Good morning. We will continue our discussion in the mid-same paper. The fourth question, by the way I forgot to mention, on the third question I suggested that we could use a common mechanism for addition and subtraction, generalizing what Leela Swizala and my TA had suggested of perpetually borrowing and only carrying when necessary. There is another method akin to the what the binary system uses in computers called one's complement form of representing negative numbers. Its corresponding theme is nine's complement. So if you have a number which is let us say one, two, three and the number is negative, the nine's complement will be you subtract each digit from nine and write whatever is the result. That's called nine's complement. Somebody from amongst you had discovered this mechanism which was very nice. So in the final answers that we will put up on the web you will have all these alternative ways of doing high precision arithmetic, namely addition and subtraction. Needless to add the multiplication will still be a larger issue. So the final take away from that problem is that while we consider individual addition and subtraction of standard numbers to be a fixed time cost that is in a constant time you can add two numbers. But when the numbers become large precision then if they have n digits even the addition subtraction cost will be order n algorithm at least. We move over to the next problem where we had these two arrays A and B each has m and n elements respectively and all elements are integer. Incidentally one of the arrays has been sorted, array A has been sorted. So the question here is there may exist pairs of elements in two arrays. Each array if you sum up all the elements let's say first array sums up to someone, second array sums up to sum two and the sum one and sum two will be normally distinct. Now there might exist a pair of elements one in one array and the other in the other array such that if you swap them both the arrays total to the same value. You want to find out whether such elements exist and if they do you want to discover them and print them. That was the problem. So here is the sample answer to that question. I start with declaring two arrays A and B. I have a host of variables declared here. m and n for example are going to be the actual sizes of the two arrays. I and j are traditional indices that I use. I could actually get away with any names but these are traditional and if you have two arrays invariably I will be used as an index of the first array, j will be used as an index of the second array. That's just a convention. Similarly if you have two dimensional array I would be used to represent rows and j will be used to represent column index. Someone and sum two are the two sums that I will calculate. If is the difference between these sums we shall see why that difference is relevant and x and y are any two elements that I am looking at. I read the numbers in two arrays. I have simplified the for loop instead of putting an opening brass then putting the statement and then closing brass. Note that whenever there is a single statement in the scope of for iteration that statement can be written immediately following the closing bracket here. So this is a perfectly valid for iteration. This will execute m times reading the values of a 0, a 1, a 2 etc up to a m minus 1. Same thing about the b i. I now proceed to find this sum of each array all elements. So this is again a simple thing. I start with sum equal to 0, sum 1 equal to 0 and add up all elements of a, sum 1 plus equal to this. Similarly all elements of b sum 2 is equal to this. Now I calculate the difference between the two and I take the absolute value of the difference between the two. It so happens that if the difference is an odd number then I will never be able to find out two elements x and y as required. Is everybody convinced about this fact? No. Let us do some very quick arithmetic. Consider sum 1 minus sum 2. This is my difference. Since I am not sure which one is larger number, I am taking this to be the absolute value. Now look at it this way. When I shift an element x somewhere here and y somewhere here and I swap them effectively it means that from someone I am subtracting x and adding y. In exactly the same way from sum 2 I am subtracting y and adding x. Do you agree that this is what would happen to the sums if I swap these numbers? Now finally I want both these totals to be equal after the swap which means this value should be equal to this. Forget the sign now. In which case if I transfer terms on both sides I get sum 1 minus sum 2. I move sum 2 to this side and I move this to this side. So I will get this equal to 2x minus 2y which is 2 into x minus y. Now x minus y can be any value all or even but because there is a multiplication factor of 2 the difference must be even. If the difference is not even then such pair x and y cannot exist which after swapping will result in the constant sum. Although for solving the problem this observation is not necessary but if you do that this might reduce a significant amount of computations unnecessarily in case the arrays are not compliant with the requirement. So all that I am doing here is finding out the absolute difference and finding out whether the modulo 2 value of the difference that remained there is 0. Note that difference modulo 2 if it is equal to 0 it means that the difference is even. If it were odd I would get 1 as the remain. So this is the message that I give difference of sums is not even desired elements do not exist and return 1 end of the matter. Now I want to do the following things. I want to locate the elements meeting my criteria. So if x is an element of A and y is an element of B then we need to find x and B such that sum 1 plus y is equal to sum 2 plus x. Is that correct? No. Nobody is looking at the equations carefully. When I swap x and y, x has to be removed from array A and y has to be removed from array B. This was a deliberate mistake in the command to find out whether you are alert.  I just wrote the correct equation. Sum 1 minus x plus y should be equal to sum 2. Yeah that is right. Essentially for sum j we are looking at B j and then within that for sum i we must have a i equal to sum i minus sum 2 plus B j. Well these two sums when I swap this sum will have to be written correctly. I will ask a question as to what should be the correct equation when we look at the program. The program itself is pretty simple and that is the whole point. I start with some element B j. So notice that I am moving j from 0 to n minus 1. It automatically traverses the entire array B. Then I calculate x as equal to sum 1 minus sum 2 plus B j. I want to find the desired value x in my equation. So subtracted B j from here for i equal to 0 i less than m i plus plus i check if a i is equal to x. So I search in the second array and if I find I print a i and B j. If I don't find it since array A is sorted if I miss finding it it is unlikely that the next higher element will ever meet the criteria. So the point here is I can terminate the inner loop because I am looking at this sorted array. If I don't find an element at a certain point beyond that I am unlikely to find. So else I abandon the search and I close the loop. Is this program correct? Ok. Write the correct program. Has everybody figured out that this program is wrong? Ok. So let me ask somebody to say why it is wrong. That person down there. Sir the first time it goes in the loop with a i equal to 0 it checks if a 0 is equal to x. If the condition is true it prints it otherwise it always goes in the L's and breaks. So it will never check anything except a 1, a 2, a 3, anything except a 0. Always it will only check a 0 if it is true otherwise it will break the loop. That is one mistake but there is a major mistake in the equation that I am checking itself. Equation itself is wrong because it should be someone minus some 2. Yes what is the minus 2 y whole divided by 2. You are transferring the values on either side. Anyway this mistake you will realize is the direct consequence of the previous conceptual mistake which is written here. Please note this particular mistake is actually insulted by design and the purpose is to demonstrate to you that even though I may make such mistakes but if I have written comments here and then try to implement those comments into logic then there is a chance that later on when I read the English comments I will be able to find the mistake or somebody else who might read those comments might find the mistake. Therefore whenever you have any semblance of complex logic implemented in your program do not forget to rewrite it in plain English words and put those words in comments. This is called inline documentation of your algorithms. You might ordinarily for large software be required to write not comments but commentary huge number of English language pages describing data structures, algorithms, everything. But within even a single program or a function it is advisable to write such comments which will help you in identifying an error in logic implementation. You will notice that whatever is written here is correctly implemented in so far as the equation is concerned. However he has correctly pointed out an additional problem here that I will not do anything worthwhile in this. This need to be corrected. I would strongly suggest each one of you at least those who did not get the answer right in the exam should actually try to write down on a notebook the correct answer to this before I put up the final answers on Monday on the website. Question 4b was relatively simple. It is stated that if m is equal to l then what is the time complexity of the algorithm that you have used in the solution. So in our program we have an outer iteration executing n times every time considering one value from b. For each outer iteration we have an inner iteration also executing n times checking every value in a. Somebody may argue that the second iteration may not execute n times and you would be right. Sometimes you will find the element within the first few elements. Sometimes you may still have to search at the end. Since array a is not sorted sorry array b is not sorted you might find initially small element larger element smaller element you do not have any clue on an average therefore the second iteration may execute on an average n by 2 times even using this. However please note that n by 2, n by 4, n by a are all order n because as n tends to infinity that factor does not really matter. So any constant factor multiplied by n is still order n. Consequently if you consider both the iterations together the complexity of this algorithm is this correct? What should it be? Order n square order n is the inner algorithm inner iteration order n is the outer iteration. For each outer iteration for each outer iteration inner iteration runs completely order n time. So complexities order n square this could be excessively costly and that is the reason why it was stated in the question that one of the arrays is sorted. If the sorted array is used in the inner loop as we have tried to do this in example then it is possible to search the inner array using binary search. If you use binary search for the inner array then the inner iteration will execute only log n to the base 2 times. We have seen that in the binary search. A substantial decrease in the number of computations required. You do not see that when you have 8 or 10 or 20 elements but when you have 1 million elements log 1 million to the base 2 is substantially less than even a 1 million by 2 or 1 million by 4. And each of these executions will happen n times where outer element outer array could also be a million strong. So these things are important. I am very glad to observe that at least about 8 or 9 students from the class have actually tried to implement binary search for the array recognizing that it will reduce the amount of time. I compliment them however there is no extra credit because the question did not demand that you write an order n log n algorithm. But I have asked my peers to find out all those who have attempted binary search at least I will have the pleasure of putting their names on the website when we declare all the marks. So this problem is clear? No what should be clear is you have still to do some homework these slides will go on to the web but you have to write the correct algorithm. All of those who did not get the answer right must on your own using these hints correct this algorithm so that you practice writing the logic correctly. Please do not forget to modify the comments also to reflect the correct logic that you will use. These are not small matters they are very very important steps in writing good programs. Writing comments describing the algorithm and then writing the algorithm. We now move on to question 5. This was about images and histograms. As I had mentioned once in the class and as you would have tried to figure out from the exam question that images are typically stored as large number of pixels or picture elements. Each picture element represents a tonal value or luminescence value or intensity of light that is reflected from that point. In case of white and black images or they are called grayscale images the values range from 0 to 255. 255 is an arbitrary number later on when we consider the computer hardware we will notice that 255 happens to be the largest number that you can represent using 8 bits because 2 to the power 8 is 256 and 0 to 255 is the full range so that is the smallest unit of memory computer's memory which you can use to represent a whole number between 0 to 255. Consequently while you take an analog image and try to digitize it you can digitize any intensity value of a picture point to any number of arbitrary units but 0 to 255 has become a standard. Another reason why this standard holds is that human eye is unable to distinguish even if I sample the value at greater granularity. So black and white pictures typically are represented where each point represents luminescence value between 0 to 255. If your color images light becomes more complicated it has been simplified by saying that each point in a color image will consist of three different components red, blue and green RGB and you can have 0 to 255 values for each of these components. So you have totally a 24 bits or 3 byte representation as we call it and so on. There are many things in digital image representation in processing. Here however we are trying to look at the notion of histogram and I want to discuss the motivation why histograms are important by giving a rudimentary example of picture processing. So each element in an image array let us say 500 by 500 matrix would contain a value as above and histogram is nothing but it indicates how many pixels have the same value. So suppose there is one pixel which has a value 138. There is another pixel somewhere later which has a value 138. There are eight such pixels then the histogram value at 0.138 will be 8. Let us just look at a simple example here to illustrate this point and we will also discuss how we can calculate the histogram. I have written here a 4 by 4 image, 4 pixels. One pixel has a value 3, another 2, third 1, 4, fourth 1, 3 in the second row 1, 2, 18, 21 in the third row 3, 4, 2, 1 in the fourth row 2, 3, 0, 0. Please note that in general you cannot define ahead of time what would be the minimum and maximum value of a picture of any picture. But we know that if we have done this kind of digitization then the lowest value will be 0 and highest value will be 255. Therefore it is prudent to define a matrix H which is the histogram matrix which has 256 elements. The first element is 0, 1, 2, 3, 4, 255. Many of you have not done that because in the example I had said that I have a picture where the minimum pixel value is this and maximum pixel value is this. Technically while answering that question somebody deciding on a smaller array may be technically considered ok. But recall that your program is likely to be used to calculate histogram for any picture. Are you going to change your program every time a new picture comes? This is the first important notion that you must remember generalize your program to work on as many different problems of the same kind as it can. And that is the reason why a histogram array should always be defined as having 256 elements 0 to 255. How will you calculate the histogram values? Let us see what is required to be done. Consider the first pixel 3. Please note that this array is 4 by 4 and the array indices here have absolutely nothing to do with the indices of the histogram array. The histogram index here represents the value at which you are determining the number of pixels. Consider this for example. How many pixels with 3 do you see here? 1, 2 and 4. That means at the level of h3 you should have an entry here 4. Agreed? How many elements do you see which are value 2, 1, 2, 3, 4? How many elements with value 4, 1, 2? How many elements with value 1, 1, 2? How many elements with value 18, only 1? Somewhere here. How many elements with value 21, only 1? Somewhere here. All these others will be 0 except 0. You have 2 values which are values. So this will be 2. Is this clear? What is the final result that you want? The issue is how do you get it in the most simplest fashion? The best way is to treat every element of array h as if it is a sum variable where you are accumulating the sum. Initially I set all these values to 0. I simply start scanning the array. If I get a pixel value which is 3, I know that the element of h with index equal to 3 must be incremented by 1. So I go to the third element directly here and add 1 to it. I look at 2. I go to the second element, add 1 to it. I look at 4. I do the same thing with 4. Now I again get 3. I simply go over to the third element, add 1 more. Please note an extremely easy mechanism is suggested because of the manipulation that is so required. I use the picture value as an index to the array and increment the array value, increment the array element and I will automatically get the histogram when I have completed the scanning of entire picture. Any other way of doing it could be very complex and complicated. Now you have to figure this logic out that in the histogram the element actually represents the picture intensity value and therefore the picture intensity value should be used to represent the index of this array and since you have to accumulate the total number of such pixels at every intensity value it is best to start with all values 0 within this array and keep increment. That is the crux of the solution that is presented next. Just wanted to show you why do we need histogram? We will get back to this problem solution in another 3-4 minutes. This is a sample image. It is an 8 by 8 image. So big square that you see here is one pixel. This is another pixel. This is another pixel. You cannot see the difference in the shares here but when you see it on the screen using the slide you will see that each pixel has different value of gray shade. None of these pixels is pure white, none of these pixels is pure black. So there is no element which is 0, no element which is 255. The elements are all corrupt together in a limited range just as you had seen in the question. These are the pixel values of the sample image. This is an 8 by 8 matrix. So there are 64 picture elements and these are the sample values. Notice that there is a minimum value which is somewhere around 52 or 51. So the values 0, 1, 2, 3, 4 all are missing. Similarly there are no values 255, 254, 253. Consequently you will see that this image appears slightly blurred because the values are very close to each other. Ideally I would like to enhance the contrast of this image so that I can more clearly see the content. For that purpose there is an algorithm which uses histogram. So these are the pixel values. These are the histogram values. At pixel value 52 there is one element, 55, 3 elements, 58, 2 elements, 59, 3 elements, etcetera for each value. I have written here only values which are not 0 because at all other places the values are 0. There is something called cumulative distribution function. So you have histogram which gives the number of points at each pixel value. The cumulative distribution function says for any given value how many elements of the picture are at that value or below it. So you accumulate all of them. Notice that at 52 there is one element. At 55 there were three elements. So in the cumulative distribution these three elements plus the element prior to that one that means I have four elements in the cumulative distribution. At 58 I have 6, 59 I have 9. So the cumulative distribution will simply keep a record of how many pixels are below that value. Notice that the largest value is 154 and it correctly says 64 because 64 is the total number of elements in the picture that you have. You cannot have anything more than that. What is the value of this cumulative distribution function? Firstly I hope you can easily calculate the cumulative distribution function if you have calculated the histogram. It is merely adding the previous numbers and putting the sum next. But this cumulative distribution function helps us in what we call equalization of histograms. The histogram equalization has this formula. I will not go through this formula. I have included it here so that those of you are interested can read the complete Wikipedia article. You do not have to search many places and it clearly explains what equalization is. For our example image which has 64 pixels so you will get m into n as 64, 8 into 8 and minus cdf min, you will get 63 here. This is the formula for equalization. What happens after equalization? After equalization the values which are limited get stretched. So you have nothing at 0, nothing at 1, nothing at 2. You have nothing at 200, nothing at 255. This entire thing gets stretched and that if you map back onto the pixel values you will immediately get a better contrast image. In fact what is shown on the left hand side is the mapping on the final pixel value. If I do this, the cdf of 78 is 46. How it is calculated? I take 78 and do this round, round this operation which is described. Again I am not going through this equation because that is not our concern here. Here the concern is to show how exactly histogram equalization helps. The point is after doing this histogram equalization I will get pixel values in this fashion. Notice that the first pixel value which was minimum was 52. It has become 0 now. The largest pixel value was some 100 and something it has become 255. So I have stretched the entire histogram. Consequently the image that I will see will be like this. Contrast it with the original image. This was the original image. This is the new image. Can you see the difference? All that has been achieved by a simple manipulation of histogram equalization. Just as a better example, I have this image. This is a grayscale image of a landscape. Again let us say you have captured this photograph early morning or late evening where everything looks of the similar luminescence. You cannot identify individual aspects. However if you take this large image, push it through the pixel value digitization, do the histogram calculation, do the cumulative distribution calculation, do the histogram equalization and recalculate pixels you will get this image. First this is the histogram and CDF. So notice that the histogram for this image, the red color thing is the histogram. All the pixels are concentrated somewhere between 120 to 200.  When you equalize the histogram, the histogram sort of spreads and the cumulative distribution function becomes linear. That is all it does. But what it does to the image is really remarkable. This is the image that you get after this kind of simple evaluation. So contrast this image with the original. Can you see the difference? Now this is a very simple example but you can do variety of infinite things. And by the way, most of the digital camera hardware today is capable of doing histogram equalization on the fly. Because you have hardware implementing exactly the same complicated logic. And of course, utilities like Photoshop and whatever can do much more than this. But then that is the matter of image processing and some advanced subjects, those of you are interested can see the maths. The point here is, this is the motivation to be able to calculate histogram, calculate cumulative values etcetera and do this equalization. In the Midsum paper, the only question that was asked was to calculate the histogram. And these are the statements I have imagined 500 by 500. I have a histogram array which is 256. I am using a file called image dot text to read the image. This way I can create files, give it the same name and redirect the input so that automatically the program can read from that input. I will not go through the reading of this. It is very straightforward. If the actual size is npx by npx, I am going to read npx by npx elements in image ij. What is important is, of course this is if I am unable to open the file etcetera, this is the standard paraphernalia. Now I want to calculate histogram. As we saw the logic, I start by setting histogram counts to 0. Then I calculate the histogram values. Notice the crux of the computation is in this single statement. Histogram at image i comma j plus histogram values are all set to 0. Image i comma j is the pixel value which is going to be the index which I have to increment in the histogram array. So a single statement can do that. It is an extremely efficient way and simple way of calculating such arrays by the way are called associative arrays. We shall later on talk about them. So this is the end of it. You can print the histogram and get the problem there. You have to find the maximum value in the histogram. Well, you just this maximum calculation is routine. You have done that umpteen number of times. The only thing to remember is that the maximum value may not occur only at one pixel. There may be many pixels having the maximum value. So to print all of them, you have to calculate maximum separately and after calculating maximum, you have to go through that array once again, i equal to 0 to 256. And if any element of histogram array happens to be at max, you have to print the index at which that happens. So all the elements at which the maximum value occurs will get found out by this. Ignore this image. This I have just used to show because some batches will be doing projects on fingerprint analysis to help the national unique identity project that is that the nation has undertaken. We shall talk about that later. Okay. Thank you so much.


Welcome back to the Vermont House Government Operations Committee, resuming consideration of House Bill 48, which is a COVID response bill giving municipalities some flexibility to be able to safely hold their annual meetings during this state of emergency. So when we left off before the break, we had just heard from Secretary Kondos and now Director of Elections, Will Sending is with us. And I just before I let him weigh in on this, I just want to make very public note of the of the great work and many long hours that Will and his crew put in helping us to to safely hold an election in November, as well as all of the changes that needed to be made back when we did our primary. So, Will, I'm sure that your family has had to get used to you sitting at your computer for many long hours. And I just want you to know how much we appreciate your great work. Thank you. I appreciate it. It was quite a ride, as you all know. And I know everybody here worked really hard as well. But that actually. So were you looking for commentary from me, Rep Copeland Hansis for now? Yeah, yeah, if you can help the the folks on the committee understand the many perspectives that have gone into this and and plus understand from your perspective how it helps provide the flexibility that that towns need. Sure. And so thank you, obviously, or maybe not obviously, but I want to make clear that the bill has the support of our office. And we really appreciate it being able to work with both committees or members of both committees in the late fall, early winter to get it get prepped and ready to go because of the time crunch and necessity to move quickly here. So we certainly support the bill. I won't take I'll try to be brief today and focus mainly on questions you might have. And I know there's some other folks here that you want to hear from that you haven't heard from yet. And you've heard from me a lot. I think the first two provisions operative provisions are very important and very simple and straightforward and we should keep them that way. The first being the ability to move the date of the meeting. I should let you all know I talk and over the past two months really it was amazing almost since the day after the November election. It's like everybody in Vermont just started thinking about annual meeting. And I started hearing from clerks, superintendents, school board chairs, school board members, village trustees, people who run the fire districts, water districts, sewer districts, all the questions about how they were going to approach annual meeting this year. And I think that most important sort of first option to have on the table is to move the meeting date. And so that makes good sense to me. I'm glad Tucker covered that. Deadlines that are attached to the meeting day, a certain number of days before, for example, will follow those meetings that get moved. The ones that won't are those that have calendar dates, of course, in statute. Tucker mentioned a few of the ones that would be attached. I'll just mention, you know, so your 30 day warning deadline would follow any meeting that was moved your 20 days before to have ballots prepared, deadlines would move your candidate filing deadlines would move. So all of that stuff will move along with the meetings. And I think that makes your job easier in terms of just saying you can move your meeting date and that's that the important provisions will follow. The second provision also, I think I don't like to say no brainer, but to me is one that you would authorize not mandate, but authorize these municipalities to mail ballots to all voters. That obviously was successful for us in the general election. It's a different beast doing so for annual meetings in that you don't have the Secretary of State's office as a central state authority that's managing and administering the mailing of the ballots will happen on a town by town municipality by municipality basis around the state. What I am really hopeful for secretary Kondo's touched on it a little bit, but one of the sort of nuances here that's important to think about are the municipal districts, especially school districts, of course, that cover more than one town and the desire and the planning that's already going on in at least some districts to say that if one of the towns in that district is going to move its meetings or or more than one of the towns in that district, that there should hopefully be some coordination where all those meetings are moved to the same date so that also the school district meeting can be moved to that same date and all of the absentee balloting can happen with some coordination. That gets me to the first two provisions being sort of simple, straightforward, clear and make sense to adopt right now. The third provision is again giving our office the authority to implement additional procedures as we see necessary, as Tucker said, related to the allowances that are made in the rest of the bill, namely mailing a ballot to all of your voters. There are a lot of nuances with that ballot mailing and with moving the date of the meetings like I just touched on that I think don't make sense to be addressed in the underlying legislation itself and would slow down the process of that legislation significantly if we tried to. And that's why it's important to have the third provision that lets the Secretary of State's office put some of that nuance into place over the next two or three weeks. If the secretary here, he would be shaking his head and tell me that I need to have that directive ready and waiting as soon as the laws pass. And that's about right. So I think if this provision remains in the bill, you can anticipate a directive to come from our office pretty immediately after the passage of the bill to deal with some of these details. I just want to give you a few examples of that that I'm already thinking about. I'm getting a lot of contacts from municipalities that are interested in using their tabulator that don't typically. And for instance, we are already past the deadline for a board of civil authority to choose to use a tabulator for March 2nd. It's a 60 day deadline. So one of the things we'd say is that you can make that choice to use a tabulator at a later date than 60 days before the meeting. Sort of more important stuff. And I know we have a few clerks here and some of my some of our more excellent clerks are in the meeting. Towns and municipalities are going to come into this authority from different places, right, to adopt Australian ballot and or to mail ballots to all voters. Right now you have towns that conduct all their business in the floor meeting. Every article they vote is voted from the floor like my town of Duxbury. You have towns that do everything by Australian ballot. So all of their businesses on Australian ballot and they're used to that process already within those towns, for instance, that do Australian balloting. Some use their tabulators and some don't. A lot. Many don't because of the cost and being able to avoid that on annual meeting when they've incurred it for the statewide elections. And then you have towns that have a mix of those two methods. They do some business from the floor and then they also have a polling place going on and they do some articles by Australian ballot. The probably the biggest example of that is towns that do their budget by Australian ballot, but do all of their other business from the floor. There are also a fair number that elect their officers by Australian ballot, but then do the rest of the business from the floor. And I've gotten a lot of questions over the last couple of months that if this authority is granted, for instance, to move the meeting. Can we move the floor portion of the business that we do two months back in the spring, but still have our Australian ballot business being done on March 2nd? Vice versa is another question. Could we do our for business? I would advise against that on March 2nd and move our Australian balloting. Cancel postponed floor meeting. Can they adjourn the floor meeting under Robert's rules, right? And then conduct the remaining business for the towns that do all of their business from the floor? There's the related question of so if I can I both postpone my entire floor meeting until later in the spring and then also do the business of that meeting by Australian ballot. So some of those more nuanced questions are the kind of thing that we can and intend to address in a directive if we're granted that authority. Regarding that authority and the ability to put some some additional measures in place that will aid in the administration of these meetings, I just want to remind folks that that actually was the first step we took last year also and that you authorized last year. The broad authority that you gave us to implement new elections procedures included that authority for local elections. And the very first action we took with that authority was allowing the postponing of meetings and because that under the flood of calls and concerns with upcoming meetings that were happening at that point, if you remember, we were in late March. So probably a majority of the annual meetings had happened. There was still a significant number that by charter or otherwise were happening later in the spring. And then we also had revotes of budgets that had gone down in early March. So that really was the immediate imminent pressing problem last spring. And similar to what you're discussing now, you granted us the authority to take some measures to make administration of the local elections easier. Again, the first was to move the meetings. And many people took advantage of that. Many of these school districts that had meetings still upcoming in April or May. And I would anticipate and hope that many municipalities take advantage of that provision also this time. This time, you're going to have that provision in the underlying legislation. It won't rely on the directive from us, of course, to say you can postpone the meeting. So that clarity and that being available as soon as this law is passed is really important.  And I'd be happy to share it with Andrea so that you can have easy access to it. At the second directive we issued last year that had local election processes that they could use just for an idea of what you might what we might consider here. I mean, I'm going to start as a starting point with the directive as a from a draft of the previous one. That included the ability to mail a ballot to all voters, which again, this time you'll take care of in the underlying legislation if this passes. It allowed for drive up voting polling places, which ended up being a great success and something that both the clerks and the voters really thought worked well. The ability to hold your polling place outside, although it's that's my opinion that that's probably allowed under Title 17 as it is anyway. Not needing to do hand recount, hand reviews of ballots after you use a tabulator in a couple of circumstances, if there weren't any candidate votes on the ballot, so you don't have to worry about looking for writing candidates. Or if there was a write in vote count total on the tabulator that's lower than any candidate vote count. The ability to move the deadline for filing paperwork for candidates, which we again would probably do, that's the one that's six Mondays before the election and causes a lot of trouble with towns trying to do this stuff at a late date or a last minute. And then I mentioned that some of the new provisions that might come in that that provide some more guidance on sort of how you move these mixed Australian ballot in four meetings. I think it was Secretary Kondos that mentioned and I've talked about the coordination of the meeting dates between the various districts, school districts in towns and fire districts with the goal of being able to streamline right into a single mailing to voters that reside in both those districts or members of them. It actually, I think is unclear to me under Title 17. And really my advice, typically to the clerks in the school districts is that those ballots should be separate because they're actually two separate elections or two separate municipalities that just happen to be occurring on the same day. In theory, a voter should be able to request a ballot for one, but not for the other. However, I think it makes a lot of sense in the current context for us to say that if you want to, and if you have agreement between the two municipalities, school district and town, you can put those on one ballot for this year will be another possible provision. Just for clarity. Our only goal this entire time will be to offer procedures that we believe will help municipalities be able to conduct these meetings more safely. Safely, the health and safety of voters has always been our priority here. And it remains to be through this spring. And I just will reiterate that. Although I hate to say it and I wish it weren't the case. We're we're in a very similar place that we were at the end of March last year. And I think we need to take similar steps to give municipalities the flexibility to run these meetings safely. And that's what you're talking about. And I appreciate it. And I think I'll leave it there. Thank you so much. Well, I appreciate that. I will give members of the committee a moment to raise hands if they have any questions. But I did want to ask you, do you have one other thing you wanted to add? Sorry, a silly kind of personal follow up. But I apologize if I do seem a little slow. I was up late as maybe many of you were last night watching those proceedings take place. And I hope that you all I don't know if you all realize or know this, but at three thirty when the three electoral votes from Vermont were counted, were what put President-elect Biden and Vice President-elect Harris over the one hundred seventy mark. I thought that was pretty cool. Excellent. Punching above our weight. One question for you, Will, with respect to the meeting of the Joint Fiscal Committee earlier this week, I just wanted to confirm since we have a number of different municipal entities represented here in this meeting that any of the municipal entities who incur an expense related to to safe meeting in in the state of emergency will be able to apply to your office for reimbursement for the cost of mailing ballots? That's my understanding. Yeah, excellent. Hal Colston has a question. Thank you, Madam Chair. I have a similar question. Has there been any thought about a plan B in case the two million dollars doesn't carry us through in terms of covering the cost? Not that I'm aware of rep Colston, although, you know, it's very difficult to say. But I feel pretty good about that number as being able to get us most of the way that we need to be. As Jim said, it really is hard to predict because it's permissive legislation. So you don't know how many municipalities are going to take advantage of it and engage in that ballot mailing. And then it really has to do a lot with, you know, if if my school district moves its election to one date and decides to mail ballots to everybody. But the six towns within it all move their elections to a different date and decide to mail ballots to everybody. That's twice the cost than if those elections had all been moved to a to the same date and they had agreed to send everything together. I think there are a lot of these municipalities around the state. I learned every day about new ones that exist out there that I wasn't aware of that may cover many, many towns. So it's very hard to predict. I think the two million is a is a good safe starting point, though. Chris, thank you. Thank you, Madam Chair. Hello, everybody back from the inauguration across the street, which is is now over. And I just was just catching up on the conversation here. But you mentioned whether that funding would be enough. And if there was a plan B, Will was not at the meeting on Tuesday, but Secretary Condos and I were with the Joint Fiscal Committee. And they did talk about an additional appropriation. If it looks like we're running out of funding. So we plan on keeping everybody apprised on how that's going and to ask for additional funding, if necessary, and it's possible that there's also additional, if there's still CRF monies left over the reallocation of some of that for this purpose. And again, thanks, Chris. Can I add one thing too? That's a good place to add and for me to remember that I think in the in the request for those funds that sort of defines the parameters of them, which is my understanding their use. It's not only postage, but it's also for ballot printing for towns that adopt Australian ballot anew this year. Thank you. Go ahead, John. OK, thank you. Will, two questions. Are you going to put out what kind of communications are you going to put out to alert people about these changes? Because that question was raised this morning and as you just pointed out, there's all sorts of different municipalities and districts. And it's important to get the word out about these changes. Thanks, Rep. Gannon, and that it is important. And it's they're they're banging down my doors to know what the guidance is and what the rules are. And I know they're banging down the doors of VLCT as well. My wife happens to be one of the municipal attorneys at VLCT. So I get that perspective also. But importantly, so it's I have I've told you this all before, I have a very good email list of town clerks and their assistants that I use to communicate with them on a regular basis. And that's the first line of communication. So I will write a detailed memo about whatever passes to all of the town clerks. And there's about three hundred and seventy people on that list that I use after two hundred forty six clerks. The Vermont School Board Association does a lot of guidance to oh, and I see that Sue is on here as well. And I've been in communication with Sue over the last few weeks. We have a meeting when tomorrow, Friday morning, to talk about just this, which is how to coordinate communication out to school districts about whatever comes to pass. The toughest nut in the bunch is those random municipal districts. And I don't have contacts for a lot of them other than the ones I've established over the last couple of months with a number of fire districts, for instance. But we need to figure out a good communication plan to the other underlying municipal districts is what I can tell you. And I will ask the clerks when I email them the bulletin to try to distribute it to any administrators of those districts that that they have contacts for. Thank you. And I have a second question, which goes to if there if a town chooses to delay its town meetings so that it can hold a meeting outside. Are you going to provide any guidance about how to how to hold an outside meeting? Because I know one of my towns attempted to hold outdoor select board meetings without any sort of AV equipment, which led some of the members of the public to be very upset that they couldn't actually hear what was going on at a select board meeting. And I think at an outdoor town meeting, it's going to be even more challenging to make sure everybody can participate and hear and have access that they would if it was an indoor meeting. So, yes, I will. I would take any and all input and and suggestions like like yours right there is a great one to make sure you have good projection of sound and AV equipment available. Thankfully, we'll have some time to do that between now and any outdoor meetings that are held. My general guidance, the language that that I was using last last year was essentially conducted under all of the same rules and procedures that you would conduct it inside. But you're, you know, set up the guardrails, have defined areas for the voting, defined areas for the discussion, you know, where residents and non-residents might be. Do all the things you would do for your indoor floor meeting. But that's your right. It's important to think about the elements that the outdoor will bring that you need to account for. And just to quickly follow up on that, what if, you know, a town schedules an outdoor meeting and it rain or snows? I mean, just total downpour, which would dramatically limit access or maybe even cancel the meeting. Can a town have a rain date? Yes, is the is the short answer. I think those outdoor meetings are most likely going to be floor meetings, right? Not not polling places for an Australian ballot. So in the context of a floor meeting, they're conducted under Robert's rules. And this gives me a good chance to remind folks that that is another standing option for towns right now and districts right now that conduct all of their business from the floor to use some procedural rules under Robert's rules that let you do what they they call adjourn to a time and date certain. And that would be one option in that instance would have two or three voters available who can make that motion to adjourn to a time and date certain because the sky is falling with rain. Otherwise, I will tell you again, and I think in the directive last year, if I look back at it, we did include language that said if you're going to hold your meeting outside, you should have an alternative indoor location available. But I go back and forth on that a little bit because that that made it impossible for some towns to do so, because the whole reason you're doing it outside is maybe your room is too small to meet the ACCD requirements, et cetera. So as soon as we say you need to have that alternative available, it may hamstring some of them. Thank you. Right, I see that Rob LeClaire has a question and I also just want to remind folks that we have about 29 minutes before we need to go back to a joint assembly and we only have our school boards and superintendents entities with us until two o'clock. So I would love to be able to get to them. So Rob, if your question is quick, go for it. And if it's long and involved, maybe we can come back to it this afternoon. Well, you're giving me a lot more credit, Madam Chair, than I think I deserve. I don't usually ask those long questions. Anyway, Will, maybe I missed it, but are we looking to cover any additional expenses communities may incur around coming like going back to the representative from Wilmington's question, if you're going to hold an outdoor meeting, there's obviously going to be additional expenses that you're going to incur to do that. Are we talking about only covering for postage and ballots or any associated costs that they may incur? It's a good question. I was asking it myself this morning among our office. I don't know if Chris wants to chime in if he's still here. But at least my current understanding repliclair is that what governs that is the language and the request that went to joint fiscal. And the way I read that, it's it's limited to mailing costs associated with adopting Australian ballot and or mailing ballots to all voters and the printing of ballots to facilitate moving to Australian ballot and mailing to all voters. I'm not 100 percent sure about that. And I would like to be so and if it is possible to broaden that to allow for those to cover any costs related to COVID response for these meetings, I think that would be an advisable. I would think from a clarification standpoint, that's when we need to be very clear about comfortable. I agree, Madam Chair. Definitely something we can come back to. Thanks for bringing that up. So just so everyone knows, we have invited Chair Webb and Rep Conlon from the Education Committee to be with us for for this part of the discussion. And they can certainly feel welcome to come back later this afternoon as well. But right now what I'd like to do is go to Sue Siglowski, who's going to help us understand some of the unique challenges that school districts of varying configurations are going to have and let us know what your thoughts are on the flexibility that is granted in this bill. Thank you, Madam Chair. My name is Sue Siglowski. I'm the executive director of the Vermont School Boards Association. And thank you for the opportunity to provide testimony on H48. We understand that the General Assembly is on course for an expedited passage of this bill and that you're very focused on health and safety. But in light of the importance of this action to local school officials, we want to ensure that the committee understands the effects of the bill on school districts, especially the provision allowing municipalities to move the date of their 2021 annual meeting. Many school districts, as you know, are now unified districts which cross town lines and they include several towns, as you've heard from other witnesses. I spoke with one school board member this morning from a unified district that includes nine towns. And that board is anticipating the passage of H48. And so it has begun communicating with those nine towns about the plans for its upcoming annual meeting and coordinating with those towns. And so far, six of the nine towns seem to be on board to coordinate with the school district by not changing the date of town meeting. But there are three towns that have not decided how they will proceed. And when I say they're not they're not planning to change the date, they are planning to take advantage of the opportunity to mail ballots to all their registered voters. So if those three towns that are undecided right now decide they're going to move the date of their town meetings, it raises many logistical and legal questions for the school district's annual meeting and so many questions. In fact, that the school board is going to need to have its legal counsel attend its next meeting to ensure that it makes an informed legal decision and also that it prepares its warning properly. So it's definitely a big deal because of the complexities involved with allowing changes to the date of annual meetings. We think it is really important that state officials take the lead with an organized communication strategy and encourage towns and school districts to really work together to align their their dates. Clear, concise and timely communications. And that needs to really start now are critically important so that those officials can consider the implications of the legislation and their preparations for school district annual meetings. And for that reason, the committee may want to consider referencing communications and public information in the law. And with that, I will end my testimony. I know that there are two superintendents lined up to speak right after me. Thank you. So committee members, please raise your hand if you have questions and we'll get to them in between witnesses, but I want to invite Jean Collins to unmute and share her perspective as well. Thank you, Jean, for being with us today. Thank you. I appreciate the opportunity to be with you. I'm Jean Collins, past president of Vermont Superintendents Association and current superintendent in the Rutland Northeast Supervisory Union, one of those merged districts that Sue just spoke of. So I, too, appreciate the opportunity to just share with you some of the logistics challenges for this bill that might need to be worked through. One is the timelines that exist for a school district vote, which are slightly different than the timelines for the municipal vote. For example, our annual meeting is a week earlier, so our numbers start counting a week earlier for our vote. Our boards are finalizing budgets and ballots and warnings by the end of next week. We have a few days, we have probably the week after to get it done for sure, but the timing of when this bill is finalized and the timing of when municipalities might make their decision might not match with what we have to do in order to have our warning completed, our ballots completed and ready to go. What that might lead to is that if towns and I have eight towns in my supervisor union, if one or more of those towns don't choose to use March 2nd as their town meeting day, then I would be running a special election in that town. If my boards, if the timing is such that my boards cannot adjust. And I do know that some of my municipalities are waiting to see what happens with this bill before they make their decision. Only one of my eight towns has told me they've decided to stay with town meeting day. So I have seven other towns who could be different. I'm also a little concerned with the vagueness of the election could be moved to later in 2021. In the world of school budgets, we have to have an approved budget by June 1st, or else there is a formula that tells us how much we have. But that formula is seldom what we think we're asking for. And it will affect our staffing. It will affect our ability to open the school year. If I have eight different dates, that's not likely. But if I had eight different dates of a budget, our charter calls for commingled results. And so I would have to wait to the last possible date to commingle all of our budget results, tabulate all of our budget results. And that, again, could be very late for us having an approved budget that cannot be appealed by June 1st. So the open-endedness of how late the budget vote could be changed to could have a significant impact on school districts. I also agree with the need, if this if this bill passes, as I believe it will, the need to stress from the state level the ability to coordinate and collaborate between municipalities and school districts. Currently, if we run an election the same time as the municipality, then we share resources, meaning people, board of civil authority, tabulators, things like that. If we're running a special election in a small town such as Goshen, we may not have people. We already have a difficult enough time contributing to the municipal side on a regular election. So it's not just the cost of the mailing. There's a cost of a special election and the cost of actually finding the people to run that election potentially across, for me, eight different towns. Again, not likely to be eight, but a few different towns. So I think that that, you know, communication from from well sending from the state, the governor, even about the importance that municipalities and school districts need to collaborate, even if there are separate elections that end up taking place. We need the infrastructure of the municipality to be able to run an election. And if we're running it independently, my hope is that infrastructure could still be in place. I think that's it for me. Thank you. Thank you, Jean. Dave Yance. Hi, everyone, thanks for having me today. I'm Dave Yance, I'm the superintendent of the Mill River Unified Union School District in Rutland County, resident of Arlington, Vermont, which is in Bennington County between Bennington and Manchester. And I serve currently as the president of the Vermont Superintendents Association. I would like to say to the group of you that today was a challenging day to wake up as a public official. And so I just want to acknowledge the work that you do and the burden that you all have in your roles to continue to do good quality work to serve our people well. I'm just grateful for that. I'm glad to be here. Another thing I'd like to share is going after Sue and Jean is a great move on my part because they hit all the high points and I just get to say a few words and scoot away. But essentially I'd like to reinforce the importance of supporting this bill. I completely agree and we agree with the flexibility that is intended in this proposed law. It's important that that flexibility doesn't create complexity that can't be overwhelmed or overcome and that's something that we want to pay really close attention to. I think collaboration between districts, school districts specifically in towns is critically important to make this work. Any signaling that can occur from the highest levels of state government to our school districts and town clerks and communities will be helpful to make sure that it's understood that we're all in this together. I think collaboration and working together on that is important and the timing also really does matter. Just a personal example in my district so we serve four different towns immediately south of Rutland, Vermont and we approved our budget last night as a district. We will be approving our warning middle of next week and our window to issue, our warning begins a week after this weekend so in about a week and a half. So those deadlines are staring us right in the face and while my preliminary conversations with my local town clerks indicate that most everybody's on the same page and leaning in the same direction, the timing of when decisions might be made by a municipality for example, to decide that, well, we wanna move the date. That timing matters because a late move can create chaos for the rest of our systems and how we try to execute those as effectively as possible. So that's all I have to share. I'm grateful for the opportunity and like Jean and Sue, happy to answer any questions you may have. Thanks. Great, thank you. And Rep's web in Conlin, please do jump in with your little blue hand if you have a question. I guess the question that I wanna ask is, and I'll throw this out either to Will or to Tucker. And that is what does underlying statute say about the role of the municipal clerk in helping to administer these school district elections and what do we expect is the potential range of possibilities for collaboration between schools and their member towns? I can help address the first question and I will punt the second question to Will. So the answer to the first question is that it completely depends on what type of district we're dealing with. So for example, the statute say that the district clerk for a town school district is the town clerk. So we can immediately set that one aside. For incorporated school districts, the statutes are far more vague about the relationship between municipal officers and incorporated school district officers. For the union school districts, there are clear divisions between what a district officer is and what a municipal officer is. However, municipal clerks and the board of civil authority do play a role in the delivery and collection of ballots and the municipalities. So the answer is depends on the district. In some cases, it's very ambiguous. And I think in the past, it hasn't been the law that has been guiding the relationship between the districts and their member municipalities. It has been the kind of practical implications of having a single annual meeting date and all of the resources are carried at the municipal level. And that should lead into Will with the second question. Thanks, Tucker. And that is spot on in my understanding of the law also. I think it's important to acknowledge that it was the Singletown School District Statute that came first that said the town clerk shall be the clerk of the school district unless it's otherwise voted. And I would say that as the union school district statutes were being written and put into place, I just had to say they're woefully inadequate in terms of election administration in those union school districts. And particularly the role of the district clerk in that process and the fact that if you just think about it, there is no equivalent body for a union school district to a board of civil authority. There's no group of people who have the authority, who have the responsibility to run elections in the district. And so it becomes this, there's a few references like Tucker mentioned in the ballot processing end of things for union school districts. And actually, if you read it carefully, it's specific to budget votes only. So there's an argument that those only apply in the context of the budget vote itself when ballots are being commingled or not. Actually, it talks about when they're not either. So it's very limited and very vague. And Tucker is correct that it's, I think that underlying section that had clerks be the clerk of the Singletown district sort of followed with the growth of these union districts in some cases where those town clerks who had been doing it for the town school district for years just kept doing it for the union school district too when those came to be. But the situation this year and all the coordination that Gene and David are talking about brings that to a real head, right? Because, and also when you're moving these meetings from floor meetings in a lot of these school districts to balloting, now when you're then also asking the clerk to serve the election administration portion for the school district, you're talking about a much bigger job. You're talking about mailing out ballots and processing them on their way back. This is a big hole and something that's just gonna be tough to overcome but they're gonna have to work together too because I don't think you can legislate it right now. We've been working for two years with Donna Russo Savage from the agency of education to bring a proposal to you all for the union school districts and election administration. But that obviously can't be done in the next two weeks. So chair Copeland answers or whoever asked them, forgetting who asked the question now but what you did, what the range is it's as wide as you can think. There will be clerks who dig their heels in and say I'm not doing anything for that school district but it doesn't say in law that I have to do to those that are already planning on helping and trying to coordinate the process and figure it out. And I would say there are more on the coordination side of things but the absolute range is wide. Rep Webb. Thank you for including us. And well, that was actually very, very helpful as we consider moving forward. We do know that we are not that far from force mergers through Act 46 districts that towns and districts that had trouble working together followed by COVID-19 where they actually in some ways found that they were working better together now that they were merged. I guess what I'm hearing from the superintendents and the school board association is more in line with requests for communication I'm not sure if I'm hearing something specific to language within the bill that you feel that you need or is it really just a matter of communication to bring these folks together? And I guess that's perhaps to Sue. I think it is communication and if there is a way to include some language in the bill to make that clear that would be preferable but if that is not going to happen or even if it does I think it's really important for this communication to occur from the state level and of course our association is very willing to be able to pass that message along and as Will said I'm actually meeting with him tomorrow morning so hoping to cover some of that in our meeting tomorrow. If I may also, if it were possible to ask the municipal board of civil authority to help with the election in the bill, great. But at a minimum the communication from the governor through city of towns and leagues I mean, all the league of cities and towns all the way through would be really important. And then again, I would go back to think about when the end date of this postponed election might be because leaving it open could have significant dire consequences for school districts. Peter Conlon. Thanks, just a quick comment about I think it's important to get a little more clear on the funding and what the money can be used for. I think if a school district you start having to hold a special election because the dates don't line up it's gonna be very helpful to have some money available for that. Absolutely. Other questions from committee members from the perspective of how school budget voting is treated in the bill. Okay, so I do wanna just echo what I hear the school folks saying and that is how important it is for them to be able to rely on the expertise of these local municipal elections officials and our boards of civil authority. And this is a difficult time. We all are feeling the strain of months and months of a pandemic closure and all of the associated adjustments we have to make to how we normally do business in order to ensure people's safety. So I would just ask and hope that schools and towns are able to work together so that if the dates don't line up there will still be that collaboration between the school district and the local elections officials to make sure that the voters can weigh in on their school budgets. So thank you all for being here. Anything back to Sue or Jean or David that you'd like to say before we shift gears? Thank you for listening to us. Absolutely. And RepsWeb and Conlin you are welcome to stick around and you are also welcome to come back and join us since we're a little unsure of what this afternoon's floor schedule is going to be like. We don't know exactly when we'll be back in committee but please do join us if you would like to this afternoon. So at this point I think it probably makes sense to push pause on our consideration of the bill and I apologize to those of you who have been sticking with us all day long but we do have a two o'clock joint assembly to hear an address from the governor and then the house will be back in floor session to debate the passage of a resolution recognizing the terrible events that happened in our nation's capital over the last 24 hours. And so we will get back into committee just as soon as we can. Does anybody have any questions or clarification or announcements before we go back to the joint assembly? All right. Thank you all for your patience and stick with us. We'll be back as soon as we can get off.