Good morning, everyone, and thank you for joining us. My name is Yulia Pamphill. I am the director of the Future of Land and Housing program at New America. It's been nearly a year since Russia launched a full-scale invasion on the territory of Ukraine. And in that time, the Ukrainian military has fought its way to considerable battlefield success and has liberated significant territory near Kiev and in the countries east and south. But now these regions face a long road to recovery, even as Putin continues to bomb critical infrastructure, apartment complexes, and other civilian targets. According to a December 2022 estimate from the World Bank, Ukraine's recovery estimate is projected to cost at least half a trillion dollars. But innovative tools, funding mechanisms, and reconstruction methods can help Ukraine rebuild more efficiently, transparently, and equitably. Further, there's increased political movement in Canada, the United States, and elsewhere in the west to use seized Russian assets to help pay for this reconstruction. Today, we are pleased to host a two-part panel to discuss the question of how to rebuild Ukraine and how to make Russia pay for it. The panel, the event will last 90 minutes. First, we will have a technical discussion with three panelists on the question of how to rebuild using new tools and methods. We'll discuss some of the challenges that the country faces from a land tenure perspective and what can be done. I will introduce those panelists in a moment. Then we will move on to a discussion about how to use new and innovative financing methods to pay for this reconstruction, including a movement to use seized Russian assets to pay for the rebuilding of Ukraine. Before we begin our first panel, we will see a video recorded by one of our panelists, journalist Serena Sbrisky, of footage from around the country over the last year. This will be an approximately five-minute video, after which time we will move into the panel discussion. I'll introduce the panelists in a moment. After about 40 minutes, we will take about 10 minutes for audience Q&A, and then we will move into the fireside chat portion of the event. It will be moderated by New America Vice President, Peter Bergen, and will feature a conversation between Ambassador David Scheffer, former US Ambassador at Large for War Crimes, and now a fellow at the Council for Foreign Relations and the Honorable Senator Ratna Omidvar, Senator for Ontario in the Senate of Canada. Why don't we move into our panel? I will introduce our three panelists, and then we will show the video footage. First, I am so pleased to welcome Serena Sbrisky, reporter for Euromaidan Press, as well as several other outlets who has been living and reporting from Ukraine since the beginning of the war. Next, I will introduce Michael Kolod, who is the CEO of the Peace Coalition, a technologist and also somebody who has been living in Kiev since August, working on a set of really innovative pilot projects to help rebuild towns in Ukraine. And finally, Dennis Nazalov, a lecturer at De Montfort University and a land tenure expert with the Prindex Project, and one of the architects of Ukraine's land legislation. I will go off video. We will watch the video from Serena, and then we will move into our conversation. Thanks Serena for recording and sharing that video. It's very difficult to watch. So why don't we start our conversation and we'll begin with you. You've obviously been traveling widely across Ukraine for the last year and reporting extensively on the conflict. Tell us a little bit about what daily life is like for Ukrainians right now. Well, thank you so much, Julia. Thank you, everybody on the panel and the audience for joining us. It's a very important subject, and I'm glad that we're discussing it now already. It's what we need to be doing. One thing I was thinking when I was looking at the title is that how to rebuild Ukraine. I would rephrase it, I would say, how Ukraine should rebuild itself and how we can make Russia pay for it. So to give Ukraine a little bit more agency and not a little bit more agency in it because that's what Ukraine is fighting for. So first and foremost, I wanna say that I'm an observer, I'm a reporter. And although I've been living here as well, I'm certainly in a somewhat privileged position because at least I can move cities. For instance, my home in Ukraine, my home base is Odessa and I have a lovely little attic there but this attic hasn't had heat because it doesn't have electricity and internet for months now. So I kind of suffered with everybody else for a month and then I moved on and my job, my stories took me around and I was able to stay in some places that had electricity or when you stay in a hotel, you can choose the one with the generator. When you're in Ukraine now, you always look for a cafe or a hotel or wherever you are heading to check for the generator. Even if you look on Airbnb, the real one, not the one that people book to help Ukrainians, it will say generator, light is on. So there's always this just very mundane thing because when you don't have the light early in the morning, it's very hard to get ready. Like say, I was heading to Kiev for a very important meeting. It was a press conference at the office of the president of Ukraine. And I forgot my glasses because it was so dark that I thought that I didn't see anything just because it was dark. And then when I arrived to the train and then in Kiev, I had to walk around without seeing. I don't know how to find the office of the president because I couldn't see my way there. So little things like this are probably the hardest when they continue days on and of course there are way more dramatic and tragic details of everyday life because say if you are in Khruson, and I spend a lot of time in Khruson and Mikhailov, you hear explosions almost every few minutes. Sometimes they just don't stop and people get used to it. So you would be having this surreal conversation in a cafe downtown where people are talking about, I don't know, they're dogs or driving to a desert to see their grandchildren. And in the background, you hear the explosions and you know that somebody is being killed while it's happening, but people get used to it. And that's really eerie. And then of course, coming back to the subject of our discussion, you see as a journalist, I see a lot of destroyed villages, towns, cities, and that is everywhere, south and east, wherever Russians came close, you see it, say in the Khruson Oblast, you can drive for miles and all you see around is this sci-fi apocalyptic movie. And people still leave there, like for instance, there's this Posat-Pakrovsky village close to Khruson. And you can't step off the road because everything is mined and it's very hard to demine. It will take supposedly, according to the prime minister, Dennis Magal, about 10 years to demine it. And Ukraine might be the most mined country in the world, 40% approximately of its territory has been mined, was mined by the Russians.  They didn't have it for months. And you just wonder how is it possible for human beings and animals, there are a lot of stray dogs and cats to leave there, there's no food. Or if you go to Saltovka in Harkov, that just a straight horror movie because there are ruined walls you see inside of the apartments, I think everybody by now have seen this carpets or pianos that somehow mysteriously stay in there. It looks like a theater setting when you look in and you don't see it. And then of course there's the bus in East where scenes are happening right now. So you arrive to the village and it just was hit by Russian missiles.  And that's how Ukraine leaves these days. Thanks, Serena, for that. Just giving us a little bit of context. Dennis, we'll move to you next as Serena describes and as the video shows, of course, the destruction of homes and property is immense and a major component of a reconstruction effort will be rebuilding these homes and getting Ukrainians back into their homes or compensating them for homes that have been destroyed. Last October, you published a report, a needs assessment on the most urgent needs of the Ukrainian government and its citizens in order to protect Ukrainian property rights and facilitate this reconstruction. Can you provide a little bit of background on that report? And the second part of the question to you is, in your view, what progress has the government made since last fall and what challenges remain? Thank you, Yulia. Thank you, Serena, for sharing your experience back in Ukraine. It's really hard to follow your presentation because I live, I'm originally from Mykolaiv City, which is also in the South and currently I'm working with a community of displaced people here in the UK. So that brings a lot of emotions after watching the video. But back to Yulia's question. I was involved in the needs assessment in area of protection of housing and land property rights. And this is area of my expertise for many years. And what we know that any project, infrastructure development, housing, agricultural development project has to deal with rights of those people who possess this property. And what we are facing now is unprecedented scale of reconstruction work that Ukrainian people have already started. But as a part of the need assessment, what we have documented, what we have shown to the audience is that we have a huge disconnect between the ruined capacity of the government institutions in the war-affected areas and the need for protection of these land and housing property rights. So, and the scale of the problem is related to three things. The lack of capacity or scale of problems before the war, Ukraine was going through the reforms before the war. And even before the war, we had only about 40% of property rights being properly registered in the electronic register of property rights. Second, the sheer scale of the damages and lost rights. And third is the destroyed capacity, both physical capacity, but also because many people who work for various institutions, notaries, officers of various government services, they have moved out of the country or become internally displaced people themselves. So all these three components will create a problem or difficulty in starting the reconstruction process. So a set of recommendations that we have developed as a part of the need assessment back in August, September of 2022 was related to establishing the legal framework for how people can reestablish, reclaim their property rights if they lose all their documents or if they're displaced and detached from the property. And also we have highlighted the needs for primary attention to rebuilding the government services in the deoccupied territories. In terms of the progress that was made since the assessment back in September, I would like to highlight that we have restarted discussion of the key piece of legislation, the law on the compensation of losses for land and housing which focuses primarily on the residential housing units. And there were several innovations that were proposed in this law so that people can receive compensation faster. Several issues that we have identified earlier were addressed in the revised proposal, however not all of them. Some of the key issues related to large scale compensation or portfolio compensation of rights related to other properties than housing units related to procedures of outcourt resolution of disputes are yet not addressed and that's something that need to be yet developed with the legislation. But also we have mentioned previously and now we can see it with the recent surveys that there is a huge need in supporting individuals who lost their property or have their property damaged, particularly because these people are moved away from the area where they have their property. The recent survey that was just published few days ago by a rating group shows that more than 10% of property around Ukraine is destroyed and damaged. However, only about 30% of people have actually took any steps to claim the reimbursement or claim support in restitution of their property rights. So if this issue is not addressed urgently, if we do not support these individuals on how they can claim the existing rights, this problem may slow down the reconstruction process. And finally, and I think that would be a nice transition to what Michael is going to present, we start seeing several very powerful pilot projects all around the country of how local governments and international institutions start working together on developing and starting implementing the reconstruction plans for some destroyed cities. I just have attended a meeting today with the groups that are working on reconstruction of hierarchy and micro-life where pretty much the same issues that Michael is going to talk about are discussed, but with application to large cities and some of the most destroyed people. So I would probably pass the floor to Yulia and Michael to talk about the details of this process. Thanks so much, Dennis. And thank you for mentioning that survey. We can send it around to the audience after this webinar as well as really highlighting the importance of getting the word out to displaced people about what they can be and should be doing now to make sure that they're able to reclaim their property once this conflict ends or receive compensation. So with that, I'd like to pass it to Michael. Michael, you have been in Kiev since August. Tell us a little bit about what you are seeing in terms of the largest needs for reconstruction in Ukraine and what is the peace coalition doing about it? Sure. Well, thanks Yulia. Well, first I wanna thank Zarina and Dennis for doing such a great job setting me up. I hardly have anything to talk about which is something new for me. Yulia, Tim, Peter, thanks for a new America. Thanks for hosting such a great event and thank you everybody out there for attending. So as Yulia mentioned, I've been in Kiev now for almost seven months since early August. And as Zarina and Dennis have already pointed out, the rebuilding of Ukraine is gonna be a long and complicated process. And that's to kind of put it mildly, right? But that doesn't mean that there aren't ways to make the process shorter and simpler, right? As you mentioned, Yulia, it's gonna be dreadfully expensive to rebuild Ukraine. I mean, I've seen estimates anywhere from 349 billion by the World Bank to 1.1 trillion from the European Investment Bank. So, I mean, those are big numbers, right? But that doesn't mean that Western taxpayers and supporters of Ukraine are gonna need to fill the bill, okay? So if I was to kind of qualify, what is the biggest problem right now in terms of rebuilding Ukraine? On the ground in Ukraine, I would say it's a lack of belief that it's actually going to happen. There has been an unbelievable outpouring of support from the West in terms of military aid and humanitarian aid and things like this for the population and people being displaced and taken into homes in Poland and across Europe and the UK and in Canada and everywhere else around the world. But there hasn't been as much attention focused on the idea of compensation, restitution and rebuilding. And this is, so what this is leading to is kind of a lack of belief. And this is something that is, I would say primarily focused on the kind of resident population of Ukraine. So it was funny, not funny, but I mean, I noticed in one of the videos that's arena played, she visited Borjanka. And I visited in August, my colleagues and I visited the same building that she showed. It's one of these, and it's kind of a sadly a common sight, but it's one of these large Soviet blocks where there's literally two pieces of the building left and the middle of it was bombed right out of it. A Russian aircraft dropped the bomb right in the middle of this civilian apartment building. 350 people lived in the building, 30 people die in the basement and this happened in March of last year. And so we visited in August. So this was about six months after the building was literally rendered uninhabitable and nothing had changed. The building hadn't even been torn down, the site hadn't even been touched. Some of the residents, one of the residents we talked to Alexander is kind of become a bit of an activist in Borjanka and he's trying to advocate for, getting the building at least torn down so they could start reconstruction, nothing. Some of the residents in this time, it was 35 degrees Celsius outside and they were living in a temporary shelter, these box shelters that were built in the football stadium in Borjanka. It was too hot to be in the structure in the summer and it was going to be uninsulated in the winter. And we are now a year almost later, Yulia and nothing has happened at this building in Borjanka. So, there's this lack of belief amongst the people and there are reasons for it, most notably the fact that the government of Ukraine doesn't have the money to start a large scale reconstruction process. Okay, and this is something that we're gonna address the Senator and the Ambassador and Peter are gonna address in the next section. But because of the, I guess the peculiarities of whatever of international law, when you set out a compensation program for the people of Ukraine whose houses have been damaged or destroyed or as part of this process, the technicality is they're filing claims against the government of Ukraine. And then it's incumbent upon the government of Ukraine to put those claims together and take them and file them against the International Criminal Court. So, there's a challenge in trying to reconcile giving people hope that their homes are going to be rebuilt and giving them false hope because they don't have the money to actually start the process. So, this is basically ground everything to a bit of a halt when it comes to the rebuilding process. And where you do see, you know, kind of areas of light across the country are in projects like the one that Dennis was talking about in Mikhailayev where these are externally funded initiatives to take on the rebuilding of a particular area, a particular place. And so what we kind of did is, you know, we didn't want to take on a huge project but we realized there's so many different aspects of this challenge. You know, Yulia, you need to, we need to get people back to Ukraine as soon as possible, okay? From wherever they're internally displaced or externally displaced. And in order to do that, we need to, there needs to be a more efficient and say, let's just say efficient process for claiming for damages, okay? And then once you've got a lot of claims filed, you need to have the money to pay for those claims. And when you have the money to pay for those claims, you have to make sure that it gets deployed inside the country in a way where you get as much as transparent and as efficient use of that money. You know, a couple of weeks ago, I think everybody here probably will have seen there was a big kind of anti-corruption, you know, kind of operation happened in Ukraine because it is a challenge in a lot of these former Soviet bloc republics is internal levels of corruption and bureaucracy that just grind processes to a halt. So you have to think about a way that, okay, if we get the money and we get it quickly and we get the people back in quickly, can we deploy it quickly? So there's just a whole bunch of problems. And, you know, so what we did is we put together a pilot project to address all of these problems. We're gonna rebuild two villages outside of Kiev, places that Zarina mentioned nobody's heard of. One's called Andreevka and one is called Kozarevichi. They're both within the Kiev oblast. You can drive there to both of them in about 30 minutes. And the goal is to test the whole thing. Let's do efficient claims. Let's get the money in, let's deploy it. Let's build new villages, da-da-da-da-da and prove on a process that can hopefully scale across the country. And it's just to put some practical application to a lot of the policy and good work that people like Dennis and Zarina and, you know, the senator and the ambassador and you and Tim and everybody do on a daily basis. So that's basically it in a nutshell. Thanks, Michael.  Dennis began to speak about and then Michael elaborated on these pilot efforts to, you know, to borrow the term, build back better, to build the country back better socially, economically, politically using innovative tools. And I'm curious, Zarina and Dennis, what would this look like and what are the most promising approaches that you have seen thus far? Oh, you're on mute, Zarina. I will jump in and I don't know if we're supposed to have just flowing straightforward discussion or we can argue a little bit because from everything I've seen, I have slightly disagree about the disbelief because wherever I go, I see Ukrainians just starting to build back, you know, they are still being bombed and I see them and I hear the sound of construction and I've seen a lot of buildings being restored all around the country. And that includes Michael Ive, by the way, they're going really, really fast there, Dennis. And on Borodianca, I spoke to a lot of locals and they had, this is just how complex it is. There were a bunch of people and they were at the time when I was there, there were some posters outside on the balconies that survived saying that we want to stay. We don't want to have this building being completely demolished. We want them to kind of like building between these two things, which is kind of like to layman, it seems absurd, but this is their homes. I went inside with a woman who grew up in the apartment on the sixth floor and it's emotional for her. She doesn't want this building to be demolished. So it's not that straightforward, it's psychological. And lastly, I don't know if I agree that right now the goal number one is to get people who fled to Europe to come back. Like, come on, just today, when Putin was making his quote unquote speech mumbling something about how the West started the war, whatever, they've hit her son with 20 guards, killing six people and a friend of mine is there right now and he just sent me a picture. I was distracted because I got a picture of literally, and forgive me for being graphic, puddles of blood on her son pavement. So I disagree about the need for people to come back until we as the collective West help to close the sky over Ukraine. I personally don't want anybody to come back. I've seen too many lives being destroyed. So that's, and again, we can debate. It's not, it's just my opinion. I never stand, you know, say that that's the last and written in stone, but that's what I think and feel as for the innovative ways of restoring it. I had a very inspiring conversation with the mayor of Mikhailov, Mr. Sinkovich, who is a very, very impressive mayor. I've talked to a lot of mayors and compared to what they do and everybody has something to offer, but Mr. Sinkovich's background is in high tech. So he's very excited about bringing in innovation. And last time I spoke to him three weeks ago, so for an interview and you can watch the whole interview on the channel, I can share the link later. And he was talking about using DEA, which for those who don't know is a very unique digital electronic database program that pretty much covers every aspect of life in Ukraine. It's very advanced, like you can sit at home on your bed and do banking, get your passport, get married, I hear. I haven't tried, but you know, there are all kinds of things available that for us sometimes borderline privacy, like they are aiming for an electronic passport, which I know in many countries I know go for many reasons. So Mr. Sinkovich got together with the Minister of Digital Transformation, Mihaila Fyodorov, who several months ago was telling me all about DEA and it is very advanced. And they are going to use it in order to register the loss of property and have this electronic documents. And I'm not gonna go into every detail because A, I don't know every detail and B, it's better when you hear it from Mr. Sinkovich, which you can, it's in an interview, but it's out there. They also are using the GIS system he was telling me about and it's for those who do not know it's a geographical information system and they geographic information system. And supposedly according to Mr. Sinkovich, they have the best one in the country. It was built before the war in 2000, well, before the full scale invasion. I don't think we'll have mentioned that yet, but I think we should that the war started in 2014, which we have now is a full scale invasion which started about a year ago on the 24th of February of 2022. But the war was going on for almost nine years, three days short of nine years by now. So that geographic information system was built in 2016. And it's a multi-layered system and those layers would include pipelines, the land, the real estate. And now during the war with cooperation with the Keith Economic School and Dennis, you might have heard about it, they have added a new layer for distractions. And so based on that, they make estimates for the amount of money needed for restoration of the destroyed objects of infrastructure, real estate, and they mark it on the map and then they add ground and satellite, marks our images and also drone images. And they, I understand, have the help from the government of Denver, which sponsors some additional work. And so this way they were able to come up with an estimated preliminary sum of losses, which I believe is about 900 million euros according to Mr. Sinkavich. So this is definitely innovative in one way of looking at it. And as for the source of money, I was just talking to Mr. Anders Aslund, who is the former senior fellow on the Atlantic Council. And he was telling me that the reasons for which the various ministries of justice and finance and Western banks are reluctant to freeze or to use the Russian assets, the Russian central bank assets and the Russian oligarchs frozen assets, which amount to 19 billion in Switzerland only are not satisfactory. But I also heard that Switzerland actually did freeze this money and is willing to find the way and find the legislative mechanism to transfer this money for the restoration and reconstruction of Ukraine. So this is the way to go. And also in the Atlantic Council recently about a month ago, so there was an interesting article by a Ukrainian businessman who's in charge of some agricultural sector. I think he's a private businessman though, who was talking about establishing a financial corridor which will be kind of similar to this grain initiative where there was a grain corridor where with a special help and the way the loans would be built. And it's a very interesting article. I just recommend for those who are interested to look it up because it seems to be offering some good ways of doing it. Yeah, so let me follow up, Zarina. I agree with you on several points, particularly about refugees. And that's the advice that the Ukrainian government was provided. And that's what we are trying to explain to refugees that it's bad to stay in a safe place until it is safe to return. But what is important is that many of these people, about 30%, that's what we see from the surveys, about 30% of the refugees internal and external have no place to return. Right, and until the... But the only reason why these people are actually coming back, many of them are coming back and then returning again to a safe place is the questions about the property that they left behind. They worry about whether it is safe. They are not sure how to claim the damages when this reconstruction process is started. They all fear about losing their rights to their housing, to their land and so on. And again, referring to the survey, about 2% of people have already started the reconstruction, not waiting for the government, not waiting for the international aid. They're doing what they can do. They patch the windows, they patch the roofs, they clean the yards. The life is going on in the areas that are on the front line, no matter what. Regarding DEA, one point that I would like to mention, DEA was one of the first applications, the first tools that people can use to claim the damages and lost property. Within few days after the war started, this application was upgraded and enabled people to actually document the damages and upload some of the photo evidence of the destruction. And most of this information is now transferred to the state registry of damages. The final point is that with the pilot projects similar to Michael's and several other, one thing that becomes clear, we would need to have a very different approach to the rebuilding of areas far away from the front line with single buildings or pieces of infrastructure being destroyed and cities like Bakhmut, like Lysichansk, and unfortunately, many other places like that where close to 90% of all structures are destroyed, where people have lost everything, which places which are not livable, even though there are people who stay in these cities. So I think what we see now, there are ideas and solutions to these places that have smaller scale destruction, but we yet have to rethink how to deal with the places that are unlivable and we don't know when people will be able to return to any sort of normal life in these places. Yeah, I agree. And I've seen those places. I've seen the cities like I mentioned before that they were completely burned out and nothing is left. But one thing I forgot to mention also with Dia, and this is something in regards to what you were saying, Michael, is the corruption issue. Mr. Sinkiewicz told me, I wasn't convinced, but that's what he told me, that Dia will help to handle this corruption issue because computers don't take bribes, which is true. But then computers are run by people, but they believe Mr. Ferdorov and Mr. Sinkiewicz, they know better than I do. I think that this will help to bring some objectivity to the project. Thanks, Dennis and Zarina. We will, I will ask one more question and then we'll move on to a little bit of audience Q&A. To those in the audience, please feel free to drop any questions that you have. And I'm already seeing a few being populated. So this question, this last question is to all three panelists, we've spent a lot of time talking about destroyed homes and property, but of course a major issue is civilian infrastructure and Zarina, as you alluded to in your opening remarks, just basic, the provision of basic necessities. So in your view, what's needed to get Ukraine's civilian infrastructure back up and running? I'll take a first shot at that one, Yulia, if you don't mind. You know, at the end of the day, right, it was the damage of destruction in a lot of the villages and towns and cities around Ukraine was in certain respects intentional and also indiscriminate, right? I mean, artillery will hit one building and another and another. And so when you're talking about rebuilding anything, a neighborhood, a city, a village, it's not just the houses that people live in. It's the schools that their children go to. It's the clinics that they have to go to to see a doctor. It's the local administration buildings that they need to go to, to get their permits or do whatever they do. It's the small businesses that employ them. So Andriyvka and Kozarovici have some, some kind of agricultural-based businesses. There was a furniture manufacturer in Kozarovici where the owner was just taken away by the Russians. And so, I think that if we're going to rebuild these places everywhere in Ukraine, it has to be from a holistic view of how do you plan, take the opportunity to not just put new roofs on and put nails and windows and things, but to replan these villages as part of a greater, kind of a regional effort to consolidate things like medical services and education and healthcare and employment and all of these things in a better way than they were before. Just, you know, we've got an opportunity to do it. Let's think about it in a second. Let's plan it so that the people can come back have a roof over their head, a school for their kids to go to and a job and a store for them to buy their groceries up. I would second, Michael, and that's exactly what we can and we should start doing yesterday, in fact. Because the question is not just to rebuild, but to rebuild better, more efficient. We can talk about the reconstruction of isolated buildings, but also using the modern technologies, using better isolation, making the houses more energy efficient and self-sufficient to the extent, but with the largest city, the starting point is really this holistic approach that Michael is talking about, starting with the master plan, talking about rebuilding the cities that are more attractive to people which are more ecological for people who live there with better transportation, with better and more accessible green spaces and so on and so forth. So I think currently at this stage of development, globally we have a lot of knowledge and skills developed for urban planning and all these skills are currently necessary to start working with small villages like near Kiev or larger cities like Kharkiv and Mykolaev, but the starting point is pretty much the same. We start developing these master plans that would make the cities better, more attractive, but also will preserve the heritage of those cities that make those cities unique and attractive to their citizens. And I completely agree with the previous speakers and I want to add that this discussion wouldn't be complete if we didn't look, and you said it Dennis, the keyword ecological at the whole environment, we can't take just reconstruction and forget about the nature around it. And I'm not even talking, we've mentioned that, restoring the energy infrastructure, water pipelines or gas pipelines which are being heat deliberately by the Russians and destroyed, like in many cities, they've done it because that's their policy of terror. They want people to be demoralized and surrender because of difficult living conditions. There's even a word for it now, Holodomor as opposed to Golodomor, which I understand hard to catch for known Ukrainian speaker, but there is a death by a hunger, which of course was engineered by Stalin. And now there's death by cold, which is an attempt of being engineered by Putin. So just like in Odessa, it was like almost unlivable where I was staying. And of course in other areas, it's even harder. But also there is an issue of the whole environment. And we're talking about fires close to Chernobyl or Zaporizhia nuclear power plants where the nuclear waste are being stored. So that already presents an issue. The rivers that a spillage are happening on a big scale like in Mikhailov, the oil deeper was heat and the oil covered the river with a thin film. And then a lot of fish died because they didn't have enough oxygen. Or in the Black Sea, there were thousands of dead dolphins cast upon the sea. And that's also because of the mines, because of the acoustic interferences from the Russian submarines and radars and also because of the pollution. So I can go on as you can tell forever, but it's air, it's water, it's the soil that is heavily mined, as I have mentioned. So we need to think about it holistically as everybody here is bringing up. Just adding a small point to what Zarina is saying, just think about the amount of the rubbish or the debris from all this destroyed building. We have to develop ways to reprocess it or safely remove it from the cities so that people can start rebuilding. Absolutely, I did the story at the Hirson dump, city dump. I'm not gonna go into that, but it's an issue. So I'll ask one last question again to all three panelists, just a quick last question from the audience. And then we will move on to the fireside chat. And the question is you all have mentioned the large numbers of displaced persons, either inside or outside the country. What should those people be doing now to ensure that when the time comes, they can come home and they can get back into their homes and prove that those homes are in fact theirs or that they're eligible for compensation for any homes that have been destroyed? If I could jump in first on that one, I'm gonna say it's kind of simple, but and something that maybe a lot of people aren't, isn't in their mind is gather all and any evidence you have. You need to gather any evidence you have. If you've got pictures on your phone, don't delete them to clear up space to take pictures of where you are.  If you've got online bill payments, keep all of that. If you've got documents, passports, drivers licenses, land titles, take pictures of them, store them, keep any evidence that you have of your existence in Ukraine, especially as it relates to your personal and your family identity and your personal and your family location, like where you lived, get all of that together and be ready to submit it, but get as much of it as you can. If I may follow up, I think the key point is not to wait until it is safe to return. There are actions that must be taken now and yesterday. First step, as Michael said, to make sure that you have these records, but also there is an online process, how people can check for whether their existing rights are properly registered. And if not, to start the registration process, no matter whether your property is damaged or not, better not, but to make sure that your rights are properly documented and secured by government, that's the first point in this process. Later on, when the property is destroyed, when the documents are lost, it becomes way more difficult to restore the property rights. Thank you, Dennis and Michael. Zarina, any last words from you, either on this question or just any wrap up party words? I'm not in a position, I don't handle this aspect. I report, I did see people reporting what they have lost. And some of them just go to the police station, like in Kerson, I've seen people doing that and actually was helping with that, but I don't have any practical advice on that. My major thing is what Dennis said, just I guess hard as it is, perhaps it's better to wait out. I know victory is coming, I know it's coming soon, but it is probably safer, especially if you have children. Right now, it is deceptive safety, even in Kiev where it seems very, very normal, but I wouldn't, especially if you have people dependent on you. I would think about it and check about it before returning back said, as it is to say that. And I just want to thank everybody to have an interest in that because of course as a person who sees this destruction on a daily basis, I'm very invested in seeing some positive changes. And I want to keep this discussion as positive as it has been. There are solutions, there are people who want to help, there are very capable mayors I've been talking to all over Ukraine, and not just mayors, but the governments, and I'm very, very inspired by Ukrainian people and by everyday life, I see people, you know, one, that's what I'll finish with. My favorite pictures that I took in all my almost year in the war on Ukraine is the picture of a lady who is gardening with the background of the black sky because the oil depot was just being blown, you know, there's big explosion, and she's gardening and taking care of her property. And that's what I've been seeing everywhere. I just didn't take as good pictures as this came out. And that gives me a hope. I know that Ukraine will be restored. I just see it in people. And that will be my closing statement for that. Thank you. Thank you, Zarina. What a wonderful way to close this panel. I would like to thank our panelists, Zarina, Dennis, Michael, and turn it over and introduce my colleague, Peter Bergen, who will take us through the fireside chat. Peter is a man who needs no introduction, but I will briefly introduce him anyway. Peter is a vice president at New America, where he is the vice president for global studies and fellows. He's also CNN's national security analyst and a professor of practice at Arizona State University, where he co-directs the Center on the Future of War. Peter is the author and editor of 10 books, three of which were New York Times bestsellers. I can go on. Peter, I will turn it over to you to kick us off for the fireside chat. Thank you, Julia. Thank you, everybody, on the previous panel. We all learned a lot. So I'm gonna introduce our two next panelists, both of whom are real experts on the issue at hand. The first is Senator Ratna Omidvar from Canada, who was appointed to the Senate in Canada as an independent senator representing Ontario in 2016. She's the chair of the Standing Senate Committee on Social Affairs, Science, and Technology. She served as a deputy chair of the Special Senate Committee on the Charitable Sector. And she's the vice president of the Canada-Germany Parliamentary Group. She moved to Canada from Iran in 1981 and is a well-known internationally recognized voice on diversity, migration, and inclusion. And our other panelist is Ambassador David Sheffer, who is a colleague of mine at Arizona State University. But he was the first ambassador, U.S. ambassador for war crimes in the Clinton administration. He's been involved in all sorts of war crimes, tribunals, including the Special Court for Sierra Leone, of the Khmer Rouge Tribunal. He negotiated the creation of the International Criminal Tribunals for the former Yugoslavia and Rwanda. And he has written books on this subject. He's presently a senior fellow of the Council on Foreign Relations. So let me start with you, Ambassador Sheffer, just to kind of give us a broad overview of the question of, I mean, you know better than everybody that there have been relatively few successful prosecutions at the International Criminal Court. Even in the case of Bosnia, there were about 91 successful prosecutions despite all the many, many, many thousands of war crimes that were committed, which is not to say that the enterprise wasn't worth doing, obviously. But how do you get funds for reconstruction? How has it happened in the past? How have funds been recovered? Have there been successful examples of restitution for these kinds of crimes that go beyond simply a guilty conviction in a court? Thank you so much, Peter. It's a great pleasure to be with the Senator and you on this panel. Well, first, I think it should be understood that there is a paucity, a lack of actually acquiring reparations as a result of criminal prosecutions. Even those in leadership circles who have been the primary objects of prosecution of the war crimes tribunals for the last 30 years, even if they have independent wealth squirreled away somewhere, very rarely is the tribunal in a position to actually identify that wealth and seize it. In fact, it's been almost impossible to do so. There's been a long struggle, I think, at the International Criminal Court to explore how to ramp up their ability to deal with assets of suspects and defendants particularly, in terms of how to identify them, where to track them down and try to seize them for the purpose of part of the sentencing of the individual if the individual is convicted. So there's a real lack there. I think the most successful process was actually the UN Compensation Commission that was set up after Saddam Hussein's invasion of Kuwait back in 1990. And that process was very much aimed at seizing or having control of Iraqi assets and of Iraqi oil wealth in order to pay claims that Kuwait had against Iraq. So that was not a criminal court procedure that was rather a negotiated political process but mandated by the UN Security Council, which of course helps. And it was fairly successful in actually acquiring the necessary funds from Iraq to rebuild Kuwait. Ukraine is on a scale far in excess of Kuwait. I mean, the destruction in Ukraine is unprecedented essentially in terms of property destruction as well as the claims that families of those who have been killed, civilians who have been killed would have. So I do think that ultimately we need to be looking at a process which provides the necessary financing without necessarily requiring criminal convictions in a criminal court against individuals but also may not necessarily require judgments from, shall we say the International Court of Justice against Russia as a state for responsibility for reparations. Those are ideal outcomes. And if we get them, that's tremendous because that undergirds national procedures to freeze assets, apply them in the interest of victims and the restoration of Ukraine. Those kinds of convictions or judgments are tremendous foundational stones legally for that process. But we also have to be looking at options that may not necessarily have the benefit of criminal convictions or of state judgments and how we can ensure that some of these funds can actually ultimate or that funding can actually be raised. And I know that the Senator will want to speak to how Canada has been at the forefront of legislating under law the seizure of assets so that ultimately through judicial action those assets can be made available without there necessarily being a finding of criminal culpability or of state responsibility. Well, Senator, you've been instrumental in moving forward this legislation that the ambassador referred to and part of it is seizing the assets of Roman Abramovich. Many people may know he used to own the Chelsea Football Club before the invasion of Ukraine, but a very well-known figure in the UK. So tell us about how that came about and what your larger intention is here also in terms of providing some kind of roadmap for other countries to do this kind of thing. Thank you, Peter. And I can't but help agree with the caution that Ambassador Shaffer has raised around the seizing of assets. My proposal, which was actually I began to think about it in 2017 and tabled it in the Senate in 2019 way before Ukraine was on the horizon linked my concern around corruption and what I saw as its inevitable linkages with this governance and displacement. So I know in Canada has a list of sanctioned assets and we have the names of those who are sanctioned but we don't know how much money is in the institutions where their assets are held. So I proposed a bill whereby Canada would be able to hold corrupt foreign officials to account based on the fact that they are guilty of or they have committed human rights abuses and created mass force displacement to account for their misdeeds but also to provide some restitution to the victims of their crimes. So frozen money and lots of jurisdictions have frozen money through Magnitsky sanctions and others but I will submit to you that frozen money is dead money. It is no good to the victims and this was a lever that I used to sort of free up those assets and put them to use where they are most needed. My bill in Canada had cross-party support but it was a private bill. It was not supported by the government so its passage to approval would have been very long and rather complicated. But then in 2021, of course, we all know 2022, sorry, Russia invaded Ukraine and the government of Canada adopted this bill as one of the many, many measures that Canada was going to provide to help Ukraine and I wanna state once again how very supportive Canadians are of helping the Ukrainian people regain their land and their freedom. So the invasion of Ukraine changed everything. The bill that I proposed and the government has adopted does not go through criminal court, does not require a criminal conviction in a criminal court. It is a uniquely political tool in a way because it is the government of Canada and in other cases it will be other governments who decide on the basis of evidence that they have access to on petitions made by civil society organizations that the assets of a certain individual or a certain state entity because that is possible under our law can be seized and repurposed to help the victims. Our government is silent on how they will actually repurpose with what accountability with transparency. There's some judicial process built in, but not to the extent that I had provided for in my bill. So I look forward to how the government of Canada is going to action the repurposing of Roman Abramovich's assets, $26 million is not a lot of money, but it can make for an important case study of how to do it and to do it right. The government of Canada and I recognize that Canada is not the place where most of this corrupt money is parked. Most of it is parked in the UK, in the EU and possibly the US. And Canada's motivation is to lead as a middle power, take some risk where others may not be able to take so that others follow our footsteps. And already we are seeing interest in the idea in the UK which is interested in the state-held assets of Russia in the EU, which is discussing a version of this intervention at the EU parliamentary level. And the US has already passed a law, perhaps Ambassador Sheffer can enlighten us about this. And of course, in 2016, the Swiss passed a law. There is history to this. The Swiss have a very similar law. They have already repurposed billions of dollars of assets and I can provide some examples if the time permits. Thank you. So Ambassador, what is the US done that's new on this issue? Yes, the US at the end of the last year the Senate adopted a law that does open up the window for freezing assets ultimately for use in reparative rebuilding initiatives in Ukraine. And that was part of the large appropriations bill that was finally adopted in the early part of January. But we need to see actually just as Senator Omudvar mentioned with respect to Canada, there's a lot of logistical and procedural issues that swirl around this law as to how far it can be taken by for example, the Justice Department to actually not only block those assets but allocate them towards specific objectives and what the courts will actually require before that can be accomplished. I think it's tremendously strengthening that there's now a federal law on the books because that's a great gateway in the courts to actually make this happen. In the absence of it, there were a host of legal issues that would dissuade one from seeking to do that in the United States in part because and there are so many arguments but one of them would be, would you have to prove in the court that the United States is at war with Russia over Ukraine because that would open up a gateway clearly for the use of frozen assets? The United States, I don't think would wanna go into the courtroom and literally claim that they are at war with Russia. So this law provides a much better foundation to work these arguments in the courtroom. We don't have any test case yet but the fact that the laws on the books I think very much inspired by the fact that our neighbors in Canada under the senators leadership did adopt such a law very much influenced by that precedent is good news in the United States. Ambassador, you've advocated for the use of social bonds to address war crimes. Can you tell the audience a bit about what those bonds are and how they might be applied to the Russian case in Ukraine? Social bonds to put it most simply are bonds which seek to achieve a social purpose as opposed to a commercial profit making purpose which so many bonds do seek to do. But in this case, this social bond is somewhat similar to our familiar notion of a municipal bond. You put a municipal bond out in order to build the sewer system in your community. It's gonna require a lot of money up front. And so you do that but then the government the local government pledges to repay that bond the principal and interest for those who invest in the bond. So it's a governmental liability so to speak but a social bond is a much broader concept whereby you look at a particular social priority whether it be the environment which is where some social bonds we call them green bonds at the time and still do started to emerge around 2010, et cetera to look at a particular problem. And when the COVID-19 pandemic occurred there was need for an enormous amount of funds to cover the contingencies and the realities of the COVID crisis. And it jumped started the social bond market particularly in Europe and even in Asia as well with the Asian banks. So that social bond is grounded on the fact that the investors in the bond believe in the social purpose. And they are prepared to put their money up front provided one and possibly two things happen. One that there's a good sovereign guarantee of the bond so that they know that 10, 20, 25 years from now they will get their principal back. That's important. Social investors are investors, private investors who believe in the social purpose. They're ready to commit to the social purpose of the bond but in addition to that they might sometimes want an additional incentive or not incentive but they may accept an additional requirement in the social bond which again is tied to the social objective which is take a slightly lower interest rate on your bond and we will use the differential for the good of the social purpose. Take the lower interest rate and ultimately you will still get your principal back but the total amount of interest that you get back on the bond may be less than what would actually be earned on a typical conventional commercial bond but because you have a conscience you have a social conscience you as an investor are prepared to have a slight discount on your profit in order to facilitate that but let me just say the great objective here is for governments not to be burdened in a crisis situation with an enormous amount of money that has to be raised quickly and they simply cannot do it in their own national budgetary procedures and processes it's not possible. So you go to the private market to raise that money but the governments are involved and sometimes in a contingent liability basis to guarantee it and then we work out how that's actually paid out 10, 20, 25 years in the future. I think we'll also be talking Peter though about since the guarantee would be a collateral it might also be that these frozen assets ultimately could be considered collateral as well for these bonds. Senator, what do you make of that proposal? I think we have to look at ways of bringing private money into this conversation. Absolutely, the rebuilding of Ukraine estimated at $1 trillion is not gonna come from the tax coffers of a collective of nation states. I do think inserting the social bond concept into a conversation about asset seizure and repurposing adds another layer of complexity. Both the conversations have layers of complexity. You know, on the asset seizure side there's transparency, accountability, due process, the law, all of that. And on the social bond side there's guarantees, payments, contingent liabilities but I think in this case two plus two may well make four. And I put that out for a couple of reasons and I'm gonna extend the conversation not just generally to social bonds but more particularly to social impact bonds where the payout or the liquidation or the payout to the investors is contingent upon the delivery of a certain objective. It's easiest imagined in the context of Ukraine particularly with reconstruction of buildings, schools, infrastructures, infrastructure grids, et cetera, et cetera. And the investor gets paid at a certain point where there is enough proof that the project is either 75% completed or about to be completed. And then the government would be called on to provide the investor and therefore maybe liquidate the frozen assets. So I think there is a real possibility for a reason that I appreciate perhaps more because I was part of crafting this law and that is the reason of accountability. No government will want to take frozen assets, seize them and repurpose them without providing accountability for the public good that they are providing to the victims. This is an incredibly sensitive point. Canada has already once repurposed assets back to Libya at the request of the Libyan government. Mama Gaddafi had billions of dollars of assets worth in Canada. We repurposed them in good faith and we don't know what happened to that money. We all know that Libya is not exactly the most stable of countries and that money could have been used. So I think this is an opportunity of bringing two different conversations together and creating a movement possibly predicated in Canada because we're closest out of the gate based on the $26 million of Roman Abramovich and tying that money to a social impact bond where the $26 million is used by the government to back its contingent liability for the reconstruction of Ukraine. I'm thinking about it in a very practical, pragmatic sense. Proof of concept would be necessary here. So potentially using seized funds as a collateral for these social bonds? Yes. So the Libyan example is interesting. So Gaddafi had billions of dollars in Canada which Canada seized and then repurposed but then the money disappeared or what happened? We froze the money. We didn't seize it. On the request of the new Libyan government, it's their money, we released it back without any conditions. And at the same time, there are calls on Canada as part of the World Order to help Ukraine, to help the Ukrainian people, to help the Libyan refugees. And we ask ourselves, what happened to that money? You know, in an interesting way, Peter, I might just add, Senator Omenbar has inspired me to leap to the following statement which is that at the end of the day, one, if the frozen assets can be repurposed and that's the challenge of course, if they can be repurposed so that it is those funds which are actually allocated towards payment of the reconstruction requirements, then the sole investor is Abramovich. He becomes the social investor against his will but we can honor him as the social investor in the use of his funds through the procedure that the Senator has opened up in Canada. I'm sure you'll feel very good about that.  You may have seen the New York Times just a few days ago, it was a big story. It was the world's largest construction site. It was the title of the piece but essentially, you know, making the point that there's a lot of opportunities here that people are beginning to look at. So what's needed from, I'll start with the Senator from governments, donors, nonprofits, private sector to help support the recovery whenever that is. Well, I think we need to think of a 2023, 2024, 2025 Marshall Plan, call it what you may but that was the initiative where various nation states and private sector companies and civil societies put the heads together to rebuild Germany after the war and I think that's a model we need to consider as we engage in these conversations about reparations to Ukraine. And I think the other essential part of this is the official reparations from the state of Russia to Ukraine for the mayhem and devastation that it has caused. There is history, the world history tells us how invading states are dealt with. The ambassador gave an example of Iraq. There are other examples in history. So a mixing and mingling of reparations from Russia plus the investments of nation states, private investors and civil societies to rebuild Ukraine. We should begin to have that conversation right now. The question of reparations is an interesting one because of course the Treaty of Versailles imposed very onerous reparations on the Germans so much so that you could make at least a partial argument that it helped precipitate the rise of Hitler, et cetera. So who decides what the scale of those reparations are and how do you do it in such a way politically? Ambassador Sheffer that it doesn't sort of create another crisis down the road and also sort of relatedly the cold question of Ukraine's entrance into the EU, presumably that would be very helpful for reconstruction on the other hand from what I can gather it seems like it's not gonna happen anytime soon. So how do you, some of these political questions, how would you try and address them? Well, first, bear in mind that Ukraine's application to the European Union, you're right, will take time of years before that's realized but also consider the political attitudes of the other European nations in the European Union. They're not exactly that enthused as far as I can tell to be socked with years and years of reconstruction payments for Ukraine. I mean, they've already been through the pandemic. They put a lot of money out for the pandemic. They put a lot of money out for the 2007, 2008 financial crisis, particularly in the Southern Rim nations of the European Union. And so the added the tolerance for somehow Ukraine's admission into the European Union being sort of an open ATM for Ukraine to soak EU money into Ukraine. I don't say that critically, I just say that's the attitude that would be seen. We've got to be very careful about that. I would also point out that I think the situation with Russia is very different from Germany after World War I and certainly after World War II. Namely, Russia is not a devastated country. It's not destroyed. It has an economy and it has oil wealth. And so that is available for reparations. The question is how politically do you negotiate that how do you get cases in front of the International Court of Justice ordering such reparations? And that is the huge challenge but that's part of the negotiating scenario with Russia. I do think it's absolutely implausible that the rest of the world is called upon to rebuild Ukraine when there is daily devastation of Ukraine by Russia and somehow Russia holds no liability financially for rebuilding Ukraine. That is an implausible argument to politicians. And I think there has to be, that's the great challenge politically in the future is how to negotiate the liability of Russia for reparations. Well, on that note, thank you very much, Ambassador Sheffer. Thank you very much, Senator Omidivar. I'm gonna hand it back to my colleague Yulia Panfil. Thank you so much, Peter. Thank you, Ambassador Sheffer and Senator Omid Bar. I invite all of the panelists to come back onto the screen. I'd like to thank everybody for your participation. I also just wanted to make a slight correction. I aired when introducing Zarina in addition to writing for Euro Maidan Press, Zarina also writes for Byline Times and produces videos for EBT News. But really I just want to leave you with a few reflections on the resilience of the Ukrainian people who are beginning to rebuild and continuing to tend to their properties even in the face of the destruction they're facing and Ambassador Sheffer's final words that it's inconceivable that the perpetrator of this devastation against Ukraine would not have to pay for the damage that they cause. So thank you all so much for joining us as final words. We will rebuild and rebuild. Glory to Ukraine. Thank you. Glory to the heroes. Glory to the heroes.


Citrus fruit has long been thought to be beneficial for health, but the exact mechanisms behind this were unclear. Researchers used the nematode kinohubditis elegans to study the effects of nomalin, a bitter-tasting limeloid found in citrus fruits, on lifespan and health span. They found that nomalin significantly increased the lifespan and health span of the worms, and that this effect was dependent on the insulin-like pathway DAF2, DAF16 and nuclear hormone receptors NHR8, DAF12. Further analysis revealed that nomalin also activates the human-pregnant X receptor, HPXR, which is the mammalian equivalent of NHR8, DAF12. Nomalin was shown to bind directly to HPXR, and when this interaction was disrupted, the lifespan-extending properties of nomalin were lost. Dietary supplementation with nomalin was then tested in two different mouse models of aging, and it was found to improve health span and lifespan in both cases. This article was authored by Xingjie Fan, Yingxian Yang, Yingxia, and others. We are article.tv, links in the description below.


The Allen Institute Minescope OpenScope dataset provides valuable insight into the differences between apical and somatic processing and plasticity in visual cortical pyramidal neurons. It contains high-quality 2-photon calcium imaging data from both the apical dendrites and cell bodies of these neurons, which was collected over multiple days in a wake, behaving mice. This data enables researchers to study the changes in the responses of these neurons over time, providing important information about the roles of apical and somatic processing and plasticity in neural networks. This article was offered by Colleen J. Gillan, Jerome Alecog, Jason Epina, and others.


Hey, this is Gabriel with the Long Beach Public Library. Every summer we hold a month-long series of Steam Summer Workshops we call May Create Design. This year, we'll be offering a six-week virtual workshop series on video game development. Our series is catered to 7 through 12th graders and is free to all participants. Our six-week game development course will consist of the following sessions. A welcome week, game design and narrative, game programming, visual art for games, game audio and music, and a wrap-up week to tie everything up. In our welcome week, we will present an overview of the upcoming sessions and get warmed up by talking about video games. In week two, we will dive deep into the creative process of game design. In this stage, students will learn how to put their ideas to paper and create their own game design document. Week three will have students breaking down their games into programmable parts through the process of decomposition. In construct three, students will also learn fundamental programming concepts like global variables and conditional statements to make their game playable. Students will then learn how to turn their ideas into visual graphics by learning tools and techniques that will help their vision take form. And to add more dimension and set the mood to their games, students will learn about music theory and how to incorporate sound and music to their projects. And last in the wrap-up week, students will have a chance to focus on their specific projects and share their work. In addition to the weekly workshop, an open lab session will be available each Thursday where students can ask questions, work alongside instructors, and have a chance to listen to industry professionals. We are really excited about our Make Create Design video games edition and if you'd like to learn more, go to lbpl.org for more information.


So, warm welcome to the 22nd lecture on the subject of digital signal processing in its applications. We briefly recapitulate what we did in the previous lecture and then go on to the details of the current one. We have been discussing the whole theme of discrete time filter design for the past few lectures. So far, we have come to the following point, we have agreed that we cannot meet the ideal specifications ever for the piecewise constant standard piecewise constant filters. We have also identified that we need to relax the ideal specifications by introducing tolerances and a transition band. We have also agreed subsequently that having made these relaxations, a realization is always possible and the realization is possible either with infinite impulse response filters or with finite impulse response filters both are possible. We first decided to look at infinite impulse response filter design and that is because it takes a cue from standard analog design. So, we can take advantage of the standard analog designs that are available in the literature to design discrete time filters by an analog to discrete time transformation. And we identified what we call the bilinear transformation, subsequently we said that having made a transformation from a discrete time filter to a corresponding analog filter that is to be designed. One needs to then convert from an arbitrary kind of analog filter for example, a non low pass filter to a low pass filter. So, there is a transformation in the analog domain itself which we will study later. So, we will first look at low pass filter design and then we look at how we can generalize to other kinds of filters in the analog domain. And therefore, we were looking at the design of low pass analog filters and there again we agreed there are 4 possibilities depending on whether the pass band or the stop and the stop band are monotonic or non-monotonic and we said if it is non-monotonic then the best choice is equi-report. So, yesterday we looked at the case of monotonic stop band and monotonic pass band and that corresponds to what is called the Butterworth filter design. And the Butterworth filter design we have identified how to design the 2 parameters that characterize the Butterworth filter. The 2 parameters that characterize the Butterworth filter are as follows. The parameter called the order n and what is called the half power frequency or omega c. We have also written down the equations for obtaining the order and the half power frequency. Both of them have a range associated. So, the order has a minimum that is required and of course, you can take any order more than the minimum but the most appropriate choice is to take the integer just above the quantity that we get. You see because the order corresponds to the use of resources, the more the order the more the resources that you need to employ and therefore, you would like to use as small in order as possible but sufficient to meet the specifications. And therefore, you choose the ceiling or the integer just above a quantity that we calculated yesterday. Having chosen the order we can then choose the half power frequency again in a range and that range comes again because of the operation of ceiling. Now having chosen the half power frequency we then have the complete analog system function. So, the analog system the analog magnitude function more appropriately. So, the analog magnitude function is 1 by 1 plus omega by omega c to the power 2 n and this n is known and omega c is known the complete analog magnitude function is known. Now we need to complete the design by identifying h analog s. So, once we know n and omega c we know h analog s into h analog minus s which is 1 by 1 plus s by j omega c you see how do you get the analog system function you get it by replacing omega by s by j. You see s is equal to j omega on the imaginary axis when we wanted to find the frequency response we replaced s by j omega and therefore, to go back to the system function we need to replace omega by s by j. Now of course, this is acceptable if the function can be continued all over the complex plane as we have done here. In other words you know the function as restricted to the imaginary axis and you are assuming that it can be subjected to what is called analytic continuation. That means, you may continue that function all over the complex plane with the same expression. If that is acceptable then this replacement is valid. Now here this replacement is valid because this continuation is acceptable it is an analog it is an analytic expression in the analog domain and therefore, it can be continued all over the complex plane. Anyway once we have this now it is very easy to identify the poles and zeros of this analog system function all that we need to do of course, we can see very clearly there are no zeros at all and the poles can be obtained by equating the denominator to 0 and that is very easy to solve s by j omega c to the power 2 n is equal to minus 1 and you see you need to take the 2 nth root of both sides. So, you need to write minus 1 in a way in which you can identify all the 2 nth roots and therefore, you should write minus 1 as e raise the power j 2 k plus 1 times pi and odd multiple of pi any odd multiple of pi in the argument creates minus 1. Now you need to write this because you need to identify that when we take the 2 nth root on both sides you are going to have 2 n possible solutions and to identify these distinct solutions you need to identify the multiplicity in the phase of minus 1. So, now let us solve this equation. So, therefore, s by j omega c is e raise the power j 2 k plus 1 by 2 n times pi simple and therefore, s is equal to j omega c times e raise the power j. Now you can see the angle it is 2 k plus 1 by 2 n multiplied by pi. So, of course, you could write this in the form in its polar form clearly this contributes this and this contributes a magnitude of 1 and this really contributes the magnitude and therefore, the polar form. So, in fact, we should you know we should identify there are roots indexed by k. So, we should write s k here you know there are the roots are indexed by the integer k s k is omega c times e raise the power j 2 k plus 1 by 2 n times pi plus pi by 2 the plus pi by 2 comes from this term j here this adds the phase of pi by 2. So, this is the magnitude and the phase. So, it is very clear that all the s k's have a magnitude of omega c and therefore, all these roots lie on a circle with radius omega c a circle centered at the origin with radius omega c in the complex plane. In fact, just to get a feel of how the angles change of course, they all have the same magnitude, but just to get a feel of how the angles change let us enumerate the various angles for the case of n odd and n even. So, let us take the case of n equal to 3 and n equal to 4 that will enable us to see how these angles are distributed. So, for the case n equal to 3 let us write down the angles pole angles the pole angles are of course, given by pi by 2 plus pi by 2 n k pi by n and if n is equal to 3 then pi by 2 n is pi by 6. So, you can of course, you see all that you need to do is to identify that there are 2 n distinct poles here. So, if you run the integer k over 2 n consecutive values you will be covering all the poles. So, you could without any loss of generality start from k equal to 0 and in this case it could run from k equal to 0 to k equal to 5. So, in general you see you could have started with k equal to 1 it does not matter, but you need to run over consecutive 2 n values. So, let us begin with k equal to 0 your pi by 2 plus pi by 6 then you have and then subsequently move in steps of pi by 3 that is what this says each time you increment k by 1 you are adding an angle of pi by 3 let us catch these poles on the complex plane this is the complex plane this is the circle of radius omega c this is the first pole located you see this is the real axis and this is the imaginary axis. So, we could call this sigma k and capital omega k to denote the real part of the pole and the imaginary part of the pole. So, the first angle as you see is pi by 2 plus pi by 6. So, pi by 2 and then another angle of 30 degrees here. So, here we are this is the first pole this angle is pi by 6 subsequently we move in steps of pi by 3. So, when you move in the first step of pi by 3 you would reach here move the second step of pi by 3 and you would take the complex conjugate of this move in one more step of pi by 3 and you reach here and then of course, you have one more there. So, as you can see there are 6 poles and they are located at angles 0 pi pi by 3 2 pi by 3 and you know you can of course, calculate the remaining ones. Now, it is very interesting and quite satisfying to see that the poles are symmetric with respect to the real axis and also the imaginary axis. The symmetry with respect to the real axis is to be expected that is because you want the poles to occur in complex conjugate pairs. You want the coefficients of h and log s to be real and therefore, the poles must occur in complex conjugate pairs and they do occur indeed in complex conjugate pairs. Here of course, you do not need a complex conjugate wherever there are real poles they occur singly and wherever there are complex poles they occur in conjugate pairs that is to be expected. Now, in addition there is a symmetry with respect to the imaginary axis. Now, why do we have a symmetry in fact the symmetry more than the imaginary axis is with respect to the point 0 the origin. Now, why is that symmetry there because you have already created h and log s into h and log minus s. So, for every pole at s there is a pole at minus s and therefore, there is a symmetry with respect to the origin and that symmetry reflects as a symmetry with respect to the real axis and a symmetry with respect to the imaginary axis. Now, of course, as we expect there are no poles on the imaginary axis. If there were a pole on the imaginary axis stability would be affected the filter could never be stable. Just as the discrete system if there is a pole on the unit circle the filter cannot possibly be stable and therefore, here too there is no pole on the imaginary axis. And all that we need to do now to identify h and log s is to take away the poles in the left half plane. So, these poles these 3 poles give us the poles corresponding to h and log s and therefore, of course naturally these 3 poles are the poles corresponding to h and log minus s. Now, you see let us write down therefore, the system function corresponding to h and log s. In fact, let us call these poles since we have indexed them with k this is s 0, this is s 1, this is s 2. So, h and log s is equal to something divided by s minus s 0 s minus s 1 into s minus s 2. Now, what must come in the numerator of course, there are no zeros. So, you need a constant you need to put a constant. Now, what constant need you to put? You see the constant should be such that when you put s equal to j omega and when omega is equal to 0. In other words when you put s equal to 0 this should evaluate to 1. Now, when you put s equal to 0 what you have here is the product we write product like this product k going from 0 to 2 of minus s k because you want to we want this to evaluate to 1 at s equal to 0 and it is very easy to identify this product. You see if you look at it minus s 1 is of course, omega c minus s 0 into minus s 2 is mod s 0 squared because they are complex conjugates and therefore that is omega c the whole squared. And therefore, this product is essentially equal to omega c cubed very simple. In fact, I leave it to you as an exercise to work out the corresponding set of poles for capital N equal to 4. I shall straight away draw them I leave it to you as an exercise to work out these poles. In this case you would have 2 poles in each quadrant and they would have a separation of pi by 4 which is 45 degrees. So, this I will just mark some of them this is pi by 8 this angle is pi by 8 and this angle would be pi by 4. In fact, all the poles will be separated by an angle of pi by 4 and of course, you can draw the others. So, this together would amount to h and log s and here too you can number the poles. So, you can call this s 0 then s 1 and so on. And therefore, we can now write down h and log of s that essentially takes these 4 poles because they are in the left half plane. So, h and log s would be s minus s 0 s minus s 1 and the product of minus s k in the numerator which is essentially omega c to the power 4. I leave it to you as an exercise to complete the details of this. Now, having written down h and log s our job is almost done. The next step of course is to replace s by 1 minus 0 inverse by 1 plus 0 inverse and then we have the discrete system function and that completes the Butterworth design. So, much so for the design of Butterworth low pass filters.


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