Thank you. Welcome to Senate Education, Thursday, April 7, 205. A couple of housekeeping items or maybe one house education committee did vote out a universal meals bill today pilot program they're calling it for one year using 29 million of the education surplus funds. Just to discuss at some point, I know that I have concerns in this committee, they didn't put any money in for PCBs. I do am worried about 29 million dollars going to a pilot program for one year. But we will have that discussion. I think part of my concern is, you know, it's, you've got a lot of middle and upper middle class for monitors as we talked about this committee that would certainly benefit from that and we haven't, you know, reached up at, you know, honestly, over the past several years, we haven't, and I'm not sure if where I would put my first dollar. So that's just where I'm at. Yeah, so they put it in a bill or passed it, you know, they put it in, they put it in the S 100 bill is my understanding from the chair. So now this will go to house. The universal meals from last year. Sorry about that. I've been clear. So they expanded it to lunch and. Yeah, I mean, I'll be honest. And as I've been upfront with the advocates in the hall. There are choices. And me, the choice of 29 million disappearing for one after one year. I'm more inclined to myself to do something where we've got PCBs and school construction and all those kinds of things that are more long term. And permanent. And permanent. Yes, I really genuinely worry about that. It's worth the same. Yeah, yeah, and you know, we'll jump into it and maybe there'll be ways to find to deal with all of these issues, but we need to know what that pilot and tips is that for the whole state, you know, I mean, I could think it's worth a million. There's a way of doing something much smaller. So there's that this bit of housekeeping is to keep everyone aware of where things are. And I think we're going to have to plan the terms of decision making, because obviously, we're going to want to have the PCB stuff in there. So is it going to, are these two bills going to collide or are they going to end up together in appropriations where the decision will be made. So I, are you already. So what I convey to the chair of appropriations and I believe I'm representing everyone in this or was accurately representing your committee's issues that we are would like PCBs to be addressed. And I think she will look to us though to help navigate whether or not. I think it'll be a combination of this committee appropriation and ways. I talked to center coming this morning as well about this. And, you know, again, I don't want, I don't know where the whole Senate will end, but I think there, there are, there are some, I think generally there are some concerns about a one year pilot 29 million gone. And we might not address other issues. And we've had we have a request from our committee for a significant appropriation for the food shelf. Yeah. Okay. And they are further apart. The food bank. That's what I meant. Yeah. So for today, though, we're going to continue our work on as 27. We're going to follow up with Colin Robinson. The NEA who he and his long shop, you may recall, gave us the outline of the future workforce shortage idea how to address it. There were some questions around funding I'd like him just to talk to us about the flow of funding that you raised and others. Back at 727. Then we have you have UVM coming in on S one or an act relating to education military families, which is now part of age 517. And then S to 48, I have a memo here that I think many of you have seen online, but it's not here is a paper copy of it. You don't have a copy that I asked the state colleges and UVM to come in to talk about. And then finally, as I mentioned yesterday, we have Peter teach out and Harrison start coming in for. Here's their positions on this. All interesting stuff, perhaps starting with the most interesting this St. James each 727. I think we finished one and just to yesterday. So we're looking at the last chunk, which is three. Yes, and definitely do you have. We're looking at the second four. Yes. Okay, please. So, three is for section. So, remember, we started with redesignate a section devoted to redesigning to statute taking them out of chapter 11 and bumping them up to chapter nine. And then section two of this bill repealed chapter 11 and then section three was chunks one and chunks two together. The section four, five, six, and seven are they comprised of three. And they are session law meant to address withdrawal withdrawal processes that are already underway. So the first section is section four, and that is withdrawal actions approved by the state board. New districts with an operational date on or after July 1, 2023. So this section only applies to a withdrawal action initiated pursuant to provisions of 16 dsa section 724 that were an effect prior to the effective data section three, so current law. And this graph will call it former section 724. And if each of the following actions occurred prior to the effective date of section three, which is remember chunks one and chunks two. So, here's the posture of this application, the state board of education has given final approval to the voter approved and the voter ratified proposal to withdraw from the union school district. The state board has declared a new school district to be reconstituted. The state board established the new school district operational date is July 1, 2023 or after the voters of the new school district elected school board members, the voters of the town so then the union district voted to approve the financial withdrawal associated by the board of the new school district and union district, and the state board charge the new school district and a board with performing the transitional activities necessary to assume sole responsibility to the education of resident students on the identified operational date. So then that basically described the Rickston situation for the session law was meant for Dr. through this process. And there were other terms in the process but it's various stages so they had to have gone through all of these. Yes, so section five will address the Joe situation section six will address the Lincoln situation. So for section four, what this section would apply only to a withdrawal action that had already been approved. So the voters have already voted on it and state board has already approved that under current law. Section seven. It's on, it's very short it's on page 22. So, so ripped in is partly through their process. I think they are already all the way through the process. Okay, these guys. Yeah, section four section four, which is these are for generally anybody who's all their way all the way through their process. Anyone who meets this exact criteria. Yeah. If you look at your testimony from various stakeholders on who meets this criteria. Ripton was a town that was commonly referred to previously, but technically this section would apply to any, anyone who meets the criteria. I think there's probably only one out there that says. I apologize. I was looking for a moment at the other part of the bill. And this is allowing ripped into what it is allowing so it is allowing ripped into you'll see eventually. We have to give the state board an update on how it's doing in preparing to meet its operational date. So this is just an overview of what section four is requires the town I don't have to rest in. It requires the town, the new school district to give the state board an update on its plan to meet its operational date. And then the state board. I don't have any information. And because we're getting one out. Well, we don't, I don't work a town in Addison County. What I heard. So the state board is going to make it is given. The state board required and then the state board is going to say, great, it looks like you're doing great. Or the state board can say, we have some concern. Here they are. The town, the new school district has two options. You're going to go full team ahead. Or prior to October one of the operational date. It could take the off ramps that section four create. And you'll see the off ramp in section five and section. And the off ramp allows us to get out of the process. It allows them to ask the state board to essentially void the withdrawal approval and keep them as part of the Unified Union. And then the section then allow them to withdraw sort of in the law. They've already done that. They've already withdrawn under current law. They remember current law says there's a vote of the positioning down. Then it goes to all the rest of the towns in the district. And if they all say yes, then it goes to the state board for approval. So what the piece that we're waiting on is the state board's reaction. The state board has already approved. I think. No, I was going to say so. I to hear if they've already been through the process. You're going to have to take testimony on that. I think they're coming tomorrow. I think so. It's an excellent question and it will help put this draft in perspective and I, I may be misremembering, but I think there was a lot of testimony. Prior to this draft being the use of language being huge in the house. So it may have made more contextual sense. You will now have the framework with which to interact with your witnesses in this section. But yes, I know that sounds very confusing. That this is addressing a withdrawal that has already happened for all intents and purposes. Under under current state law. They're done. They're withdrawn. They have an operational date that they are theoretically working for. So this gives them, there's nothing, and there's no take backs in current state law. There's no view over. So this gives them an opportunity to say, we would like to continue to remain in the union department. So that, that was basically a discussion of section four. And real quickly on page two, the state board is, or the new school district is required to give a status update with the state board of education. I'll point out the date of July 22 on page two. So the status report is due to the state board on or before their regular July 2022 state board meeting. I don't know when in the month of July, the state board plans to meet, but if this act takes effect on July one. So that's a quick turnaround. So it would just be either a date to change or something to contemplate in the effective section, effective section. And then the gas report essentially have to tell the state board what they are doing, working towards their operational base. So the state board would use that and gives the new school district an opportunity to be heard and it may in its discretion to take testimony from others, including the rest of the union school district that they just withdrew from and a week. And then just like in the section seven point four that we looked at yesterday and jumped to they're going to issue a preparedness recommendation or a determination so the state board could determine that it's likely that the new school district will not be prepared on operational date. Or on page three, it could determine that it's unlikely. Or that there is a reasonable risk that the new district will not be prepared. And then that that opinion needs to be posted on page three line 11 needs to be posted on the new school districts website. And then the topic or the contents of the state board report or recommendations needs to be scheduled for a topic of public discussion in the new school district. And then prior to the operational date and after any public discussion. Just a minute ago, they can go full team ahead, working towards the operational date, or prior to the October one before the operational date, and I'll explain that date in a second. And then on its own motion so the, the board of the new school district can vote to warn a vote, or it could warn about it petition to do so by at least five percent of the voters in the school district. And that vote is to see if the new school district is going to request with the state board of education on view the withdrawal. The final date is so that if there are, if they're, if the off ramp is taken, there is time to address that contract before the new school year. If it looks like the new school district is not going to be a new school district. The questions decided so the vote whether or not to ask the state board of education to undo the withdrawal action is decided by Australian ballot. And then I'm on page four line four through 11 or just about certification of the vote. And then if the new school district online 12 on page four of the new school district request the state board to take action, then the state board shall reverse and void earlier declarations approving withdrawal and reconstituting the new school district. The withdrawal action initiated to the former section 724 is concluded. And the union school district shall continue to be solely responsible to the education students residing in the town that positions for withdrawal. However, on the top of page five, the new school district and four shall continue to exist for up to six months after the day I went to state board reverses and boards earlier declaration to wrap up. I don't want to make any other declarations or actions necessary support that with undoing. Yes. Has, has, has this all happened by any school yet under. Yes, I believe there have been multiple throughout. Would you say. This is based on the process is they use the. It's an improvement. This is brand new. It was the original language and concept, which was always through discussion and testimony by how bad the original proposal came from the state board of education on how to address these districts that are currently either underway or in this particular process already happened, but there might, might be some changes. Do you tell us a brick didn't testify. Multiple people in various different capacities. But I did not hear every witness I was not there for all time. Nope, I'm just. So, along with accommodating towns that are in the process gives the town that has already done this, the opportunity to change them up. Yes, it gives a new school district that has formed and we've all of the criteria on this one. We have the opportunity to say, we no longer want to withdraw we want to remain a part of the union. And that happens from 5% of the voters. The school board itself could decide to put it to a vote, or they could be forced to put it to a vote by a petition of 5% of the voters, and then the voters of the new school district to decide whether or not to petition the school board to, I guess you could look at it both ways, undo the withdrawal or remain in the school district, the same, same. That's it. The main thing of the section four, and it adds state board review. To the process to the process that we wouldn't have now so without this. Britain will just be one. This requires another review because the way the law was written, we didn't have that review before they had only make that one time. So, I could see somebody correct and saying this is owners, not an apartment. And they could, I mean, but they also created more that recommendation. Just, it's a process. So, I thought you said that. So the status report that's required is the school district is a shout. Okay. So on or before the regular July 24 to FB me name the new school district shall submit a written status report to the board. I understand. I'm sorry, but whatever they could ignore the state board. Yes, the off the off ramp is totally optional. The board's is the preparedness teams unlikely. Thank you. Thanks for going ahead. Correct. Ignore the board's warning that they're unlikely to be prepared. They have to hold a meeting to allow public discussion of the board's recommendation. And then it's up to either the state board itself to decide to take the off ramp. Or if they're petition to do so. Warn a vote on whether or not to take the off ramp or if they're petition to do so that 5% voters to warn a vote on whether or not to take the off ramp. But if neither of those triggering events happen, then they can just go full team ahead with preparing for their operation. Okay. So I come from a background with city governance, municipal governance and land of elder regulations and we're always the caution spot zoning and I feel like we were cautious to the beginning of this conversation, not necessarily name a specific town is that at all relative with what we're doing here, but it seems like we are crafting language in order to address the root scenario is that at all factors discussion. That is intent is solely in your wheelhouse. I as neutral legislative council didn't feel comfortable using the names of the town constantly throughout. I just wanted to, you haven't heard testimony from witnesses. I wanted to put a little context around what you, the way in which this will probably be discussed and I which witnesses, but you don't need to delicately walk around. That's for you to decide. Do we do it. The energy world, and then we just say that there was legislation that was only for IBM, but we would say again, we'd say any chip manufacturer over 500. Located within the border. We don't have any caution as we're discussing this we need to be more So this is so my dog here is to walk through the language. There's no town names in any of these sections. So my the only and maybe I just won't do it going forward. It was just you haven't heard. So when the state board gave this proposal they obviously gave context from a policy standpoint that I'm unable to do and you haven't had that yet. So just to do a chance to set the stage and it was perhaps the fourth time. But this, none of, nothing in Trump three references a county. And theoretically, even if this legislation was drafted with one time in mind, it applies to any town that fits this specific criteria. And then the section four is set to repeal on July 1, 2023. So it's a limited, it's a limited amount of time before that process happened there. I believe their operational date is on July 1. So. Well, no, I just got a letter from the representatives and senators from a loyal county that are talking about this withdrawal section. Yeah, they're coming in tomorrow. They are. Yeah, they are. Okay. They are more likely to be interested in section five. Okay. Continue. Any questions on section four. Okay. Are we okay on time at two 30. Yeah, no, we are okay on time. Actually, is calm. All right, if you don't mind, we'll break on this and we'll come back to it. Probably. Is that okay with you? On the work. Thank you. Mr. Robinson, nice to see you. Good afternoon. Good to see you all. So thanks for coming back in on the teacher workforce shortage. For those watching, and I'm not sure center lines, if you were here when we actually jumped into this. We're talking with our colleagues and appropriations about the possibility of doubling the proposal you put forward, which would bring us to maybe 300 teachers over the next couple, couple of years. We'll start to address this teacher shortage and you've heard from this committee are concerned. We know that there are other workforce development bills going. And this would likely end up in our miscellaneous education bill, or even more likely perhaps directly in the budget. So we're in conversation with Senate approach that being said, we have some questions. And one of the questions is, can you take us back and tell us a little bit about how this money flow. I had a conversation in the hall. And it really helped clarify things for me. Then we talked about a little bit committee. I thought best to have you and just to tell us again how sort of how this would actually work. Yeah, absolutely. Thank you for the record con Robbins, Vermont any a and thanks again for the committee's focus on this. So, as it relates to the, to the flow of money and the appropriation sort of outlined it here is as a practical matter. I think what would make sense is for it to actually be appropriated. It would eventually flow to the school districts. But of course, you know, because we're not talking about necessarily every single school district participating in this or some school districts might have 12 participants and some might have one. It can't be a direct allocation per district. And so the construct that we believe would be most appropriate would actually be for the funding to flow to the agency of education to then be paid directly to the school districts on a per participant level at the amount that we talked about on Tuesday, which is the 50 figure. And so for a district that had 12 participants in this program, they would get 12 times 4750 for district that add three teachers that have three times 4750. I think that's the way it would programmatically and financially probably have make the most sense to flow to the districts. So I partly raised this because of my personal experience with my spouse who earn a master's degree paid for by a public school district in the great state of Vermont to the Southern New Hampshire University, which was marketing up in this area. And as she was taking that program which he had a good experience with I kept thinking with those dollars be better kept in states and they are public dollars. You see any avenue for this these monies that going through this agency of education to have some sort of restrictions that they could only be used for a must take college programs. Yes, yes. Yep, that's a great question, Senator Chitenden. So as outlined in this proposal, and remember, just as a baseline for the committee and a reminder for those who might not have heard previously. This is scaling up a program that is being stood up in the Northeast Kingdom right now, right now. And, and so to that end, the specific arrangement and the credits that will be offered are through Castleton State University or Northern Vermont University at Castleton. And so that is the institution of higher education that would be receiving the tuition dollars. So as outlined in this proposal, those dollars would, those tuition dollars would actually come through previously budgeted allocated professional development dollars from the local district. So teachers at the local level is, I think you're sort of alluding to Senator Chitenden have access to professional development funds. So in this program, those professional development funds would be used to pay for the three credit course at Castleton or Northern Vermont University, Castleton. I apologize for probably not speaking the name of the university correctly today. My apologies for missing that I received a lot of memos this week. No problem. Senator Hooker. Oh, sorry, if you mind if I just ask one quick question. So with the pilot program that we're sort of standing from the kingdom, did those dollars go to AOE now that I was talking with my colleague, Juliet Longchamp about that. And, you know, if you remember the origin story on that was seven curriculum directors came to her and said, Hey, we need help. Right. And so I believe they're braiding different funds, some Esther funds, some other local funds available but I also understand there are some districts in the kingdom that want to participate in this program but don't have the resources to do it. And so what is there any is AOE involved right now we're putting AOE sort of in the center, you know, to distribute the funds, but right now they're not. That is correct. I mean I see. But what I will, what I will say is that my colleague Julie has been in multiple conversations with the licensing division at the Agency of Education that she works with frequently and probably daily. Okay, thank you for that center hooker. I'm just wondering yesterday I think Senator Chittendon mentioned visa and the possibility. And since I'm not sure whether AOE has the resources that they need. Yeah, and just wondering if that's an alternative. May I respond. So Senator hooker I think the proposal that we that we're talking about here and now is structured the way it is because it's ready to go now. And, you know, obviously back in February we spoke with you all about possible role for Vsac in helping develop and grow the teaching profession and the teacher workforce and I think that that would be a really really great conversation to dig into. And I think it relates to this specific proposal that as envision the structures already there for these funds to go to Castleton and visa could very easily have a role in the in the future or for future initiatives. Mr Fisher, would you identify yourself for the record, and then we just curious about the AOE flow through. I'm Ted Fisher for my education. I'm our director. And I apologize. I'm a slightly of a disadvantage. I'm not familiar with the program. I'm just wondering if you could bring me a little speed on. I think I've got some kind of clear question. You know your own program that the agents that Mr Robinson, his team at NEA started in the kingdom to improve the workforce around teachers. And we know that we've already heard I think from was out of Mr Robinson or his long shot about about 1000 openings already for the fall. I don't want to not address this. And this seems like a really a program that's already happening there's some success and we're told that you know at an investment of about $1.5 million we could get about, we could go toward getting 300 teachers from from local school, people that are already in the district already working maybe in education. They might need to finish a couple classes they might need to, you know, they need to get their certification, etc. So just to make sure I understand what you're considering the idea is for I'm sorry, Colin, I'm speed on this but on your your kid I'm sure my colleagues are on your consideration is to give money for higher education courses or things to help get part of that degree and get part of life in terms of things. Well, it's a little bit trickier than that. I mean not tricky, but it involves, you know, identifying teachers at local districts local schools would service mentors there's a process where you know people would help them get certified, etc. We're looking for the same education to sort of be the past for some of this money. Yeah, and just for clarification Ted so it's it's going through the peer working to provide wrap around supports to guide teachers through the peer review process that your licensing division stands up. So, so it's fundamentally deeply integrated with the peer. It is guiding and supporting teachers on provisional licenses or aspiring educators who are starting the year next year on a provisional license to successfully complete the peer review process that one has to go through in the licensing division. Absolutely. Okay, so I just have to put in our director of education quality after all day. Great. Where he stands on this, if I, you know, the last thing about the digital world is sometimes I get a response right to do with you. I wouldn't suggest and request that we come in and talk to you about this. Mr holidays here tomorrow, but it'd be great to get this resolved actually today possible. Okay. Yeah, great. Is there a reason that you are here. I mean, I don't mean that. No, I appreciate you being here. Stay as long as you like that wasn't that I'm looking at the agenda and nothing else popping up so it's great if you're just here. I don't mean that. I'm glad to be dry. Sure. Great. Absolutely. We can listen in but I like to be in the room. I appreciate it. I really do. I didn't eat it. I just sit here all the time, but it's a new thing. It is. Can I just ask, Mr Fisher, if you could clarify something that came up yesterday, you mentioned the thousand openings. Yeah, yes. Great question. That's a good question for Dr holiday. What we have seen is a pretty, we have seen an increase. We, this is not a new problem. And it's, and it's depending on the, both the part of the state and depending on the type of life, right. So the type of specialty. The quality division puts out a report every year. Yeah, the federal government on what are the shortage areas so that by licensing category so middle school social studies or oftentimes. And actually, probably more familiar than I, but a lot of times like music and art sometimes are shorted area depends on the, even in Vermont, the small state might attend on the region of the county. And just because it's not on the thing we often said, just because a particular specialty isn't on that list doesn't mean that he's been a shorted in part of the state. Right. So that's free code. Now we are seeing. Christian books and entering the profession right so anything that you see for free code and you can, I think at this point for you. It's a good question. Mr. Robinson, you have an answer to that. On the, the number of jobs. Yeah, generally this number of 1000 that opening is it that where we usually are or is this really high or I think it's higher. But anecdotally, it's higher. I will say similar to Ted, nobody's sort of been following the data as closely as perhaps, you know, would have collectively been useful. But anecdotally, it's higher and it's also early so as a, as this committee knows from other conversations, teachers usually get issued their contract sometime in April, and then return it. So we will, if we're seeing these numbers in April before teachers have received or maybe haven't returned their contracts for next year we can anticipate greater openings. I think also and you can ask Dr. Patrick Hallie about this tomorrow. By the way, he has Juliet Longchamp has shared this proposal with him. He's seen it so he can he can speak to it and his perspective on it. But I believe there's also been a significant uptick in provisional licenses over the past two years. And I think there's something like 800 or so folks on provisional teacher licenses right now. Compared to pre pandemic numbers which were significantly smaller. I, he would be able to tell you very specifically what that was. And those provisional licenses are for two years and what's envisioned here is helping somebody who's on a provisional license, essentially sort of matriculate to a highly skilled classroom educator with a full endorsement and license so they can stay in the classroom and build a career. Great. I think it's exciting. It really is. And I'll be good to hear. Is it Dr. holiday. Tomorrow on this issue. So, great. Yeah, please. I have one more point of clarification my colleague, Julie is texting me. And she wanted me to point out that. So, back to the, the per person cost $1,200 of that would actually stay with the agency of education because as you can see in the breakdown the budget $1,200 is the cost of the peer review fee that goes to the agency of education for these folks to receive their, their license. So, I'm just wondering, I know that when Dr. Longchamp presented the program last time, you indicated there might be a deeper dive or another document that we could look at that would give greater explanation. Do you have that. Yes, I shared it with the committee and I believe Daphne is posted on the website. It is. It's a third time. I'm just wondering, I know that when Dr. Longchamp presented the program last time, you indicated there might be a deeper dive or another document that we could look at that would give greater explanation. Do you have that. I'm just wondering if the committee and I believe Daphne is posted on the website, it is. It's a 13 page document so there's, there's a timeline, a detailed timeline, some job descriptions. I did on that document I will say you'll see an organizational chart. I did want to flag for the committee underneath the, the sort of breakdown of the cost. There's something that talks about application process and student teaching equivalent, and I clarified with Julie that is the existing peer review process requirements, as the agency of education has them right now so that's not something that's unique to this specific program those are the baseline processes established for the peer review process that an educator would have to go through to complete it. So that was the point of education that was just to provide that clarification. We have that in our email but it's not on the web page yet. Okay, then you have it in your email and I'm sure it will be on the website website soon. Yeah. No rush. Thank you for Mr Robinson. Yeah, I'm giving Patrick some updates for so he's a more service to tomorrow. What is the, what is the dollar for you're looking at right now. So it was a $727,000 I think that would help us get to that 150 teachers. We doubled it in our sort of informal conversations and said it'd be great to try to get 300 teachers and therefore whatever that ended up being And the, we were able to update the document to reflect that 300 figures so in the document that Daphne is going to post it will reflect the 300 person conversation of the committee. Yeah, no thank you very much. You're okay. Okay. Oh, thank you. Thank you. Okay, Mr Robinson anything else from you on this. I mean we were just curious about the flow and that's really helpful. No I appreciate the committee's interest and fast work on this and definitely as it as it moves into other committees please. And I think that the committee is as you need to move that process along, and obviously is, as I think was noted, you know, I think this is the beginning of a conversation around around this issue and happy that we're able to come to committee and time to see this potentially be useful for the acute need here now. I appreciate it. Mr Robinson if you don't mind, given that we have spoken with the chair of approach, if you would reach out to that committee and just make yourself available. You know they are planning to move everything fast and furious and we can certainly our less counsel is working on some language that we'll have that we could put in the budget, but it'd be great if you just make yourself available to them so that they know, you could kind of talk to them about it. Absolutely I have other things to connect with that chair about so I will happily add this to the list. Thanks for your time I appreciate it. Thank you.


Both clouds and snow cover have a high albedo, which can appear in similar shades of white on visible satellite imagery, so let's go over some ways to distinguish between the two. For starters, regions of snow cover often reveal details of the local terrain, which appear somewhat darker. On this visible satellite image, we can see this swath of white shading, from Ohio through Northern Pennsylvania and into New York and New England, to the north of this line. But the fact that we can pick out some surface features indicates that this is snow cover, not cloud cover. We can see the unfrozen finger lakes in New York, which had a much lower albedo since the snow did not accumulate on the water. Lakes Erie and Ontario were largely unfrozen too, and that gives a nice contrast between the low albedo of the water, which appears dark, next to the higher albedo of the snow cover on the ground, which appears brighter. We can also pick out heavily forested regions, because deciduous and coniferous forests also appear dark on visible imagery. Regions with dense forests mask the high albedo of the underlying snowpack, because trees often lose the snow that accumulates on their limbs fairly quickly. So the satellite sees the canopy of trees instead of the snowpack on the ground. The heavily forested Adirondack Mountains in New York really stick out, as do some forested areas in Northern Pennsylvania. Further to the west into northeastern Ohio, the more agricultural landscape appears brighter because there are fewer trees, and the satellite sees the high albedo snowpack better. Of course, if you have a loop of visible satellite images, distinguishing snow cover from clouds is even easier, because snow cover doesn't move, but clouds do. If we look at this loop, which spans from about 14Z to 1630Z, you can see clouds streaming over Ohio and Michigan into western Pennsylvania and New York. The leading edge of this cloud cover looks pretty wispy and not very bright, and we can still make out some of the snow cover beneath it, suggesting that these are thin cirrus clouds. If you look closely, you can even see some linear features within the cirrus, indicative of airplane contrails. The clouds entering the left side at the end of the loop into northwest Ohio appear brighter and have a higher albedo, indicating that they are thicker than the cirrus streaming ahead of them. Visible satellite imagery is a great tool for discerning cloud thickness, and identifying areas of snow cover when clouds aren't too prevalent. I hope this video helps you with your interpretations of visible satellite imagery.


So thanks to the organizers for inviting me to speak. So in this talk, all of the representations will be complex representations. OK, and to remind everyone, the character of a representation row, like let's say of a finite group, is the function from the group to complex numbers defined by taking the trace of a row of G. And since we're taking the trace, characters are class functions. So they are constant on congenital classes. And another basic fact is that the number of irreducible representations of a finite group equals the number of congenital classes of that group. So you can organize all of the data of the values of the individual characters of your group in a square table called the character table. So this will be the character table of our group G. And to fix conventions, we'll label the columns by the congenital class. And we'll label the rows by irreducible representations. And where a row corresponding to an irreducible representation meets a column corresponding to the congenital class will put the value of the character corresponding to the irreducible representation evaluated at the congenital class C. And in the particular case we care about in this talk, G is the symmetric group on n letters. And then the congenital class is the symmetric group on one-to-one correspondence with the cycle types of permutations. And cycle types are then in one-to-one correspondence by just taking the sizes of the cycles with partitions of n. So that is decreasing sequences of positive integers that sum to n. And then we write lambda and then this symbol n to mean that lambda is a partition of n. And there is also a natural and beautiful one-to-one correspondence between irreducible representations of Sn and partitions of n, spec modules. And in this talk, we will denote the character value for the irreducible representation corresponding to a partition lambda of n evaluated at the congenital class corresponding to the partition mu of n at chi sub lambda sub mu. Yeah, so these are like the notations for the talk. So next I have an example of a character table symmetric group. So here is the character table of S5. So here I've labeled the irreducible representations in the congenital classes with the corresponding partitions of five. So there are five partitions of five. Here they all are. Sorry, there are seven partitions of five. Here they all are. So this is like a seven by seven table. And okay, I think one thing you might notice is that all of the entries of the character tables are integers. And this is not like in general true for character tables of like any finite group, but it turns out to always be the case for character tables of symmetric groups. So it is a general fact that the character values chi lambda mu of the symmetric group. This is always an integer. And this is the case for SN for all n. It wasn't just something for S5. And if you're a number theorist like a kind of natural question to ask if you are presented with these large arrays of integers, it's to ask like what are the statistical properties of these integers as n tends to infinity? Okay, so what are the statistical properties of the character table entries for SN as n tends to infinity? So Alex Miller in 2017 computed the whole character table of SN for n up to 38 and also computed the parity of all of the character values for n up to 76. Okay, and then he looked at kind of various, I guess arithmetic questions about the distribution of the entries in the character table. And I guess the most basic question you can ask is like as n tends to infinity, what proportion of entries are even and what proportion are odd? So here I have a graph taken from Alex's paper that plots the proportion of entries of the character table of SN that are even for all n between one and 76. Okay, I guess this is pretty suggestive. And next I have another table taken from Alex's paper in which he looks at how many or what proportion of entries of the character table of SN for n up to 38 are divisible by small prime powers. So he looks mod powers of two, three and five like up to the third power. And yeah, it's really difficult computationally to go much beyond 38. Like first of all, the size of the character table grows so quickly as n increases like pretty soon.  And even kind of the, like even if you wanted to like compute a random character value, this also takes a pretty long time, typically it seems. But at least based on this small amount of data, Miller made the beautiful conjecture that as n tends to infinity almost all of the entries in the character table of SN are even. Okay, so he conjectured that n tends to infinity, the proportion of odd values in the character table tends to zero. And so this was like also a reasonable thing to conjecture because we've known since the 70s that it's true in the first column of the character table. So for the degrees of the irreplaceable representations. And this was shown by Mackay. This was 1972, but the character values, Thai, Lambda and then the partition of all ones, which just gives you the degree of the irreplaceable representation is almost always even. And he in fact found a formula for the number of odd degree irreplaceable representations. And then following Miller's conjecture, some partial progress was made and Morodi. And then in 2020, I was able to confirm that this conjecture is true. So almost every entry in the character table of SN is even. So the same in the same paper, Miller made the more general conjecture that the same holds for any prime. Okay, so now fixed P and we have the same thing as n tends to infinity, almost every entry in the character table of SN is a multiple of P. And this was proved by sound and I. And also with a degree of uniformity quantitatively in the prime P. So then in a later paper, Miller made the even more general conjecture that the same thing holds for all prime powers. Okay, so we'll fix now Q is a prime power. And again, as n tends to infinity, almost every entry of the character table of SN is a multiple of Q. And the topic of my talk today is about a proof of sound in me of this most general of Miller's conjectures. So precisely what we prove is like, first let's let n be large. So just larger than some absolute constant so that all the logs and log logs that are in our proof are actually defined. These will let n be large. And so we also can get a degree of like quantitative uniformity in this argument as well.  That's almost like 10 to the minus three log n over I think like log log n squared. So Q be a prime power. So then the proportion of entries in the character table of SN not divisible by Q is like big O of E to the minus log log n squared. So then by the union bound as a corollary, we get that if you fix any natural number, like say K, then as n tends to infinity, almost all entries of the character table of SN are divisible by that K. So before we had this for prime powers, we can only do it for like K square free. So maybe I'll pause here for a second to see if there's any questions about like the statement of the theorem. Then I assume there are no questions. So I'll start talking about the proof. And the proof relies on combining like four key intermediate results, which I'll tell you. So the first is a lemma. Should we call the combining parts lemma? If you've seen me talk about the prime stuff, this is just a more general first question. More general version of the combining parts lemma for my previous talks. So it says if we let P to the R be a prime power, okay, then we assume that mu is a partition of n and that new is another partition of n that is obtained from mu by replacing P to the R parts of the same size. Let's say M in mu by P to the R minus one parts of size P times M. So same total number of numbers were like same total size of the parts, though P to the R times M, but now I've combined them into P to the R minus one parts. So then the character values for mu and new are the same mod P to the R. So chi lambda mu is then congruent to chi lambda mu. Mod P to the R. Okay, so then I guess this is the case for all partitions lambda event. Okay, so for an example of what this combining parts operation is. So here we'll take the prime power to be four. So then the character values chi lambda 3, 1, 1, 1, 1. So four ones, these are the same as when we combine the four ones and the partition 3, 1, 1, 1, 1 into two parts of size too. So same mod for all character values. So for the people who know a bit about the representation theory, the best end, the way that this lemma is proven, it's really not hard. You just reduce the polynomials appearing in Frobenius's formula for character values, mod P to the R. So this is not very difficult. But to tell you about the next three lemmas, I'm gonna have to introduce a bit of, I guess definitions, notations, having to do with partitions. So for any partition, you can form the associated young diagram. Which is just like a left justified collection of boxes with each row containing number of boxes of the corresponding part of the partition. So for four to one, you get the young diagram with four boxes in the first row. So there's like, because the first part for the largest part of size four, then two boxes in the second row and then one box in the third. So this is the young diagram of the partition four to one. And each box in a young diagram has a corresponding hook. Again, this will be a definition by example. So I'm gonna just redraw young diagram above. I guess I could have copied it because this is an iPad. And then the hook for a box. So say this box in the like upper left-hand corner is the collection of all boxes to the right of the box in the same row. So all these boxes along with the boxes and the same column below. So all of these boxes I've drawn blue through form the hook corresponding to this box. And the length of a hook is just the number of boxes in it. So this is a hook length, there are six boxes. So this hook has length six. And for example, I guess, so this hook has length four. And you can do that with any box in the young diagram. So if you have a partition of N, the young diagram has N different hooks. And we say that a partition is a T-core. If none of its hooks have length, a multiple of T. Okay, so you can check that this partition four to one is a five-core. Okay, so longest hook has length six and you won't find a hook of length five in the diagram. So yeah, that's the definition of T-core. And the next key intermediate result, lemma that says that almost every partition lambda event is a T-core when T is large. So because we do things quantitatively, we'll let L be some parameter, which if you just care about a fixed prime power, like you can just take L to be some sufficiently large constant. So if you wanted to prove the result mod four, you could take L to be 25. So then for any natural number T, of size at least one plus one over L times square root of six over two pi square root of N log N. All but, oh, I don't know what happened there. All but a big O of log N over and the one over two L proportion of partitions of N are T-pores. Yeah, so maybe I'll give you some context for like this lower bound. So the expected largest part of a random partition of N is asymptotically square root of six over two pi square root of N log N. Okay, so yeah, that's exactly what appears here. So this is saying if T is like substantially larger, then the typical largest part of a random partition, then almost all partitions of N are T-pores. Okay, so that's what's meant by if T is large. So this is the second kind of key intermediate result. And the third is the like, like the kind of key new input into the argument that let us do prime powers instead of just primes. And it's a new divisibility condition for a character value and a prime power. So this is the divisibility condition. Okay, so we'll let M1 to MR just be distinct national numbers. And we'll assume that mu is a partition of N and it has parts of sizes M1 up to MR. Hi, Sarah, sorry to interrupt, but there's a question in the chat, a question of whether you could just provide an idea of how to prove the lemma for T-core partitions. Oh, yeah, so for this, I guess there's a couple of different ways you can do it. I guess you can use like, if you wanted even more information about the distribution of like the number of T-cores, you could use like On's like, like generating function identity for T-core partitions. Or I mean, there are just some, I guess basic inequalities, like for the number of T-core partitions that you can just plug in the asymptotic for the number of partitions of N into, it's the number of partitions of N and then the number of partitions of N minus T and like mess around with basic facts about T-cores to get this. Yeah, so this is not a like difficult lemma. Thank you. Yeah, I hope this is helpful. Okay, so for the divisibility condition, which is like much, much harder to prove, this is where like most of the work of the proof goes into. So we have distinct positive integers and M1 up to MR and then mu is a partition of N with parts of these sizes, all appearing with multiplicity at least P to the R, sorry, P to the R minus one. So each appearing at least P to the R minus one times in mu. So then lambda is a partition of N and it is a simultaneous sum K I M I core partition for all our tuples of Ks such that the Ks are non-negative integers between zero and R minus one R minus one, that sum to at least P to the R minus one. So if lambda is a simultaneous, this quantity core for all of this many our tuples, then the character value K lambda mu is a multiple of P to the R. Okay, and yeah, I will postpone saying anything about this proof until the end and then only if I have time. So I told you like three, the three intermediate results, three out of the four, the first one says we can do this like combining parts operation and not change the congruence class, my P to the R of our character values. So you might as well combine all the parts that we can until we can't combine any more parts. So nothing appears more than, or nothing appears at least P to the R times. And then it's, I think then reasonable to guess that if you combine parts in this way that you'll end up with many kind of largest parts M one up to MR that appear with large multiplicity and that the M one up to MR are large enough so that this quantity is sufficiently large that almost all partitions lambda are this quantity core partitions. So then the next key intermediate result is that we show that this is the case. So we show that this combining parts operation leads to many large parts as many largeish parts with large multiplicity, largeish multiplicity to be more consistent with my vague notions of large. So what we show is that like starting with the typical partition of N if you combine parts in the way that I told you from the first lemma until you can't any more then you're gonna have enough largest parts to satisfy the divisibility condition or so that typical lambda satisfy the divisibility condition from the previous lemma. Okay, so starting with the partition mu event you repeatedly replace every occurrence of P to the R parts of the same size M by P to the R minus one parts of size P times M. We do this until we arrive at a partition mu tilde also of N in which no part appears P to the R times. So you can't combine parts anymore. Okay, so then except for a big O of E to the minus N to the one over some constant depending on P to the R proportion of initial partitions mu, mu tilde has the parts we want. So it has at least R distinct parts. Let's say M sub J each appearing at least P to the R minus one times and satisfying P to the R minus one times M and J is at least a good bit larger than the typical largest part of a random partition event. Okay, and this is good enough to make the whole argument work. Yeah, so the proof of this is we can create a kind of convenient generating function whose terms are an upper bound for the number of like bad partitions mu. So those such that mu tilde like doesn't have this nice property. And yeah, we've picked this convenient generating function in such a way that we can kind of more easily evaluate more easily like upper bound its coefficients which then would give us an upper bound in the number of bad partitions mu. So now that I've told you the is four key intermediate results I'll let's give like now or let's write down an outline of the proof which I guess I've said verbally. So first, by repeatedly doing the combining parts operation the first lemma tells us that the accounts of the character table corresponding to mu and mu tilde are a congruent mod P to the R. Okay, so then it suffices to show that almost every partition mu character values chi lambda mu tilde are almost always multiples of P to the R. Okay, so then by combining the divisibility condition with the fact that almost every lambda is a T four or T large events suffices to show that mu tilde has many large parts with a high multiplicity, okay? But this is exactly what the last time I showed you said, okay, this is the lemma label that combining parts leads to many largest parts with a high multiplicity. Yeah, so these are how the different parts of the proof fit together. And it seems like I have enough time to say a bit about the divisibility condition and it's proof, which is like, yeah, this was the really fun part. So first I'll tell you about the Myrnihan-Nakiyama rule, which is a recursive formula for computing character values of the symmetric group. And first I need a bit more, it's notation. So here's the young diagram of the partition 333 or it will be. So it'll be like a three by three collection of boxes. And so here we have a hook of length four. And so any hook touches like two boxes or at least two boxes on the boundary of the young diagram. So we have the box all the way to the right on the horizontal arm and then we have the box leg all the way at the bottom on the vertical arm. And we can also connect these two boxes along the boundary of the young diagram. Okay, so right here we have a hook in blue and then we have the corresponding border strip, Bs of H where we connect the ending parts of the hook along the border strip or along the border of the young diagram. And for any hook, there's another quantity associated to it called the height of the hook, which is just the number of box or the number of rows the hook goes through minus one. So this hook has height equal to two because it goes through one, two, three rows. So then we subtract one to get a height of two. And the Murn hand Nakayama rule says, so if you let sigma be a permutation that factors as product of two permutations, one of which is a T cycle and then tau can be whatever else but the supports have to be disjoint. Then my partition lambda then the character value chi lambda sigma is a sum overall hooks in the young diagram of lambda of length T, negative one to the height of the hook and then the character value chi, the character corresponding to the partition whose young diagram you get by removing the corresponding border strip from the young diagram of lambda evaluated at tau. So both of these, so this is now a partition of N minus T and this has a, or corresponds to a, also a partition of N minus T. Okay, so it gives you character values of SN in terms of character values of like SN minus T. This is why it's like recursive. Okay, so it can give you like a very, I guess very vague sketch of the proof of the divisibility condition and it's basically just repeated applications of the following lemma does a lot of the work in the proof. So now more generally, you let sigma be a permutation in SN of the form of tau times now a product of, maybe you can't see this, P to the R minus one T cycles and all of the supports of these permutations are disjoint. Okay, so now we let for any lambda partition of N we'll let L denote the set of partitions lambda prime of N minus P to the R minus one times T that you can obtain by removing P to the R minus one border strips from lambda of length T. Okay, so then lambda is a partition of N. Oh no, I already said that. So then if lambda is a P to the R minus one times T core, then character value chi lambda sigma is the prime P times some sum of character values over L. It ends up being an integer linear combination of these character values. So then, okay, we've now gotten that some character value is multiple of P. And then the idea is to like repeatedly apply this lemma. I guess you apply it R many times to get a divisibility by P to the R. And the existence of this complicated looking like hook condition in the divisibility criterion basically comes from having to ensure that this always holds. Okay, so another part of the proof of the divisibility condition is checking that if you make this complicated core assumption on your initial lambda, then even when you remove like many different parts you still know that it's a, I guess, T prime core for enough T primes that you can apply this lemma. And the proof of this lemma was very fun. Basically the way it works is you apply because you have P to the R minus one T cycles. You apply the Myrna-Hend-Nakiyama rule, P to the R minus one many times. So then you definitely end up with a linear combination of character values of this form, right? Because either just the character values correspond to lambda that you get by removing P to the R minus one border strips of length T from lambda. And this is what the Myrna-Nakiyama rule like has in its recursion. And then, yeah, the thing you have to show is that each one of these appears with both the same sign and a multiple of P many times. And to do this, it's send this very combinatorial argument using the abacus representation of partitions. And yeah, that's all I'll say about the proof. I wanna end with there's still kind of many interesting opening questions about the character values of the symmetric group. So I'm gonna highlight two of these suggested by Miller's data. So the first is question of what proportion of the character table of SN is positive or negative. So based on his data, Miller conjectured that the portion of positive and negative values should be roughly equal. And then related to this is the question which is the most interesting question to me of how many zeros are in the character table of SN? So what proportion of the character table of SN is just zero. And for the second question, I'll show you some data in a second, but it's like, I think, yeah, it's hard to guess like what the answer should be based on the data. I'll say that like obtaining for this one, getting at least a constant times one over log N proportion is pretty easy. You can just use, there's this like old result of Erdition-Laner about the distribution of the largest part of a random partition event. So you can combine this with the Marinette-Nakayama rule and the fact that or the quantitative version of almost all partitions of N or T cores when T is large to get this one over log N proportion of zeros. And I think this is the best known. I don't think this has been improved at all. Okay, so yeah, I like these questions and here's some more data I stole from Alice's papers. So this one, this is the graph of the, or it plots both the density of positive character values in this set of non-zero character values and the same for negative in the character table of SN for all N between one and 38. And yeah, you can see they both appear to be approaching one half. And so this is actually from a different paper of Millers that's on the archive. Like maybe this was like the original version of the one that ended up published. And here is also the data for the portion of zeros in the character table of SN for N up to 38. Yeah, I think here it's really hard to tell like, yeah, what's going on? Like is the density of zeros approaching some positive constant or is it decaying like one over log N to zero? Yeah, who knows? So that's all I have.


All right, thanks everyone for coming out to my talk. So my name is Dan Noble. I'm a senior lecturer and future fellow at the Australian Astroniversity here in Canberra, Australia. So what I want to overview today very briefly and very quickly is the Orchard package that we developed a couple of years ago, and more specifically, I want to introduce you to version 2.0, which has a number of substantial improvements over 1.0. Now, given the time limitations, I'm not going to live code, but I provided you with a vignette of sorts to allow you to move through and understand Orchard's functionality. And I'll post the link to this vignette on the video. But basically, it'll tell you here how to install the Orchard package. It'll direct you to the GitHub page, which is hosting it because it's currently not on Cran. And it just sort of emphasizes the need to make sure you have an updated version of R because it'll be needed to play well with the YIN needs package for Orchard to work. OK, so what are Orchard plots? So Orchard plots are plots of meta regression models. They're force-like plots, to so to say. And they're specifically interested in predicting the meta and lift mean within levels of a particular moderator in a meta regression or multilevel meta regression model. So just to give you an idea of what Orchard plots are, I'll introduce you to this limb data set, which comes with Orchard. And this is a study done by Nat Lim, Al Senior, and Shinichi Nakagawa, looking at the correlation between offspring number and size and mother size offspring trade-offs. So we can fit a meta regression model normally using the metaphor package. And it's rma.mv function. Orchard requires you fit meta regression models with metaphor objects. It only takes metaphor objects, so you'll need to use metaphor. But that's OK because metaphor is an incredibly versatile, flexible, and very powerful meta analysis package. So if you fit that model and we're interested in trying to predict the meta and lift mean across this different file, you can generate an Orchard plot quite easily by basically feeding in the model itself, along with the specification of the mod argument, which tells Orchard plot which moderator you want to plot. You feed it the data and a group. The group is needed to specify the sample size for the groups within the brackets here. So this could be study often. And that can differentiate between k, which is the total number of effects. So from that, there are a whole bunch of different options here. You can transform it if it's correlation coefficient, or ZR to correlation coefficient, which is what's being done here. You've also got colorblind friendly plotting options, because we have so many levels I've suppressed here. And what you get then is a nice Orchard plot, which depicts the meta-analytic mean, these dots here. They're 95% confidence interval and the 95% prediction interval along with the raw data in each one of these levels of file up. These data are weighted by their sample size in this particular instance, but it could be precision. It just depends on what you're interested in plotting. Now, one of the nice features is the ability to subset. So you'll notice here, there is a lot of data, a lot of levels where there's very little data, where we can get around that, because the EMEANS package allows us to make predictions at certain levels. And so what I want to show you here is how you can subset the data to certain levels, and also how you can use another function called mode results to capture the model output in a table, which can be useful for publications. So another way to specify this is using the mode results. And here, mode results takes the exact same arguments that Orchard plot does on its own. But here, for this particular situation, it will capture the model results in a table. Again, we'll feed in the file information, but this time we have a new argument called at. And this allows us to make predictions at particular levels of moderators in the model. In this case, we want Cordata, Anthropona, and Mollusca, because those are the levels where we have most of the data. And not only then do we get a limb MR results as a table, we can feed that into Orchard plots to generate the Orchard plot itself, where we have the menalic means and confidence and prediction intervals for each one of the levels where we have sufficient amount of data. Of course, you can then use this mod table, which is held in the limb MR results object, to produce a nice table of those mean estimates and confidence intervals. Now, often when we have meta-aggression models we're interested in plotting continuous variables. This is less common in meta-analysis, but still reasonably common. If you think about requiring, or looking at publication biases, like time lag bias when you're interested in year. And we can easily capture that using the bubble plot function. Bubble plots then allow you to, they take the, again, the same arguments, but they allow you to plot a continuous moderator, in this case year, and you can have an interaction with other different categorical levels to understand how those moderators vary within those categories differently. So this is just an example of an orchard plot. And again, we've effectively just feed it in the same sort of arguments that orchard plot takes. Now orchard's great because when we rely on the EM needs package, it means that instead of a single moderator, multi-level meta-aggression model we can take multi-moderator progression levels and we can basically marginalize means across different levels of other moderators. So for example, if we turn to a different dataset, this is a fish dataset from Odead Al, which is published in 2019. They fit much more complicated meta-aggression models where they've got different trait types with varying degree Celsius differences between treatments and different experiments design. So here we can just fit all those moderators in this meta-aggression here. And you can see it can get quite complicated. This is the output from that model. But what we can do here is because we have those at and by arguments built into orchard plot, we can basically set the predictions up so that we predict say at five, 10 and 15 degree Celsius differences between the treatments. And we can then marginalize over all the other elements or moderators that are in that model, okay? And so this is basically an example of the kind of orchard plot you'd get where you're predicting the degree differences. So if you had a five or 15 degree Celsius difference between your two treatments, what would be the anticipated change in effect size magnitude in each of the different trait categories? Now, one thing that you'll notice often in meta-analysis, particularly with subgroups, is that the variability in those subgroups can vary quite a bit. And this violates the homogeneity variance assumption. We can actually relax that in metaphor models. Metaphor has a great option here by including a category or moderator within the random effects, which allows us to estimate depending on what level. In this case, it's a different residual variance across the different trait levels. And again, we can feed that model in. And here it will then recognize that this is a heterogeneous variance model in a plot, variance is differently across the groups, depending on what the best estimate of variability is in those groups itself. Now that's just a brief introduction to the package. Obviously I don't have a lot of time in 10 minutes, but there are a number of other features like I squared and R squared functions that allow you to calculate both point estimates and bootstrapped estimates of I squared and R squared, as well as submerged function, which allows us to take different model results, objects and merge them together to create a single orchard plot as well. If you wanna find out more, check out the vignette, which goes through quite a lot of detail. And I'm happy to take any kind of questions you might have about orchard 2.0. On that note, thanks for listening and hope you find it useful.