are talking about the very best candidates for the position of presidency, I'm sorry, more than 80, 90% of those who have signal to the fact that they want to contest the presidency, they are not in that pedigree. They are not in that category at all. So the fact that we still play to sentiment, the fact that we still play to religious card is enough reason for us to rethink at this moment in time. Let me give you this example. Why on earth do you think as a nation we still have the federal character principle in our constitution that in itself is a hindrance to getting the best brain? Because you are saying if you have so-so here, you must have that there without looking at the competency, without looking who is best fit for the job. So if you have Mr. A from Quarra, you must have Mr. B from Anambra, you must have Mr. C from Ademara and so on and so forth. Without, like I mentioned, taking into cognizance these people, what will they bring to the table? So the conversation, we are just starting. And by, like I mentioned, the process that we've been in since independence, up to date, we are not yet ready. We've got a whole lot of things that we need to place for us to move forward in terms of getting the very best brains and the best hands to manage this country. But at the moment, we still play to religious card, we still play to terrible cards. It's unfortunate. All right, thank you so much, Mohamed.  As by the way forward, how we can get about better elections, better leaders, better governors, a better president irrespective of religion, tribe or ethnic groupings? Yes, there are a whole lot of things to do. And I think first and foremost is education and then education and then education. Education I mean overhaul of our own system from primary to secondary and tertiary institutions. People understand in fact that this country is not meant for a particular people or a particular cater of people or people from a particular religion or a particular tribe that it's meant for us all. We either decide to make it go to better it or want to destroy it all. So like I mentioned, education is key, is very, very vital. You can imagine we have more than 10 to 15 million children out of school, all over Nigeria. You know, nobody's talking about them. So it's shocking. So my own advice would be that we need to educate people. We need to go back to school and we need to implement education. Then that would channel every other thing. Even in terms of voter education, people are not coming out to vote. The last election we have less than 30% or 35% of the people registered who are eligible to vote, coming out to vote. It's shocking. So my own advice, like I mentioned, would be education. We have to restructure, we have to go back to a classroom to teach people and we must implement it in order to move forward. Thank you so much, Mohammed, yet again.  Chinedu, I'm afraid there's as much as we can take. I will take a short break now and when we return, I'll be giving you my take. As a 2023 general elections approach, the issue of zoning is once again central and as usual contentious. Why zone the leadership of the country to a particular region when any qualified Nigerian from any region is eligible to contest? Beyond 2023 elections, Nigerian leaders must begin to realize that the zoning policy is not a lifetime replacement for the missing unity in the Nigerian state. They must assist from widening the existing divides, be sincere with the people and truly unite a country so that we all can look beyond the limitations of region, ethnicity, and religion. Then and only then can we begin to truly assess the competence of competence. If Singapore, a country with multi-racial and multi-religious populace can unite and progress, it is definitely not impossible for their country, Nigeria. My name is Justin Akademiplos, politics returns tomorrow, see you then. South is, South is, because that is our turn. We're supposed to be a, have a president for next election, you understand? Because when you check everything, how the country is going, how the presidents are, where the presidents are coming, the regions, and you believe that we are, I'm saying the president will come supposed to be. I don't care about that. It's just a good person, a good person, that's all. I think God is the one that have a financing. And secondly, we need a God-fearing person in this nation of Nigeria. Eastern parts, it's fair enough, it's fair enough to come from the Eastern parts or I don't know if Yoruba should be the Western, right? Okay, because we are tired of the Northern side of the people who really know us and then. We also want something like, let's say, let them give a chance of younger persons instead of this old old man. Okay, the number is coming out now. For me, I don't think he's okay. The decision is from Cabals. Where they want, that's where they want. But, of course, if you look at it, you see that the rotation they are doing is not balanced. Since after war, they say Yoruba people will not rule them. That's shown they make, understand on it. So, if I have to say, Yoruba people have a chance to rule, but at first they deny them not to rule the country, what are we going to do? Nothing. South is, south is, south is because that is our role. We're supposed to have a president for the next election. We understand. Because when you check everything, how the country is going, how the presidents are, where the presidents are coming, the religions, and you believe that.


I bear witness that there is no God but there is no God. I bear witness that there is no God but there is no God but there is no God but there is no God.


So farming cakes in power world is by far one of the most displeasing, hideous things about the whole breeding system in the game. I do hope that in the future they at least do something about the cooking time for them as well as all things do get easier the higher the ranks you get and those level 4 works through stability powers become more apparent, it's still a chore I don't think any of us do enjoy. In today's video guys I bring you what in my opinion is by far the best way to indeed get the ingredients to make cakes as well as talk about the options you have in cooking them. How's it going guys, my name is DPJ and before we go any further I'm giving away a couple of copies of this game or any game of your choice. To be in the chance of winning simply drop a like on this video, leave a comment down below, make sure you are subbed and have those notifications turned on. Winners are picked from the comments section and announced at the end of the week so good luck. So getting cakes for the use of breeding is something we all do within power world but what are the fastest ways of getting cakes? Is it through the ranch and using powers to get those ingredients are there other means? Well yes, actually there are and that's why I bring you guys today. All ways to get cakes which include ways faster than waiting on powers at the ranch to cough up what you need or to be honest these methods could be used in tandem with the ranch to get those ingredients at a faster rate. So firstly cakes require flour which you get from the milk you have in wheat, red berries which can be grown or picked, milk which you need in mass arena 4 and the ranch, eggs which require chickpea in the ranch and honey which requires bigardy and again that ranch. Now for these materials you can actually get much much easier and quicker and that's through people buying them from the small settlement vendor. Weak milk, berries and eggs all cost 50 each. Now I truly recommend you grow your own wheat and berries and here you get way more than you will ever need in doing so. So milk and eggs will probably be what you need here for me personally it's more so eggs than it is milk I think egg is the number one and mostly used and consumed ingredient to make a cake obviously so maybe just maybe eggs you want to buy or need. And while to be honest guys 50 each these are cheap when you consider how easy gold is to get in this game and that's what I recommend you do. I recommend you use this simple tip and farm gold to purchase ingredients while at the same time you have these powers in your ranch creating some ingredients for you. So the quickest way to make gold without a doubt in this game is to simply craft nails. One ingot gives you two nails, one nail starts with 160 gold, you do the mass people, how easy is it to get ingots so how easy is it to make nails and how easy is it to just sell these nails and buy said ingredients. There is no excuse as to why you shouldn't be filthy rich in this game and well if you ain't now I'll teach you. So to start there are loads of spots or spots in this game plenty of them you'll see in a few on screen now these are some of the less popular ones I've seen floating around the internet so if you're playing on an official server try checking out a couple of these spots coordinates as you can see on screen now. Now all you need for this entire set up is obviously the base basics, power box, power beds, power feeding box, storage and you are good to go here then you need mining powers. Anubis in my opinion does this amazingly you also need a transporting power again Anubis is great at this and in reality that's all you really need unless you plan on smalting the metal into those ingots at this working base you're about to set up then it's the case of getting even something as basic as the primitive furnace to cook up those standard ingots for you this works. Now in regards to a power that's efficient in kindling obviously the best in the game is the Germantide Ignis found right here on the map these are the goal too for that kindling but I do understand people watching this video will struggle getting one but there are many other options too like the Arsox who is an easy catch who's a level 2 in that kindling Pyrene is the same you have level 3's in Ragnarok Blazhau and Reptileville these are great kindling options and there are plenty of others out there for you now obviously with the cakes it's the cooking time which is a drawback a simple method in more or less half in times logically is by doubling up on the furnace and doubling up on those kindling powers this was a method I use as a starter player looking into breeding the more cookers the more kindling powers you have the more cakes you'll get in return doubling up of a single cooker simple now I would recommend the base cell for farming ore that you put down a few springs and that food in that feeding box a bare minimum is is foods that will restore that sand like cookberries salads etc but once that base is set up sit back relax while they farm the ore for you you then make it cook and then simply use those ingots from that furnace and craft those nails you plan on doing that at the same base to you obviously need that station at work station but they are newbies will make these as quick as any other power in the game as it's the handwork which is the best for you here now while we're on the subject of a new business no excuse not for you to have some of these already in your setup simply breeding a relaxorus and accelerate these give you a newbies I mean that's the easiest combo you can get but get yourself this base working pal it's by far the best in the game but yeah once you have those nails ready head to the small settlement and sell those nails and then purchase the ingredients you need even better guys which is something I recommend you doing catch this vendor and place him at your base which is what I've done it saves you a ton of time in stressing about fast-travelling back and forth from the small settlement can sell them and buy them from him in your base it really is as simple as a vet and it saves you a ton of time now from this draft alone from this work base alone you'll be able to buy more eggs and milk than you'll ever need even if you purchase berries and wheat to the same result will occur from here though you still need that honey here I do recommend you having a couple of these bee pals within your ranch what I will say is honey is the least needed ingredient so obviously it will be the least used so you will see your stocks just accumulating in the background while everything else drains out now I could say go out and slay bees for honey cinemas too but it's best if you can just catch a few or even breathe a few there are many combinations to breed in these early game the easiest in my opinion is a malpaca and a tansy these guarantee you'll be guarding and there's no excuse in you being able to catch you to low-level pals real early on now if you have that ranch set up therefore have a chica pea and a mozzarella here dropping that milk and eggs for you because if you don't and you have that ranch set up already you really doing a disservice to yourself from here guys I'll simply craft those cakes now in regards to the ranch obviously certain powers are needed to get what you want but can you increase the rain which they drop said ingredients in the long run under my testing work speed passives seem to affect the animation of which power drops said ingredients this will affect all the production time for sure but other than this nothing else I have tested resulted in faster eggs milk or honey drop obviously discounting the fact that the condensation machine which we start sacrificing said powers this will affect the drop rates that you will see so do keep this in mind actually have a video guide and in depth a lock on how you can actually increase ranch drop rates which I'll link down below or you'll find on my channel now there is another way in which I tried and tested and getting those cakes as it was recommended to me on my discord and that was going out and slaying those lavender's here I tried this I slayed away I caught away I caught and then slayed away I did it probably about 40 times in total I didn't get a single cake this was also with a party for who are said to make neutrals drop more items neutral power shot more items although I saw a few of the other things drop more consistently cakes were not dropping for me whatsoever I even adjusted my words and and nothing was happening for me here guys so under my testing the vendors although can drop cakes are just not efficient enough keep in mind if you do try and do this for yourself so they only appear at night but yeah guys the fastest way to make cakes in game in my opinion is to actually just purchase ingredients while also making your own there's no real or legit efficient option that I have come across I've been using this method for a while now and I've not run out of cakes and probably never will so yeah I hope it helps you out too but there we have it guys guys if you enjoyed the video leaving a like really helps out feel like what you see I want to see more power would be sure to subscribe and hopefully guys I will see you on that next one


What about the extra symptoms from autistic burnout? You could have an extremely low social battery to the point where you are ghosting people that you like and you've got no reason to ghost people for. You could withdraw from people. You could not go to certain social events so that you can do more work or like so that you can just relax. Like you just literally can't add that into your daily life or it would cause you like panic and put you at risk of having like a shutdown or meltdown is a very real thing that happens.


Hey everybody, so I was recently asked by one of my patrons exactly how long he thought it took me to restore a CRT. Now we're talking actually taking something apart, cleaning it, recapping it, recalibrating it, putting it back together, and then sending it on its way. So the monitor that I seem to be unable to get away from the last couple of weeks has been the Commodore 1702. I have yet another one in my shop that someone brought locally and they wanted a cap kit done to it. Now this cap kit has 39 capacitors in it for this monitor, so it's a pretty good size little kit. It's not huge like a PVM or anything, but this is kind of a standard CRT that would be more on the easier side to recap and service as compared to something a lot more complicated like a PVM or BVM that would have probably this many caps on each circuit board and then it would have four or five circuit boards. So we're just going to see exactly how long we're going to start just by taking it apart here in a second, disassembling it, getting the boards out, and then I've got all the tools here. So we'll be ready to go. I'll set up a stopwatch and have a couple of cameras going and we'll zip through this thing. And the point here isn't to just go through this and do it as quickly as possible. I want to kind of time this to see how long it takes this job to be done in a quality fashion. So all right, what I'm going to do now is we're going to switch over, look at the other cameras, and we're going to just get started. The stopwatch will get set up. And again, so I'll record each segment and time each segment. And then at the end, we'll put each segment together and see how long it took the entire job. And then we're going to get started. I'm just going to go ahead and sit started here. And now let's get started. I'm just going to start by taking our screws out going from there 50 seconds. All right, so it took a total of seven minutes for that first section. Well, six minutes and 50 seconds to be exact. But we've got the chassis pulled, the main boards pulled. This is what we'll be servicing. There's only, since I've done this thing so many times, there's only one more piece we need to really be worried about to get in and service that. And that's this little slide bar down here on the side. And it's just held in with a couple of screws. And that way we don't actually have to take these boards out of this frame while we restore it. But the issue with this one is it's just, it's really dirty. It's got lots and lots of dust and dirt building in it. And it smells like it's got some cigarette smoke in it. So it's probably been in the house of a smoker. So that's another, it'll add another little bit of time that we normally probably wouldn't have spent time cleaning. And I'm going to show you some points on this board where you can really see just some excessive buildup of dust and soot. And that's really what happens when you smoke on these things. So especially like in this back area where our potentiometers are. Okay, so there's a whole bunch of stuff down in this area. See if the other camera will show it any better. Just lots of soot and that's just beyond what we'd call regular dust. That's definitely got some tar and cigarette buildup in it. So we need to really clean this thing off before we start servicing it. So that's going to take some time. Let's go ahead now and set up the timer and we'll dust off this chassis and clean it up. And then we can start removing the capacitors. Alright, so I've taken just my brush and brushed all that soot and stuff off everything. And since this is a pretty simple circuit board, it's safe to use, you know, just an old horsehair non-conductive brush that's not going to do any damage to any of the parts. And I don't have an environment out here that's conductive to a lot of static electricity. However, that's something that you should be aware of when you're using brushes to dust. There are some people that like to use anti-static or electrically neutral or safe brushes. Now, as I go through here, I just want you to see that we're going to add basically another seven minutes of time. We're up to 15 minutes. Give or take a little bit total on our rebuild so far. And that's just to get us to the point where we've got our chassis cleaned. I do have the cap kit ready, but first we're going to need to use our HACCO now. And let's see how long it takes us to get all the caps out of the board here, the power supply board, and our neck board. Right at about the six minute mark, my HACCO FR-301 decided to get a real nasty clog. Now, I actually was forced to take a timeout and go clean the tool. It took about 30 minutes, but I'm not adding that time to this procedure because it was obviously unforeseen. So anyway, I did take a break here at about the six minute mark to clean that. And then I restarted the timer and got back to work. After I fixed my HACCO FR-301, it took 12 minutes to remove the rest of the capacitors. So if I add all that together, we're looking right at 18 total minutes to remove all 39 capacitors. We're going to start on our first section of our recap now. That's going to be our neck board and our power supply. So just five caps and then we'll bust into the big board, which has 34 caps and see how long that takes. The rest of the main board, which is 34 capacitors all here in this kit. And I've left my clock. So we left off right at 12 and a half minutes. So let's just resume that and see how long this takes. We'll come back and see at the end what the finished job looks like and how long it takes me back. So I did just finish up those 35 caps and I'm at a total time of under one hour and five minutes. Now again, that's all the caps. We'll combine that to our total time on the job. Now I've got to get this back into the frame and shell with the CRT tube. But before I do that, I really need to clean that out too because it's got a lot of smoke and nasty build up. So we'll start the timer on that and see how long that takes to add that of course to our job total. All right, we're really going to get in here now and start cleaning the inside of this. But again, it's got a layer of dust covered in cigarette smoke soot. So I'll let you take a look at that before we start the timer just so you can see. I want to show you some of this so I'm going to zoom in a little bit and then we're going to start cleaning it and we'll start our timer. Just a real thick layer on there though. I'm going to use a brush and just an old t-shirt here. Next I'm going to put the chassis back into the frame here and the bezel with the screen. And that way we can test it. And the other pieces of plastic are inside soaking in hot water so that they can be cleaned. That's just going to be about a 10-minute job and I'll time that and add it in at the total when we put it all together. But this right here should just slip into the bezel and then we can... The last thing I'll do is add just a small bit of dielectric grease up here around the anode and two and a little on the cap. And that's just going to give it a little bit of lubrication and extend the life of those parts just, you know, without doing too much more. We're just going to do that. It's also going to make sure that we don't have any small bits of hair or dust in here that could make it crackle when it turns on. Okay, ready? Pretty much ready to test it now. I'm going to flip this around. I've got the Super Nintendo plugged in. First off, let me make sure it's on the front input. Let's hope it's all good. Add green blues all there. All right, so it tests out great. You can see everything, all the colors, the tube looks good. And what I need to do is calibrate it. But before I do that, I'll go inside and clean the rest of the pieces. Again, that should be about 10 minutes and then we'll be able to reassemble the rest of the parts, start calibration and finish this whole thing up. Again, right now we're sitting at, after I get done cleaning, about two hours in total time for everything. As you can see, the S-video input or as we say, Commodore video is working as well as our mono audio. All right, so this didn't need a whole lot of adjustment, just a little bit of vertical centering and vertical size adjustment. And that's pretty much it. That's a good thing about this monitor. It seems to do really well after recapping and then a slight adjustment, generally speaking. And it always maintains a pretty solid picture. All right, so that's the completed restoration. And I think that at the end of the day we came in at less than two and a half hours. But I'm filming this before I edit it and actually count up the time. So I will add the exact time below and you can see if I beat that two and a half hours, I believe I did. Just some of the challenges I encountered. Of course, when you try to do something like this, you're always going to run into some kind of problem. And this job was no different, but the problem really didn't pertain to the monitor itself. My problem this time was in my FR-301 HACCO desoldering tool. It actually got extremely clogged up about five or six capacitors into the removal job. I removed five or six of the 39 capacitors and it just clogged up, seized up. I was not able to get anything through that till I was able to clear that nozzle. And that did cost me 30 minutes of time actually to clear that nozzle. I'm not adding that as part of the job because that's something that's not really part of the job. It is part of the job, but it's not part of the pricing for the customer. That's already got to be built in for tools and things. So there's just something to think about anytime you try to do something that seems like something will happen, but just stick with it. I was able again to clear that after about 30 minutes with the work. Other notes on this restoration. I did actually go and discharge the tube and the anode cap the way you're supposed to with the discharge tool.  You're not supposed to do that while the monitor is plugged in. It needs to be unplugged first off. And you need to make sure that you're not touching any metal. Just use one hand when you're discharging it. But that's the official way you should discharge it. And also doing it like that is not going to damage the tube in any way. Whereas if you use that tool and poke and prod around the back of the tube, you could scratch it up and hurt even the connector sometimes on the anode cap itself. You could damage that. One maybe final note is the adapter I use for S video to get it into this. I know some people have asked about that. This is just a simple circuit board that has a S video input. And it breaks it out to where it has ground and luma on this side and then chroma on this side and ground. And all that basically does is separate those lines. And it was on B and C for the other end of the connector. So you could make any kind of adapter you wanted to. All this is doing is breaking it out nice and clean like that. And then you could run B and C cables for this, which is what I normally do. Or in the instance here where we've got it on this monitor, we will use that adapter to get into the Commodore video. But hey, that's it again for this beautiful monitor. And hopefully maybe we could get on to something else besides the Commodore monitor because I have plenty of other things to do. And I'm not just typecasting myself all the time to do just Commodores. I like them and they need to be worked on. And each approach that I make as a video will be different. So I hope you guys enjoyed this one. If you did, please leave me a like and let me know what you think with a comment below or any questions you may have. I appreciate you joining me and I'll see you guys next time with some more retro content.


A bus rollover on I-87 Northway Southbound occurred Friday between exits 22 and 23 has closed all lanes in both shoulders. According to authorities, drivers in the area were advised to seek alternate routes, multiple law enforcement agencies and first responders are on the scene.WTNTV reports authorities said there were multiple injuries and that there are at least two serious injuries.


Hello, and welcome to This Week in the City. Highlights brought to you by the Public and Media Relations Department. I'm your host, Alicia Utsi. Well, this will be a very busy week in the city, since it is also National Youth Violence Prevention Week, and the City of Columbia will be hosting two events this week to highlight how we can bring youth together to talk about youth violence and ways to prevent it. On Wednesday, there will be a public forum focused on human trafficking, and on Thursday, there will be a community event, and everyone is invited. Please visit our website at columbisc.net for more details or contact Parks and Recreation at 545-3100. It's also MDA Boot Week here in the city. The Columbia Fire Department will be raising money for the Muscular District Association, and they will be holding their annual boot drive to collect funds for this very worthy organization. For details on locations where you can donate, visit our website at columbisc.net. Also this week on Tuesday, Columbia City Council will meet on March 20th. A 2 p.m. work session and 6 p.m. regular meeting will be held at City Hall and Council Chambers. If you can't make the meeting, always remember that we live streamed the meetings from our website at columbisc.net. You can also visit the website for agenda items. Also this week, we celebrate the 10th anniversary of Together We Can Read, and on Wednesday, March 21st, more than 130 readers will be in Region 1 schools reading to 3rd graders all at the same time. We want to thank everyone who volunteered to be a guest reader for this year, and we also want to thank Region 1 for their decade of partnership bringing the joy of reading to our children. As we roll into the weekend, don't forget about the Midlands Heart Walk. You can still sign up for the City of Columbia's team. Just visit our website at columbisc.net. And also on Saturday, it's the annual Mayor's Extravaganza. Come out, let's move, and let's have some fun while you visit Finlay Park from 2 p.m. to 5 p.m. for this annual Extravaganza, which features food, fun, and lots of movement for the entire family. For more details, call Parks and Recreation at 545-3100, and you can definitely find information about this event on our website at columbisc.net. Well again, we have a very busy week, and there's lots for you to do. We hope you have a great week in the city.


rotation to speak in this wonderful seminar. So I will talk about some joint work with Hang Buyi about negative moments of the Riemann-Zeta function. So I want to, maybe not everyone here is doing analytic number theory, so I want to start by giving some introduction about the Riemann-Zeta function. So how do we define it? Well, when the real part of S is bigger than 1, then the Riemann-Zeta function is given by Dirichlet series, one over the Dirichlet series of 1 over n to dS. And it also has an infinite Euler product, so an infinite product over primes of 1 minus B to the minus S inverse. So when the real part of S is bigger than 1, things are relatively easy and well understood. Now it's more interesting what happens to the left of 1. So it turns out that the Riemann-Zeta function has a meromorphic continuation to the whole complex plane, and it has a simple pole at S is equal to 1. And it satisfies a functional equation so we can relate zeta of S to zeta of 1 minus S. So because of the functional equation, it turns out that the most interesting place where we can, where we want to study the Riemann-Zeta function is the so-called critical strip. So we're in between the lines with real part of S0 and real part of S1. Fundamental question about the Riemann-Zeta function is the question about the location of its zeros. It turns out that understanding zeros tells us a lot of information about, for example, distribution of primes. So we know that the Riemann-Zeta function has so-called trivial zeros, that's negative even integers. And the Riemann hypothesis says that the non-trivial zeros of zeta should all lie on the line with real part of S equal to 1 half. Another big open question is the Lindelof hypothesis, which is actually implied by the Riemann hypothesis. So the Lindelof hypothesis gives a strong upper bound on the sides of the Riemann-Zeta function on the critical line. So the critical line is the line with real part of S equal to 1 half. So the Lindelof hypothesis says that zeta of half plus i t is bounded by t to the epsilon for any small epsilon. So here you think of t as being large. It grows, and then zeta of half plus i t is never bigger than t to the epsilon. So the main focus of the talk would be moments of the Riemann-Zeta function. So let's talk a little bit about how moments were introduced. So they have a long history. They were introduced more than 100 years ago by Hardy and Littlewood. So the 2kth moment of zeta is defined by this i k of t. It's the integral from 0 to t of zeta of half plus i t to the 2k, absolute value. The reason why Hardy and Littlewood introduced these moments is that they realized that the Lindelof hypothesis is equivalent to showing that the 2kth moment is bounded by t to the 1 plus epsilon for any small epsilon for all positive integers k. So the fact that the Lindelof hypothesis implies the upper bound is easy, the other way is true as well. Of course, they weren't successful in showing that the 2kth moment is bounded by t to the 1 plus epsilon for all k. The Lindelof hypothesis is still open today, but this started off the research into moments of zeta, and not only moments of zeta, but moments of other else functions, of else functions and families. So for a long time, moments were not really well understood, not even conjecturally, but this changed with work of Keating and Snape. So they conjectured that if you look at the 2kth moment, then you have an asymptotic formula with the main term of size t log t to the k squared. So this part was relatively well understood for a long time, and it follows by pretty simple considerations. But then the interesting question is what is the constant in front of this main term of size t log t to the k squared? It turns out that you can essentially write it as a product of two other constants, so one constant ak and another constant gk. The ak, again, it was pretty well understood, even before the work of Keating and Snape. It's given in terms of an infinite Euler product, so it's this infinite product over primes, which converges. But the gk was not really understood until the work of Keating and Snape. So before discussing what gk is, let me just explain the log t to the k squared part and the ak part. So heuristically, if you write the Riemann zeta function in terms of a Dirichlet series, so zeta of half plus it to the k, that's given by the Dirichlet series dk of n over square root of n times n to the minus it. So here dk of n is the case divisor function. So this counts the number of ways in which we can write n as a product of k integers. So if we ignore all questions about convergence and we write the 2k power of zeta half plus it in terms of Dirichlet series, we get this double sum over integers m and n, dk of m, dk of n over square root of mn, and we're integrating this m over n to the it. So you can see if m is equal to n, for example, the integral is very simple. So we expect to get a main term. Now if m and n are far apart, then we expect to get a lot of cancellation in the integral of m over n to the it. So heuristically, we only keep the so-called diagonal terms, which correspond to m is equal to n. And then we get the sum of dk of n squared over n. Say we truncate somewhere, say we truncate at t. And then we get an asymptotic formula with a main term of size log t to the k squared and this arithmetic constant a k. So this is where the a k comes from and where the log t to the k squared comes from. And in general, whenever you have a family of health functions, it's by using this kind of heuristic arguments, you can usually write down the power of log pretty easily and the arithmetic constant as well. But more interesting is what happens with this constant gk. So gk was known in a few cases, in a few small cases. So g1, the second moment of the Riemann data function was computed by Hardy and Ditton within the same 1916 paper. G2, the second or the fourth moment was computed by Ingham. Nothing beyond that is known unconditionally. For g3, there was a conjecture of Convian Gauss and for g4, there was a conjecture of Convian Gonec but nothing beyond g4 was known, not even conjecturally. So then Keating and Snape had the idea of modeling the Riemann's data function using random matrix theory. So they said that the Riemann's data function should behave in some way, should behave in the same way as the characteristic polynomial of unitary matrices. So if you want to compute the two-case moment of data, you should look at the two-case moment of the characteristic polynomial in the unitary ensemble. You compute that random matrix theory integral and you end up with this constant gk. And they conjectured that the gk that you get from random matrix theories, the constant that goes in the moment asymptotic formula for moments of the Riemann's data function. There is another way in which you can write down this, you can arrive at the same conjecture. This is the hybrid model due to Gonec, Hughes and Keating. So before we had to put in this constant ak in some sense by hand, so random matrix theory doesn't know about primes. So we had this correction, this ak factor which was the arithmetic part and then the random matrix theory part and then Gonec, Hughes and Keating had this idea of writing the Riemann's data function as a product between a part which involves primes. So they truncate the Euler product at some point x and then they have a product over zeros. So we write the zeros as half plus gamma n and we look at zeros which are very close to the point d within one over log x. And then if we assume a certain independence conjecture, so if we assume that the two-case moment is given by the two-case moment of the product over the prime primes times the two-case moment of the product over the zeros, then you actually can write down this same Keating-Snath conjecture, but now this has the advantage that you can write the ak and the gk at the same time. So you don't have to put in the ak by hand. Okay, now there is a more refined conjecture. This is work of Conry Farmer, Keating, Rubinstein and Snathes and the methods, the heuristic method they use is called the recipe. So they predict that the two-case moment is asymptotic to t times a polynomial in log t of degree k squared. And then you have some power saving error terms, say t to the one minus delta for some positive delta. pk is this polynomial of degree k squared and of course the leading coefficient of pk so the coefficient of log t to the k squared agrees with this Keating-Snath, random matrix theory conjecture. So this conjecture, the Conry Farmer, Keating, Rubinstein and Snathes one is not based on random matrix theory at all and it holds for integer k. And there is another more recent approach of Conry and Keating. They use long-distance polynomials and results on divisor correlations and they get exactly the same conjecture as the recipe gives you. So I mentioned before that in terms of rigorous results, we can only compute the second and the fourth moment rigorously, work of hard dilute, little woodwork of Ingham. For the fourth moment, Heath Brown later improved the fourth moment asymptotic so Ingham recovered the leading order term, the Keating-Snath conjecture. Heath Brown recovered the entire polynomial of degree k squared, of degree four, this case. Unconditionally, this is all that is known. For the sixth moment, Ingham computed the sixth moment conditional on certain conjectures about ternary additive divisor sums. And more recently, for the 38th moment, Ingham, Shan and Wong used similar results about, so conjectures about quaternary additive divisor sums and they recovered the eighth moment. So although in terms of asymptotic formulas, only the first four moments are known, we do have upper bounds and lower bounds, good upper bounds and lower bounds. So under the Riemann hypothesis, there are lower bounds of the right order of magnitude for all positive k. Well, this is work of Ramachandran Heath Brown. There are unconditional sharp lower bounds for k, which is greater than or equal to one due to rod zeppelin and Sanderarajan. And recently there are sharp upper bounds for k between zero and one, again, unconditional due to heap and Sanderarajan. So we have unconditional lower bounds for all positive k. Now, in terms of upper bounds under the Riemann hypothesis, there are some older results of Ramachandran Heath Brown for k between zero and two. There are sharp upper bounds for k of the form one over n, where n is an integer due to Heath Brown for k of the form one plus one over n. And we have sharp unconditional sharp upper bounds for k between zero and two due to heaps rod zeppelin and Sanderarajan. So what can be said about bigger k? So these results that I mentioned here about upper bounds mostly hold for small k or special values of k. Well, we have upper bounds of the right order of magnitude and this is conditional. So for all positive k, there's work of Sanderarajan, which shows that the two kth moment is bounded by T log T to the k squared plus epsilon. So he almost has sharp upper bound up to this plus epsilon here. And this was later improved by Harper, who under the Riemann hypothesis removed the epsilon. So for all positive k, you have a sharp upper bound of size T log T to the k squared. And these results will be important in what I will talk about next. Any questions before I move on? Okay, so the picture for positive moments is pretty well understood. We have asymptotic formulas in certain cases. We have good upper bounds and lower bounds, either unconditional or conditional. The more difficult question is, what happens for negative moments of data? And these are not as well understood. So there's a conjecture of GONEQ, which says the following. So here we're considering the negative to kth moment. Now, because we are looking at the negative moment, so we have the Riemann zeta function in the denominator, we have to be slightly away from the critical line so that we avoid the zeros on the critical line. So we introduced this small shift delta in the negative to kth moment. So now we're looking at the integral of zeta of half plus delta plus IT to the minus to k. And we want to study this integral. So the question is, how does this behave with delta? So we should expect when delta is closer and closer to the critical line, we're closer and closer to the possible zeros of zeta on the critical line, so things become more complicated. So GONEQ's conjecture states the following, depending on how big the shift is. So if the shift is reasonably big, by reasonably big, I mean that the shift is bigger than one over log T. So the families, we're looking at zeta of half plus delta plus IT, we integrate up to capital T, so we can think of this as being a family of size T. So if delta is bigger than one over log of the size of the family, one over log T, then GONEQ's conjecture says that the negative to kth moment should be asymptotic to one over delta to the k squared. And now if delta is smaller, so if delta is less than one over log T, so here we're really in the range when we're very, very, very close to the critical line, then he conjectures that the negative to kth moment should have different asymptotic formulas depending on the size of k. So if k is small, then we expect the log T to the k squared. If k is bigger than one half, then we have this other asymptotic formula, so we have a bigger power of log T. If k is equal to one half, then he actually predicts that you get a certain logarithmic correction, so you have a term here log of one over delta log T. Okay, so for k is equal to one half, something special happens and you see this logarithmic correction. However, it turns out that if you use random matrix theory again, then this partially contradicts GONEQ's conjecture. So there is work of, so there's a question if GONEQ's conjecture is unconditional. I mean, this is a conjecture, so it's not, I think the way he gets to the conjecture is by assuming the Riemann hypothesis, but everything is heuristic. It's conjecture. There's- Alexandra, what does DT means in the second display? In the second display? Yeah. So you mean the integral or? The integral minus k delta T, then DT. This part here? No, lower. Lower to the left. Lower to the left, yeah. Next one. Oh, sorry, yeah, it's a typo. Yeah, thank you. Yeah, there's no DT. Also, I would like to mention the, just sorry, when you mentioned the fourth-pile moment income and then his Brown asymptotic with power saving, I think the record is power saving T to 2-3rd. Yeah, that's right. Yeah, okay, thank you. Yeah, thank you. So if we are to use random matrix theory against to model the Riemann's data function, so now we're looking at negative moments of characteristic polynomials in the unitary ensemble. This was work of Berry and Keating and Blater, Forrester and Keating for other ensembles of random matrices, which model other families of L functions. Then these computations partially contradict Gonex conjecture in certain ranges. So for example, they suggest extra transition regimes whenever K hits an odd integer over two. So when K is equal to one-half, their conjecture, the random matrix theory computations agree with this Gonex conjecture. So you see this logarithmic correction when K is equal to one-half. However, what Berry and Keating do and Forrester and Keating later on is they suggest that when K is equal to three-halves, K is equal to five-halves and so on, you see extra correction factors. So it turns out that this has to do with a phenomenon of clustering of zeros. So for random matrices, Berry and Keating realize that clusters of eigenvalues actually start contributing when you are looking at higher and higher moments. So if we want to write down the conjecture taking these random matrix theory computations into account, this is what you would get. So here I wrote conjecture in quotes because the Berry, Keating and Forrester, Keating papers are really just random matrix theory computations. So they don't write down what you would expect for the Riemann data function. But if you are to translate their work into this number theoretic context, then this is the conjecture that you would get. So when Delta is big enough, so Delta is bigger than one over log T, then this agrees, the conjecture that you get from random matrix theory agrees with Gonex conjecture. So you'll get the one over Delta to the K squared. And then you can also pretty easily write down the arithmetic constant, a K. So this didn't appear in Gonex conjecture, but it's not hard to write it down. Now when Delta is less than one over log T, then the conjecture that you would get is the following. So here J is an integer, bigger or greater than or equal to one. So when K is equal to J minus one-half, so you have an odd integer over two, then this is what you get. You have this logarithmic correction here. When J is equal to one, so K is equal to one-half, this actually agrees with Gonex conjecture because this term Delta log T to the minus J times J minus one is zero when J is one, is one, sorry, the power is zero. However, when K is between J minus one-half and J plus one-half, then you get a different formula. So this doesn't agree with Gonex conjecture when K is bigger than one-half. Again, the arithmetic factory K is relatively easy to write down. So here new K is the case, the case coefficient of the negative case power of Zeta. Any questions about this? You can also use the same heuristic ideas behind the recipe. So recall that the recipe, the Kory-Farmer Kitting Rubinstein-Sneith conjecture was initially written down for positive K or for integer positive K. If you use the same heuristic ideas for negative integer K, then you actually get something which completely agrees with this random matrix theory prediction. But that conjecture wouldn't tell you about, it wouldn't tell you anything about what happens all the integers over two. So we could miss these correction factors of log of one over delta log P. So what is known about these? In the same paper where Gonex made these conjectures, he also got lower bounds. So these are conditional on the Riemann hypothesis that he got lower bounds consistent with the conjecture for all positive K in this range when delta is big enough. So delta is bigger than one over log T. He also got lower bounds consistent with the conjecture when K is less than one path in this other range when delta, in this small range when delta is close to the critical line. So again, recall that these are the ranges where random matrix theory agrees with Gonex conjecture. So these are the less controversial ranges. Gonex also studied discrete negative moments. So if you're looking, if you're summing over zeros of Zeta with height up to T and you're looking at Zeta prime evaluated at the zeros to the minus two K, then under the Riemann hypothesis and the further assumption that all the zeros are simple, Gonex got a sharp lower bound. So everything that is known so far is a concerns lower bounds and this conditional. So nothing was known about upper bounds. So in recent work with Hang Buoyin, we get upper bounds in certain ranges. So everything is conditional. So under the Riemann hypothesis, if delta, so if the shift is bigger than one over log T to the one over two K, then we get a sharp lower bound. So I write it here as log T to the big O of one. The big O of one can be made completely explicit and it's actually, we can make it to be log T to the K squared. So in fact, we can get sharp bounds here, log T to the K squared, maybe K squared plus epsilon, almost sharp bounds. Okay, so recall that we are expecting, in this range, we are expecting to get the log T to the K squared. Now if delta is smaller than one over log T to the one over two K, we also need, we have this condition that the log of one over delta is at most log log T. So this means that delta can be, might be at least one over log T to some constant. Okay, so we can't have, for example, delta to be one over exponential of T or something like that. Then we get this bound here. So the negative two K's moment is bounded by T to the K times this ratio, log of one over delta over log log T minus one half. So you can think of the log of one over delta over log log T, let's think of it as a constant. So for example, if delta is say one over log T, then this is one. So what does this bound tell us? Well, the trivial bounds. So if you are using just a point-wise bound for one over zeta, then the trivial bound is just T to the K times log of one over delta over log log T. So this part here is the trivial bound. So in this range when delta is small, we're saving power of T to the one half over the trivial bound. So of course we are far from getting sharp bounds in these ranges, but it's still a non-trivial bound. Any questions? And in fact, once you have sharp or almost sharp upper bounds, then you can actually get an asymptotic formula for the negative to case moment. So here I wrote the corollary. Let's assume that delta is bigger than log log T over log T. Then we can actually get an asymptotic formula for the negative to case moment. So we have a main term here, the arithmetic factor A, K, and zeta of one plus two delta to the K squared. So for delta small, this is of size one over delta to the K squared. So it's what the Connex conjecture predicts what's random matrix theory would predict in these ranges. But for these kinds of ranges, so when delta is bigger than log log T over log T, we need K to be less than one half in order to get an asymptotic formula. So when delta is roughly one over log T, you need it to be slightly bigger than one over log T. Then we get asymptotic formulas for small case. And in fact, we can write it down. So here I wrote down the error term is a little low of one, but we can write it down explicitly. It's a T to the one minus two delta times some power of log T. And similar results can be obtained for negative moments, for example, for quadratical functions over function fields. This is some prior work of mine. So this is a different family of L functions. It's a discrete family. So it's not continuous family like the Riemann-Zeta function. Any questions? Okay, so before talking about the, some of the ideas in the proof, I want to talk about some applications and some generalizations of negative, of studying negative moments. So one both application and generalization is the ratios conjecture. So this precursor to the ratios conjecture for Zeta was a conjecture of Palmer from 1993. So now instead of looking at negative moments or positive moments, you're looking at ratios. So you're looking at ratios of Zeta. So you have two Zeta functions in the numerator, two Zeta functions in the denominator. You're integrating on the critical line. So S here is one half plus IT. And you have some small shifts, alpha, beta, gamma, delta. Former originally conjecture that you can take them to be of size one over log T. Let's assume that the real parts of these shifts are positive. Then if you're looking at the ratio of these Zeta functions over Zeta functions, then you predicted a certain arithmetic formula. A certain asymptotic formula. So why is this interesting? Well, it turns out that this conjecture actually implies many interesting results about zeros of Zeta. So for example, it implies the pair correlation conjecture of Montgomery, a very strong result. So this essentially says that the pair correlation of zeros of Zeta is the same as the pair correlation of eigenvalues of matrices from the Gaussian unitary ensemble. So noticing that there is this connection between ratios and zeros of Zeta, studying ratios became something that people were interested in. So it turns out that if you adapt this method, the recipe of corn reformer, Kitting, Rubinstein, and Snays, you can actually write down a conjecture for ratios as well. This was a conjecture of corn reformer and CERN power. So this is a more refined conjecture than farmers. So it predicts some lower order terms and it's more specific. So it includes these arithmetic factors too. So you have this function A of alpha, beta, gamma, delta, which is given in terms of product over primes. You have, again, you're looking at the same quantity. So two Zeta functions over two Zeta functions. You have these shifts alpha, beta, gamma, delta. And the conjecture was originally stated for the real parts of the shifts in the denominator. So we're looking here. So the real parts bigger than one over log T. So if you recall from Gonex conjecture, one over log T was, when you're to the right of one over log T, it's the range which is in general better understood. Okay, so they predicted this asymptotic formula for the real parts of the shifts in the denominator bigger than one over log T. You have certain restrictions on the real parts in terms of the upper bounds for the real parts. These are there just to ensure that the arithmetic factor A of alpha, beta, gamma, delta converges. So they are pretty mild. But the important part is that you have the lower bound of one over log T. And in fact, they say that you can probably take the real parts to be less than one over log T. So let's say one over log T squared, as long as the shifts in the numerator go to zero at the same rate. So they should also be of size roughly one over log T squared. So what are some applications of the ratios conjecture? I should mention if you know something about negative moments, then usually you can also say something about the ratios conjecture, at least some partial results. But now what are some applications of the ratios conjecture? So a recent, very nice application which at the beginning at first sight seems not to have anything to do with Riemann's data function or L functions, is the proof that almost all integers without local obstructions can be written as the sum of three cubes. So this is recent work of Victor Wang and its condition alone, things like the ratios conjecture or negative moments of L functions. There are also applications to, for example, computing lower order terms for the pair correlation of zeros of zeta. So these were obtained previously heuristically by Bogomolny and Keating, using hard deleterate type arguments, but the computations were pretty involved. And it turns out that using the ratios conjecture, you can write down these terms in a much easier way. And you can do many other things. For example, you can compute modified moments of the Riemann's data function or of other L functions. And this can have applications to certain non-vanishing questions. So one application that I like very much is to the question of non-vanishing for L functions associated to Dirichlet characters. So there is a conjecture of Chowla, which says that if you're looking at L one half chi, so here chi is a Dirichlet, any Dirichlet character, then the conjecture says that L one half chi is never equal to zero. So this is a strong conjecture. If you focus on special families of characters, so let's say that you focus on the easiest family of quadratic characters, then Sanderergen showed that more than 87.5% of these L values are non-vanishing. And then conditional on the generalized Riemann hypothesis, Osloek and Snyder showed that more than, roughly 94% of these L values are non-vanishing. And they did that by computing the so-called one level density of zeros. So I'm not going to say exactly what this is. So the one level density of zeros is just a way of looking at low lying zeros in that family of L functions. It turns out that this gives you information about non-vanishing at the critical point. Now, if you assume the ratios conjecture, then you can actually compute the one level density of zeros for this function whose Fourier transforms have any support. And this would imply that 100% of these L values are non-vanishing. So this would give you the strongest results towards Chola's conjecture that we would have available so far. And before talking about some of the ideas in the profile, I also wanted to mention that if you're looking at the ratios conjecturing random matrix theory, so here we're looking at ratios of characteristic polynomials of certain matrices and certain assembles, then most of the times you can actually write down exact formulas. So this is work of many people. I mentioned a few here, Conry-Farmer-Zermbauer, Borodin-Straholtz, Conry-Forrester-Sneith, many others. So I just wrote down an example of such a theorem. It's for the unitary symplectic group. Here, this is the characteristic polynomial and you can write down an exact formula. So the situation in random matrix theory is very different from what we have in number theory where in most cases we don't know what's happening. So not even conditional on all the conjectures that you want. Okay, so now I want to describe some of the ideas in the proof. I hope it won't be too technical. So we're looking at the negative two case moment. Some of the ideas are similar to the work of Sander Erjan and Harper on getting upper bounds or almost sharp upper bounds for positive moments of zeta. But of course we have some extra problems coming from the possible zeros which are close to the critical line. So we start with an inequality for log of one over zeta. So if you think of the Euler product for one over zeta, you take the log of that, you can essentially bound log of one over zeta by the sum over primes of say you truncate somewhere it's size X, you have these coefficients A of P, you can just think of them as roughly one. Okay, so you bound log of one over zeta by one over P to the one half plus delta plus IT and you truncate somewhere at some point X and the point is the very important point is that you have flexibility in how you choose your X. And then you have a second term here coming from the zeros, a log T over log X times log of one over one minus X to the minus delta. So you can see that this term is going to be very big and it's going to cause a lot of problems if delta is small. Okay, so if delta is small, then this term is going to be very big. So now if we're taking the two case power of one over zeta, then we get this inequality here. So we have this huge term here one over one minus X to the minus delta to this two K over log T over log X and then you have an exponential of the sum over the price. Okay, so in order to understand the negative two case moment we have to understand the exponential of the sum over the price. And we have to be careful in how we choose our truncation or point where we stop the X. So now what do we do? Well, this idea goes back to work of Sanderarajan for upper bounds for positive moments. So we divide our primes into several intervals and the point is that primes on different intervals behave differently. So you expect that small primes behave differently from bigger primes. Okay, so we divide our primes into intervals say P is between T to the beta G minus one and T to the beta J. Again, this is a sequence which we have to choose carefully. It's not really, I'm just going to say that beta one is of size log P over log T and then we at each iteration we mod the beta J is like R times beta J minus one. And when do we stop? Well, we stop when beta capital K is a small constant. So in some sense this X the end point is a very small constant. Okay, so let's assume now that we are in this range when delta is bigger than one over log T to the one over 2K. So this is the easier range when the shift is big enough. So for each point T, we have three different possibilities. Okay, so we start with the small primes. So P one, this is the contribution from small primes. It's the contribution from primes less than T to the beta one of one over P to the one half plus delta plus IT. So in general, we don't expect the small primes to have a huge contribution. So we're looking at those points T for which the small primes have a big contribution. So we have to decide what exactly it means to be big. Here I wrote that big means that the contribution from small primes is bigger than beta one to the minus D. So with my choice of beta one, this is roughly log T over log log T to the one minus epsilon. Okay, so if the contribution from small primes is bigger than this quantity, which is maybe not that important for the purpose of this talk, then we have to show that this doesn't happen too often. So this is what we're going to use. We're exploiting the fact that if the contribution from small primes is big, then we actually gain because it doesn't happen. It happens on a set of measures zero. Okay, so we have the integral over the exceptional set is not. So it's usually hard to bound integrals over these very special sets. So we want to bound it by an integral over the whole interval zero to T. So we bound this by the integral from zero to T of zeta. And then we have this quantity here, beta one to the D times the contribution from the small primes raised to some power S naught. And we have flexibility in how we choose the S naught. And we want to choose it in a suitable way so that we actually get this contribution small. Okay, so now we have this quantity, beta one to the D S naught. And this goes to zero. So this is the important part. And then we separate the contribution from the primes with the moment of zeta. So we bound this by the fourth moment using Cauchy Schwartz and then the moment of the sum over the primes. So for the first integral, so now we want to bound each of these integrals. For the first integral we can use, we don't really have upper bounds for negative moments. So there are no results in the literature. So we don't know what to do except for use a very bad pointwise bound for the negative of the zeta function. So for the first integral here, we use just the pointwise bound one over zeta is bounded by this quantity. And this is going to be, it's going to be a very weak bound because we use this strong pointwise bound for each value of zeta. But nevertheless, we're going to win over this trivial bound because we have this quantity here which goes to zero. And then we have to compute moments of the sum over the primes, but we can do that. So this is a fairly classical thing to do, computing moments of sums over the primes. We can do that as long as the sum over the primes is not too big. So this is a sum over primes. We can write it as a Dirichlet series, a sum over n of certain coefficients. Let's call them a n over n to the half plus i t. And here n must be less than t to the two S naught beta naught. So the point is that as long as two S naught beta naught is not too big compared to t, then we can actually compute these moments. Okay, so we will end up, if we put things together, we will end up with getting this contribution from the exceptional set is little o of t. So it's very small. It's negligible. Okay, now we move on. So now if we have a point t for which the contribution from small primes is well behaved, then we're looking at what happens with primes on the second interval. So now we're saying, well, if the contribution from primes on the second intervals, on the second interval is not well behaved, so it's bigger than expected, then we also want to exploit the fact that this doesn't happen too often. If the contribution from primes on the second interval is well behaved, then we move on to the third interval and so on. So at each step, say step j, we're assuming that the contribution from all the primes up to the jth interval is small enough. So here we have these parameters, the beta j's that I defined before. So now we're assuming that the contribution from the primes up to the jth interval, each of these contributions is small, but the contribution on the j plus one interval is big. So it's bigger than this beta j plus one to the minus d. Okay, so let's call this set tj. Then what do we do? Well, recall, remember that we were bounding one over zeta by an exponential of a sum over the primes. Okay, so we had the exponential of the sum over the primes, say p up to x of one over p to the one half plus delta plus it. Okay, so essentially we want to use the fact that we can approximate the exponential by a truncated Taylor series whenever the sum over the primes is small. Okay, so we have this nice inequality here. If say t is less than L over e squared, then we can essentially bound the exponential of t by the truncated Taylor series of the exponential. We call it EL of t. So this is the truncated Taylor series at the point L here. Okay, so this is exactly what we're going to use since the contribution from primes on the say h interval with h less than j. Since this is small, then we can essentially approximate the exponential of the sum over the primes on the h interval. We are approximated by this truncated Taylor series. So we truncate the Taylor series at beta h to the minus d. Okay, so now when we take the integral on the tj interval, we use our key lemma, so our inequality for one over zeta with x to the point where we truncate being t to the beta j. So then we have this exponential here, the exponential of the sum over the primes. And now the primes go up to this t to the beta j. So what do we do? Well, as we did for the exceptional set, we don't really want to have the interval over this special set dj. We want to have an integral over the whole interval zero to t. So we bound this by the integral from zero to t. For primes up to the jth interval, we bound the exponential by these truncated Taylor series. And then we multiply by this quantity, beta j plus one to the d times the contribution from the j plus one interval to sum power is j plus one, which we can choose, we have to choose appropriately. And the point is that this quantity here is always bigger than one, okay? So we bound this by this integral. And now this might look a bit ugly, but it's actually, we can rewrite this whole thing inside the interval as a Dirichlet series. So the first part here, this is a Dirichlet series of a given length. It has length sum of beta h to the one minus d with h less than j, less than or equal to j. Now, if we look at the primes on the j plus one interval raised to the sj plus one, again, we can write this as a Dirichlet series. So it's a Dirichlet series of size t to the s times sj plus one times beta j plus one. So the point is whenever, when we unwrap this big Dirichlet series, as long as we choose our parameters wisely, this is going to be a short Dirichlet series. So we can actually compute the integral from zero to t when this Dirichlet series is not too long, okay? So we can actually show that this contribution is also going to be small. So the point is that we have this quantity here, beta j plus one to the d, which goes to zero, which helps us, okay? So this contribution is also going to be small. And then we get to the final interval where all the contribution of the primes on all the intervals up to k, all those contributions are small. So let's call this set dk, then we just apply our key lemmas and we choose the point where we try to be t to the beta k. So again, we estimate the exponential of the sum over the primes by these truncated Taylor series. And if we choose our parameters well, this is not going to be a long Dirichlet series. So we can actually compute moments, okay? And we end up with this bound of log t to the k squared plus epsilon. So recall that we expect to get the log t to the k squared. And once we have this bound, this upper bound, then we can actually get an asymptotic formula in these ranges. So this is something that happens many times with moments. If you want to get an asymptotic formula, many times you need an a priori upper bounds, a sharp upper bound in order to get some kind of asymptotic formula. So this is what we do later on. We use this upper bounds to get an asymptotic formula. So everything that I've said here applies for big shifts. So when the shift is bigger than one over log t to the one over two k, if the shift is smaller, then the problem is a bit harder because as I said, the smaller the shift is, the closer we are to the critical line. So we do the same thing as we did before, but we have to do some kind of inductive argument. So let's denote by u, this quantity log of one over delta over log log t. Again, let's think of this as a constant. So if delta is say one over log t squared, this is true. Okay, then the point is that we do this argument that I just presented and we get some kind of bound here. So recall that the k u t to the k u is the trivial bound. So now we save a little bit over the trivial bound, but then we can do this argument again. So recall that whenever we were bounding the contribution from the exceptional set, we were using some a priori bound on the negative four key moment. So we keep doing that and that each step, we use the a priori bound that we obtained in the previous step of the induction. So at the second step, for example, we end up with, so this is the previous bound that we had in the first step. And now we save a little bit more over it and we keep going. And at the end, we end up with this upper bound of size k u times one minus one over two k u. Okay, so I think I will stop here. Thank you very much. And I see that there was some question in the chat as well, so I can probably answer later after that.