Good afternoon and welcome to this IIEA webinar on Afghanistan as the crossroads. This is part of the IIEA's Global Europe Project and is sponsored by the Department of Foreign Affairs. We're delighted to be joined today by Ms. Metta Knudsen, the Deputy Special Representative of the Secretary General in the United Nations Assistance Mission in Afghanistan, that is UNAMA. Ms. Knudsen will speak to us for about 20-25 minutes and we will then go to a question and answer session. Both the formal presentation and the Q&A are on the record. Please feel free to send your questions in during the formal presentation and we will come to them later. You can do so by using the Q&A function on your screen. Please feel free to join the discussion on Twitter using the hashtag at IIEA and we are also live streaming this event so a very warm welcome to anybody joining us on YouTube. It's now a great pleasure for me to formally introduce Ms. Metta Knudsen and hand over to her. Metta Knudsen was appointed by the Secretary General as Deputy Special Representative Political for Afghanistan with UNAMA in January 2021. Prior to her appointment she served as Ambassador of Denmark to Afghanistan. She has held several senior positions with her Foreign Ministry and she has been Ambassador to Kenya, to Ethiopia, to Greece and Cyprus. Ms. Knudsen is a member of the Nordic Women Mediators. I hand the floor to you, Metta. Thank you very much Ambassador Wilhelm and thanks to colleagues at the Institute of International and European Affairs for inviting me to this seminar webinar. Ladies and gentlemen, I'm very pleased to be here with you to speak on the topic of Afghanistan and the role of the United Nations. We were afraid that Afghanistan would have slipped down the list of global priorities following the withdrawal of international troops in August last year and given events in Ukraine. But luckily that has not been the case as demonstrated at the pledging conference last week where donors gave quite an amazing level of support for Afghanistan. What happens in Afghanistan is also still extremely relevant to global affairs. From the heart security concerns of global terrorism and regional stability to important issues such as advancing a normative agenda that includes especially the rights of women and girls. We at UNAMA have had to grapple with these issues over the past seven months in ways that we have never anticipated. And to expire its nature must contend with dilemmas. But few dilemmas were as stark as those UNAMA faced in our August last year when the former government of Afghanistan dissolved and the country fell to the Taliban. The UNAMA recognized entity led by sanctioned individuals. They took over a country brought economic systems to a standstill and challenged the international community with the dilemma of how to engage with unrecognized authorities to continue to support the Afghan people. In this situation, the United Nations took the decision to stay and deliver to support the people of Afghanistan. The UNAMA had to stay if only to continue to support humanitarian operations and furthermore the United Nations have been present in Afghanistan in some form or other since 1949. We knew we needed to remain in some form. The question that we did face was whether or not that form should be political. The UNAMA is a special political mission and its continued presence created a number of secondary dilemmas. Could we engage pragmatically on issues of great potential impact to individual Afghans, such as human rights or rule of law, without unduly legitimizing a regime that had overturned a democratically elected government by force. The UNAMA first obtained the legitimacy from the Afghan people and that had a history of gender discrimination and human rights abuses, as well as having had having used in this indiscriminate attacks as a tactic of war and killed thousands of civilians. And that had shown very few signs of reform or moderation to the demands of the Afghan people. In mid-August 2021, nobody knew how the Taliban's sudden accession to power would be translated into basic governance and what policy options the new leadership would adopt. The initial engagement with the de facto authorities was on the whole positive, with fairly rapid protection offered to UN premises and personnel, and the proclamation of a general amnesty to members and servants of the former republic. There were high hopes at that time that after an initial spate of disorder and revenge killings bad as that would be, the leadership would progressively assert control over its disparate forces and enforce that promised amnesty. While many Afghans associated with the former republics succeeded in escaping, the reality was that far more Afghans stayed behind to see what the new regime amounted to. And many civil society activists, academics and others sought UNAMA's assistance in playing a mediating role with the new authorities in the hope that a modus vivendi could be found. And an important element of our previous mandate committed us to supporting a government that no longer existed, and that mandate therefore to a large extent provided little guidance. The Security Council chose to defer a decision on a new mandate for UNAMA until last month. But what the Secretary General proposed some months ago to the Security Council, as the basis for the new mandate was to begin political engagement with what the UN referred to as the de facto authorities, the Taliban regime on several clearly defined terms. First of all, the engagement has as a primary objective, the improvement of the lives of the Afghan people, but it acknowledged the reality that this could not be achieved without some engagement with the de facto authorities. Secondly, while carrying out this qualified engagement, we had to be acutely conscious of the risk that our objective of supporting the Afghan people could be perceived as one of legitimizing the Taliban authorities, and that this needed to be mitigated as the objective of recognizing a government of course rests with our member states. And thirdly, the engagement was experimental. We based ourselves on the hypothesis that the Taliban was willing to move away from extremism and violence, and towards actions and norms required to be a part of the international community. And two, that as we test this hypothesis, we need to keep our eyes open, and to be able to change strategy, if it appeared that this hypothesis was false. The Security Council to a large extent gave UNAMA such a mandate suggested by the, and in line with what was suggested by the Secretary General. But only shortly thereafter that the Taliban took a number of the decisions that have forced us to seriously question the hypothesis I just mentioned. The most prominent of these decisions was to prevent girls above grade six from going to school. While senior Taliban officials made public announcements that schools would reopen in the days running up to 23rd of March, the morning of the reopening of schools. The morning of the reopening of schools girls were turned away from secondary schools, which remained closed for them. For months, the international community had signaled that this decision to allow girls to return to secondary education was a necessary step. If the Taliban wished to gain international legitimacy. But the international community was by no means alone in wanting to see the Taliban enable all children return to school. The Human Rights Watch 87% of Afghans want their children to be educated, regardless of gender. So the Taliban's decision does not reflect the wishes of the population that they claim to represent and govern. In terms of education, not only violates the equal rights of women and girls to education, but also jeopardizes the country's future in view of the tremendous potential contributions of Afghan women and girls. The long term impacts of such a discriminatory decision discriminatory decision will affect future generations of Afghan females in terms of literacy and numeracy, and will contribute to the cycle of poverty. A couple of weeks ago, I visited public and private universities in Kabul. As the public university recently opened their doors, seeing women back in the park and in the halls of Kabul University really gave me some hope. But this optimism has been dashed by this announcement on girls secondary education. If this decision is not reversed, soon there will not be any female students entering university, even if the universities would not be closed earlier by the de facto authorities which still remains a risk. So this decision also led to condemnation by the international community, including the United Nations Security Council, and the organization of Islamic cooperation. For girls, education is not the only one which causes concern. In the days following the education decision, a slew of repressive measures from the de facto authorities were issued, which further restricted the civic space for Afghans. They restricted Afghan women from traveling from Kabul International Airport without a maharam, a male jabaroon. They instructed that public parks must be gender segregated by prescribed days, and they bought male civil servants from going to work if their peers were not sufficiently long. And this has been followed by a more recent instruction to the universities that women and men cannot attend the same scientific conference, or even participate in the same programs. With all the concerns that that raises around academic freedom and general keeping the level of quality at the universities. But from these most recent additional restrictions, the overall situation for Afghan women and girls remains extremely challenging. Life for women without a maharam, for example, widows or female headed households becomes almost impossible. As women women continue to experience exclusive exclusion from civil service employment and access to justice and protection for survivors of gender based violence remains extremely limited at best. The economic crisis has in the dire situations forced families to choose extreme coping mechanisms with stories emerging of those resorting to the sale of children or forced early marriage of girls. The media is becoming more and more restricted with the factor authorities aiming to control content. Descending views continue to be silenced including protests that counter the de facto authorities narrative civil society activists and journalists are being arrested beaten and harassed. As someone put it someone put it recently a tweet could put your life at risk. Recently, the de facto authorities instructed Afghan media to suspend any transmission of international media broadcast. It is thus very important that the international community continues to support the media and civil society and especially also women led organizations, so that they can continue to operate in Afghanistan. I mentioned that the ones looming Afghan culture of music dance and art is completely silenced. While some of the media still have women anchors restrictions are placed on radio stations to invite women women to their live shows live music is banned radio music is limited to traditional or religious music. There are paintings on the walls within Kabul city, which everybody who's visited Kabul will have noticed, they are now replaced by white walls. The color of the city is gone, as is the vibrant cultural life of Afghans. We continue to document and verify credible reports of extra judicial killings arbitrary detention in force disappearances torture ill treatment intimidation of a wide range of individuals men and women victims of such violations include members of civil society, as well as those who fall under the provisions of the general amnesty announced by the Taliban, when they came to power, they are former defense and security personnel, former government officials and civil servants. And additionally, you know, has also documented the killings of individuals accused of affiliation with ISKP or dies. What we try to stress to the de facto authorities is that they need to start taking a stronger position in preventing human rights violations and abuses, and where they do occur, they should undertake prompt effective and transparent investigations. The de facto Ministry of Justice indicated that existing laws continue to apply, pending their review of compliance with Sharia. The new court system has been set up by Taliban but as to date, almost eight months after the takeover. There is a lack of clarity on which legislation is being applied, and instructions are being provided on an ad hoc basis. There is a lack of integration of former justice personnel in the current justice system, and the absence of an inclusive engagement with communities and justice issues further undermines the legitimacy of the de facto authorities vis-à-vis the Afghan people. Since the takeover by the Taliban, the state of governance remains ambiguous. After all, power seems to be vested in the executive pillar. The cabinet is composed of 25 ministers with strong religious backgrounds and the vast majority being passed to and of course all are male. And the appointments of subnational senior officials show similar trends. What we have observed is that major decisions however seem not to be taken by the cabinet, but elsewhere in the Taliban structure, and the decision making processes remain unclear in the absence of clearly defined mechanisms and systems of governance, such as a constitution. But while improvised explosive devices, assassinations and Taliban house-to-house search operations continue, we should stress that a low level of security incidents have been reported in Afghanistan over the previous months. We must be analyzing conjunction with the drastically changed security environment as hostilities throughout the country declined, also leading to a sharp drop in civilian casualties, which of course is positive. The Taliban continue to claim that the ISIS ISKP are not a threat and are completely wiped out from Afghanistan. Reports on the ground indicates otherwise as ISKP claimed or attributed attacks continue. The Taliban also continue to face some attacks that are claimed by the National Resistance Fronts and other newly emerging resistance groups. And I should also mention that border tensions with neighboring countries such as Pakistan, Iran and the Central Asian countries continue. And all of these developments are occurring within a dramatic economic and humanitarian situation, which definitely demand more attention from the de facto authorities. Afghanistan is facing a catastrophic humanitarian crisis which fundamentally also amounts to a human rights crisis with over half of the country's approximately 40 million population needing humanitarian and protection assistance. In 2021, humanitarian partners delivered food, clean water, healthcare and other humanitarian assistance to close to 20 million people in Afghanistan. And the pledging conference on 31st of March that I mentioned at the beginning, co-hosted by the UN and member states including governments of Qatar, the United Kingdom and Germany, resulted in pledges of more than $2 billion for humanitarian quite an impressive figure taking the present global situation into account. But we need to stress that humanitarian assistance alone is not enough. Other challenges to the economy still remain. The economic situation is deteriorating quickly and challenges to international payments and on the central bank persist. The budget of liquidity has forced businesses to close, including the ones fledgling manufacturing such sector and left 80% of people in debt. In addition, development assistance has almost completely ceased since the takeover by the Taliban. From our side from you know we have taken all possible measures to inject liquidity into the economy, including the physical import of cash. And also the international community has taken steps forward and considered options to increase engagement beyond humanitarian assistance to address the huge economic challenges. However, the recent restrictions announced by the Taliban question their claim to engage in good faith with the international community with the aim to improve the situation for all people of Afghanistan. The Taliban faces a different society when that when they last ruled the country, they may not be able to respond to the demands of this change society. If the Taliban continue the path of repression, and their inability to live up to the change from being an insurgency to a government. If they continue that inability the Taliban risks that they will not gain legitimacy in the eyes of the Afghan people. Respecting human rights and inclusive governance girls education and being a government for all people of Afghanistan would also be in the interest of the Taliban should they wish to stay in power. Not as to what direction they will turn, but the Taliban will have to make that choice before it is too late. The international community including the neighbors and the organization of Islamic cooperation is united that the Taliban must deliver on three issues, girls education, political inclusiveness and counterterrorism guarantees. In the sense that some Taliban interlocutors are willing to be attentive to international concerns on these issues, especially actually on the education side where the criticism of this decision reaches far into the ranks of the Taliban. But unfortunately, there are also those within the Taliban that seem not to be willing to be attentive to these international concerns. We do not believe that we've seen the final words on these issues however. And in our political engagement we have come to realize that the Taliban faces a number of dilemmas as well related to the difficult process of transitioning from an ideological insurgency with a common outcome to a functioning government with multiple priorities and rising expectations. So we are only at the beginning of this process. And while we continue to engage, we will, we are sure that this process will continue to be frustrating. It will have setback, but it is also essential if we are to continue our support to the long suffering Afghan people. So let me end my initial remarks here and looking forward to the discussions and the questions. Thank you very much. Thank you very much. That is, it's quite a depressing picture. If I could start off the questions by asking you, are there any signs that the present de facto authority is open to dialogue with others, either internally or externally. I know there was a meeting I think a week ago in Beijing with neighboring countries. Is there any indication that they're listening to messages that would move forward on the three particular areas you identified. Our impression is definitely that they are to some extent willing to engage. We have had numerous interactions with de facto ministers with leaders within the Taliban. And we are also aware that the de facto foreign minister Mutaki participated in the meetings in China with the neighboring countries. And the challenge we see is that it seems that the decision making is read is vested within circles that are not necessarily those that we have most engagement with. So we are continuing to try and see if we can expand our in the group of interlocutors and getting a better access also to those leaders of the Taliban that we might not have reached so far. But again, as I have tried to say in my speech, I think that the most important influence is the influence of the Afghan people and the fact that they are not a range of issues are very clear that they are not happy with the present policies of the Taliban. So for us to engage not only directly with the Taliban but also in support of the Afghan people's possibilities of influencing the Taliban I think is very important. Could I ask you just in that context. What is the status what is the position of civil society at the moment if I'm in Afghanistan you mentioned the pressure that's on the media. We have seen the protests of Afghan women taken to the streets and making their voices heard. Is it very difficult for them is the first question and the second question that I have that's tied into that in part. How can Ireland, how can we in Ireland, how can we support and assist and the safeguarding and so far as they can be safeguarded of the rights of the Afghan people. Thank you very much. It's clear that the civil society is under a lot of pressure. They are of course, many of the more high profile civil society leaders that have left Afghanistan, because of concerns for their safety. But they are also quite a lot of civil society activists women activists that are still here and still trying to to keep up their activities both in Kabul and out in the provinces. In some areas, they have managed to establish a dialogue with the authorities sometimes facilitated also by our field offices in other parts of the country they are under a lot of pressure and and it's it's very difficult for them to to operate. I would say that the picture is mixed. It's only a few days ago where there was a large civil society gathering here in Kabul with more than 280 civil society representatives both men and women present and also representatives of the Taliban. We did not participate ourselves directly in this event, but we understand that there was quite a good dialogue and there was a willingness from the Taliban side to listen. But that's only part of the picture of course on the other side we have seen the crackdown on on women activists we have. We are aware of course of threats and intimidation directed towards such activists. So, so it is definitely not an easy situation. I think in terms of support brought from both from Ireland and others, what we keep encouraging is to for donors to try and keep up some of their support that they were available for civil society before the regime change. And this is even more necessary now to to continue to provide especially also core funding for for civil society for women's networks for them to to to continue to keep activities going and also still be there when when opportunities arise. So, so financial support is definitely important, but but of course also continued moral support engagement, and making sure that we always bring those civil society activists, women activists that are inside Afghanistan, bring them also to the different forums to the different tables where they can make their voices heard. Of course, with due respect for their security concerns but but that's one of the things that they continuously ask for please don't just listen to diaspora Afghans please let Afghans that are in the country have a voice. Thank you. There's a question here from Adrian Farrell from the Department of Foreign Affairs. What do the Taliban think of the recently agreed you now a mandate. And the second another question I have here from Sheamus Allen, talking about sanctions against Afghanistan, and he asked for your views on US and Western sanctions, including US freezing of Afghan central bank assets. So, when it comes to the mandate, the de facto authorities have welcomed the new Unama mandate, and have expressed their willingness to continue to work with us. But the extent to which that would will will continue is of course probably linked to whether they see the engagement with us and with the international community as delivering some of the objectives that they are pursuing. And that's of course linked to to the international recognition to also removal of sanctions and so on. And what we are expressing to them is that them with decisions such as those on education for example they have taken a step backwards from that pathway that could lead them towards at some point, maybe being recognized and being welcomed as a legitimate part of the international community. I mean the sanctions to a large extent are directed at individuals and based on specific concerns also related to counter terrorism and so on. And that's of course for to a large extent for member states to decide when they should be lifted. But where we have been engaging is mainly on the economic side, trying to stress that the sanctions against individuals should not mean that we are undermining the whole of the Afghan economy to the detriment of the Afghan people. And now we have also engaged so actively in terms of seeing if we can resolve some of the issues around the banking sector. This includes of course, close engagement with the US authorities. And we have had some progress on that and, although there's been recently a setback because of this education decision but we are continuing the dialogue, both with the Afghan Central Bank, and the US authorities in terms of trying to find solutions that would allow the Afghan banks to survive would allow liquidity to flow into Afghanistan and would allow the Afghan economy to take to have benefits of the actually increased trade that we have seen since August. I think that's worth noting that again of course because of the improved security situation, the fact that movements are easier we have seen an increase in trade across the borders with neighboring countries. And it's really important that that can be further supported to restart the Afghan economy. I have a question here from Damian power from the defense forces. Is there a sense that the Taliban are using the current war in Ukraine as a cover to implement a more hard line approach within Afghanistan. I think that the western world is very much engaged in that particular crisis, and then Peter McLoone, who is a board member of the IEA asks, does matter know what percentage of Afghans income is now dependent on international development date. And does this dependence provide any leverage in securing change. Thank you. I don't think that we have made a direct link between the Ukrainian war and the approach that the Taliban leaders are taking at the moment I think it's much more to do with some internal dynamics also related to the the power structure within the Taliban and and the needs for some parts of the Taliban to to demonstrate more clear results also to their internal followers. I think the war in Ukraine is has more been of a concern to us relating to the willingness to continue for for the international community to stay engaged in Afghanistan and to continue to provide the necessary humanitarian assistance. And as I said at the beginning so far, we have been encouraged by many statements also in the Security Council from member states clearly stressing that yes Ukraine takes up a lot of bandwidth but the countries are committed to assisting Afghanistan to keep the focus on Afghanistan. And I think what we would be concerned with in the midterm is of course the general effects that we know that the one Ukraine also have on international food prices for example, which might of course also impact the situation here in Afghanistan where a lot of the wheat and other commodities are imported. What percentage of the population is dependent on development aid. That's actually zero, because at the moment there is no development aid coming into Afghanistan, but if the question was more related to humanitarian assistance, I would say that at the moment it's about half the population that will depend on humanitarian assistance to cover just their most basic needs. So there's definitely a strong dependence on humanitarian assistance and, and our message is if that is not to continue year after year, then there is a need for the, for the donors for the international community to find ways of also supporting international development objectives, even if it must at the outset be through channels that bypass the government structures. At the recent pledging conference, there were donors pledging also support for what we call basic human needs. They're somehow beyond the core humanitarian activities and where we hope we can support more the preservation of the education system, the health system, water provisions and so on. But, but at the moment it's it's very, very limited. That's for sure. Thank you. Thank you. A few more questions here. One is from Alan Dukes, the former Minister for Finance in Ireland. And he asks about the role of other Islamic States in seeking to moderate excessively restrictive approaches to human rights and to the rights of women and girls. I think you touched on that slightly earlier when you spoke about the organization of Islamic States but if you could give us a bit more of a feel for for the pressure they might be bringing to bear. And a question then from Francis Jacobs, a member of the Institute and a former head of the European Parliament representation in Ireland. And he asks about the attitude of non non Pashtuns to the de facto authorities. Are there any efforts to reach out to them and what is happening in places that used to be controlled by the Northern Alliance. Can I just add on a slight pedestal to that last question. Are there areas about which you have very different information but which you have a lot of concerns in regard to the humanitarian situation. Thank you. The role of other Islamic States. I think this, this can become very important and we have from the enormous side, really tried to encourage also the engagement of other Muslim majority or Islamic countries in Afghanistan we are really pleased with the engagement of the organization of Islamic which also has a representation here in in Kabul with an ambassador present and one of the initiatives they are looking at is to bring in a large group of Islamic scholars after Ramadan to have a dialogue with the de facto authorities on a number of these issues relating to to education to women's rights and so on. We see also countries such as Turkey Qatar being very active also issuing statements around the education decision. And in general being being very active in dialogue with the, with the authorities we meet regularly with those countries that still have representation here in in Kabul, which of course, most of the, if not all of the neighboring countries, Iran Pakistan, the Central Asian countries we met with them just this morning and and and we find it very very important and useful the way they try also to support the objectives that we have in our engagement with the, with the Taliban authorities I think it's quite impressive. Actually, the unity that have been demonstrated across all parts of the international community of course there are different approaches, and some are more interested in engaging more directly with with the authorities but in general I think the messages that come from these countries and these different organizations correspond very much with also what is coming for example from the Security Council. As I mentioned, regarding the the passion, the, the, the, the current authorities governments and so on structure to a very, very high extent dominated by a passion, and that of course, causes a lot of concern amongst other ethnic countries that do feel alienated and removed from any influence on the government. And, and we also see that in some areas of Afghanistan where there are also non pastime Taliban. There are increasing the tensions between pastime and non pastime Taliban, especially especially in the north. And it's, it's, it's a clear message from us to to the de facto authorities that longer term stability and development in Afghanistan will depend on providing possibilities for other ethnic groups to influence government to feel represented. At the moment unfortunately we do not see any attempt from the Taliban side from the de facto authorities to engage in such an outreach to other other ethnic groups. And, and it's, it's, it has not yet been having much traction. The call has also come from former president car side for example, and, and has largely been been been ignored, probably also reflecting the fact that that internally in the Taliban they are still also balancing their own sort of division of power between different. groups. On the humanitarian situation. Of course I'm not directly responsible for that. So I don't have all the details but I would say that in general we have access now to almost all districts in the country, a country to what has been the case for decades with the improved community. The UN and its partners international NGOs, national NGOs, we to together we do actually access, almost all districts in the country. So I think the, the, the overview and and the knowledge on on the humanitarian situation is by now quite good. And of course also. It's clear that some of these areas that have been very difficult to reach before are in a very dire situation. They were already in a difficult situation before August, we have the prolonged droughts here slightly more rain this winter but still not enough to to cover all the needs in the agricultural sector. Of course, the fact that the services have not been reaching these parts of the country for a long time. The situation is really difficult but but the good thing is that we do now have access in a way that we did not have before. Thank you for that meant to two more questions and we're probably coming towards the end of the question so if anyone has anything outstanding please get it to us and shortly. This one is from Sarah Bracken. Is there, and perhaps you could talk about the requirement to have a mara and present with a woman when she is seeking medical assistance. And is that being strictly enforced, and is that a new step, or was that already the case in their previous iteration. And there's a question from Kevin Colligan from the Department of Foreign Affairs. To what extent are the Taliban aware of the difficulties and in the delivery of humanitarian assistance posed by the new restrictions on women's freedom of movement. On the mara issue. I would say our impression is on this issues as on many other issues the implementation of the different the directives are quite on evil on equal across the country. As we see very strict strict implementation of some of these demands, both on on, I mean, a dress code for women, whether women can move without the mara whether they can access medical assistance but in other parts of the country. There are not such a big issues. It's not so so so difficult and I mean I visited a number of provinces lately and I mean for example in in Bami and you still see quite a lot of women moving in the streets without being sort of to cover it up. There is a part of the market with shops run by women selling handicraft that's still open in Kabul I would say the image in the streets is slowly changing I mean they're not many women but they are still women but they are increasingly very conservatively dressed. And I think the, the fact that the population do not really know when and how these directives will be implemented. It creates a lot of fear and uncertainty and many choose to sort of maybe over comply because they don't know what, what response they would be met with. So, so, so again, I mean it differs across the country but but I think the trend that the moment is to watch more and more restrictions and more and more difficulties for the women. I mentioned before that I had visited Kabul University some weeks ago which was a very positive experience, lots of female students around I had a dialogue both with female and male students and also with female faculty male faculty. The female students dressed sort of still quite lively. When I passed the university just two days ago all the female students that were lined up outside to get into the university were dressed in black from top to toe and definitely not allowed anymore to get into the university unless they, they abide by this stress code. I mean, just the sign that that at the moment the thing things are not going in the right direction they are going towards more restrictions more rules being imposed on, especially on the women but also on the men as I mentioned the rules around the growing beards and also press code if you want to enter ministries or public offices. Sorry, I think I think you know it's on the last question. It was something about the humanitarian assistance. Yes, there was a question to what extent are the de facto authorities aware that their, their new restrictions on women's freedom of movement are impacting on the delivery of humanitarian assistance. Well, it's it's definitely something that is discussed with them but to what extent they accept this is another issue. I mean, again, lately from some of the meetings I've had with the provincial governors. I often get the argument that within their interpretation of Islam and Sharia it's very important to protect women and women are best protected if they stay in their homes and it's the duty of the men to take care of them. And that is the logic they are coming from so so. So I'm not sure that it always makes an impression on them that you try and discuss the need to have women having easy access to humanitarian assistance and also the need to have women. They're part of the delivery of not only humanitarian assistance but but also another area we we raise with them is women's access to justice, especially also for women that are victims of gender based violence that they they need to be able to to act with the with the female officials police men, female staff in the legal sector and so on. And, and they do respond to some extent I mean there are in most places there are women back in the police force for example, but in other areas it's it's not easy to to to get them to accept that this is this is necessary. Here's a question here from Arif Sahil. He says that unanimous new mandate gives stronger focus on facilitating dialogue amongst political stakeholders for inclusive governance. There is broad recognition on the need to reach a comprehensive agreement between Taliban and other political groups. What measures might you be contemplating in that regard. That could lead to national agreement as was called for security council resolution 2513 and then in Emily been she asks, do you have any remarks regarding the role of Qatar in the in efforts in sorry in international efforts and dialogue with the Taliban I think you mentioned them in the context of Islamic States and could I add in another question there and how should we interpret the Taliban decision to crack down on poppy production is that response to international pressure or is that an effort to find to find international recognition. And the, the, the part of our new mandate that talks about our role in trying to promote broad based dialogue on inclusive governance on representativity on on on all groups in society being able to to take part in in in in governance is a is a really important part of the mandate and one that we had really hoped that we would get strong strong backing from the Security Council for because that is, I mean we see that as the key issue for long term stability and also creating the possibility of sustainable development in Afghanistan if we can achieve that kind of discussion where we're broader parts of the population are included. And so so the idea from our side is definitely to to to work on these issues both at the national level but definitely also through our field offices at at the provincial level where where we sometimes see more possibilities of of furthering this dialogue I think there is a strong need here for also a bottom up approach to dialogues around inclusion but also conflict management reconciliation and so on. And the problem of course at the moment is that with the decisions on on education and some of these restrictive measures we have seen lately. And that calls into question, whether our strategy of of of or our hypothesis that we could make progress on on promoting such types of dialogue, whether that is actually possible. And as I said the jury is still out, we will continue to try and create for us where this is possible we will continue to impress upon the the the Taliban authorities that it's also in their interest to open up to wider parts of society, but whether we will succeed I think is something that that we will still have to wait some time to to see. And again, as I said, I think the strengths is very much in the demands also from the Afghan population. And that do really want to be heard and to have their interests reflected also in in what the government decides. So so again it's also very much about engaging with Afghan society and trying to support these organizations networks whatever that still exists in in the country. And as I said, I think the region, and also other Muslim countries can play an important role here and definitely Qatar is one of the countries that have played an active and positive role. We've also been really happy with the UAE, who has a strong voice also in the Security Council, and who helps a lot around the adoption of our mandate. That country is also participating quite actively in the dialogue we have with the region here in country. The ban on puppy production and the dog drug trade. I think it took us all a bit by surprise that decision. In a way, of course, it's welcome. It's what the international community and also the neighbors have asked for for years that there should be a more efficient attempt to control this sector in Afghanistan. What we are saying is that we would be very interested in seeing also plans for how this decision is to be implemented. At the outset we, there are some concerns that if if a ban on, for example, the ongoing harvest were to come into play right away. It would completely destroy the livelihood for for large parts of, especially farmers in the southern part of the country would not be able in the short in the short term to replace the puppies with other crops. So for this not to lead to further economic hardship further disaster for an already very vulnerable part of the population, it would need to be a decision that would have to be implemented gradually and accompanied by measures that can address the economic needs of these parts of the population. And then there are of course a whole lot of other challenges involved in controlling the trade, the smuggling the export and so on. We are still studying this decision and just hope to have further discussions with the Taliban authorities on what their plans are. What led to the discussion coming right now. I think it becomes a bit a question of speculation. I mean, it might, it might be linked to to diverting attention away from the education side but it might also be something that has been brewing within the Taliban for a while. And now they just found that this was the right time to to to come forward with the decision. So I don't think we can say exactly what what led to this. Well, thank you very, very much that I'm hugely impressed by the work that Yunama is doing in Kabul. I'm hugely impressed by the fact that you are living in Kabul that we are able to benefit from your expertise today. Thank you so much, and I wish you all the best and Yunama all the best with its mandate. Thank you very much and it was really a pleasure to participate and be part of this discussion also and please I mean if anybody wants to continue with some questions we are we always available here in Kabul. Thank you very much.


This is Cheryl Matsuoka, the executive director of the Hawaii Restaurant Association, and I'll write, let's meet our guest. I'd like to introduce our guest today, Victor Lim. And Victor, I'll have you introduce yourself because you are involved in so many different areas of our community. Victor? Well, hi. Good morning, everybody. Oh, good afternoon, everybody. It's 12 noon. Thank you for allowing me to join you today. I'm, as you know, I'm a McDonald's franchisee here in Hawaii in Honolulu, but I'm also a former chair of the Hawaii Restaurant Association. And for the past 15 plus years, I have been acting as the legislative lead for the Hawaii Restaurant Association, dealing with all the government issues at a state level, as well as county levels that affect our restaurant business. And so in that capacity, I'm here to join you this morning or this afternoon, Cheryl. And I'm yours. Thank you so much, Victor, for being here with me today. Hawaii Restaurant Association is kicking off the year with a special event, which is our legislative meet and greet. It's our annual event. And the purpose of this event is to network with our government officials. And, Victor, we were just talking about it a little while ago. One of the reoccurring comments that I hear from our government officials is they need to hear from our restaurant tours. Isn't that right? That's true. You know, they always say that, hey, how come, you know, usually on any particular issues, there's a lot of people that come and testify. However, with the restaurant community, hardly anybody showed up. But and I always have to keep reminding our legislators that many of our businesses, especially the small businesses, we are working owners. We work every day in our business. And if we have to be out of our business for three, four hours during a working time, you know, we have to shut our restaurant down or retail business down. So I mean, it's very, very difficult for us to do. But nevertheless, many times I act as a chairperson as a mouthpiece. But I also need a lot of help from my fellow business people that either engage with the legislators or write letters or testimony and so forth. So you know, we we got to use technology to our advantage. And also, you know, physical presence also make a huge difference. Yes, physical presence always make a huge difference. And as you mentioned, Victor, even a written testimony, calling your representative, doing a video, whatever you need to do to make your voice heard is part of what today's discussion is all about. At our legislative meet and greet, which is going to be on January 30, which is a Monday, we really want to thank our presenting sponsor HMA and our silver sponsor Giovanni Prastrami. Tickets are on sale right now, $25. And Victor, I have great news. We have really a well attended event coming up, the list of the government officials that are attending is growing every day. So we look like we're going to have at least 125, 135 attendees, Victor. You know, it's a wonderful opportunity for us because, you know, the legislators are going into session next week on the 18th. And, you know, the chamber is doing the legislative meet and greet. But we have a specific one just for our restaurant community. And that's going to be on the 30th at the Central Pacific Bank, at the tight pool, at the main lobby area, first floor of the renovated Central Pacific Bank. And that's where we're going to have a reception. You're going to have a chance to mingle and meet, you know, many of the elected officials that come by. And really, you know, they need to see name and faces. And so, you know, we also can reciprocate that way. And that way, we can actually talk about issues that affect our business. And of course, you know, there are a lot. There is a lot, Victor. And you're right. The event starts at 5.30, tickets are already on sale. So please purchase your tickets. I have a list of all the businesses that have already registered as long as well as our government officials who will be registering. So, you know, Victor, part of this discussion today is about our legislative meet and greet, which is an in-person event. And the other part of it is our Government Relations Committee. Our meeting in January will be held on January 26. It's a Thursday at 4 p.m. via Zoom. So you want to talk a little bit about what our Government Relations Committee normally, how it works and what happens during the committee meeting.  We have all kinds of people that talk to their neighbourhood legislators and have them introduce bills that impact them. And many times, it impact them maybe in a positive way, but it impact us in a negative way.  And when the issues comes up and the bills get introduced, you know, our role is really to answer in a pragmatic, logical way, because many of the legislators that vote on it, you know, only hear one side of the story and they do not understand the other side.  We got whiplash all over the place. And many of your neighbourhoods, small businesses and many restaurants have really permanently closed. And even though pandemic is supposedly behind us, the issue has not gone away yet. I was just reading something nationally put out by the NFIB, National Retail Federation and small businesses that businesses to the month of December, many of the independent small businesses are struggling to pay rent. And I tell you, even though, like I said, the pandemic is supposedly over, many of your neighbourhood businesses are struggling and still continue to struggle. And our job is to make sure that our elected officials understand what we as business community are going through, so that they are sensitive, that when they make their decision and when they cast their votes, yea or nay or sometime in between, that they take all sides of the issue into account instead of just listening to one side. That's our job and that's our role as the restaurant legislative committee. You're right, Victor. We are the voice of the food service industry. And so many times when I do speak to our government officials, I remind them that there's rising costs of product, right? All our protein costs are sky high, supplies, all of the cost of supplies and, you know, utensils, everything's going up, take out utensils. And then the fuel costs, our utility costs are going up and combine all that. I remind our legislators and our government officials, you know, our restaurant tours, they really try not to increase their menu prices, but yet they have to if they have all these rising costs. And you talk about rising costs. Actually, the increases in menu prices in restaurants actually is about two, three points lower than the increases in the cost in a supermarket because everybody faces costs from, you know, because of gas prices, transportation costs is up, the commodity costs is up, right? A shortage of anything and everything that you could ever imagine. And that's why, you know, and the economy is softening. You know, we are technically, if you look to talk to many economists, they will tell you that we are technically in a recession.  So in this time, it's very critical for us to make sure that what we can control, we control. Yes. And you're so right, Victor. You know, I speak to many of our community members, and they are afraid of a recession. They are afraid. And so they're not spending as much, as you mentioned, in luxury things. Many of the restaurant tours tell me that if they used to have a tab and they would come in and have an appetizer, and they'd have a meal, and then they'd have a dessert and maybe a couple of drinks, now they notice that that tab maybe not have that second drink and maybe not a dessert. That is definitely true in all types of businesses, you know.  I mean, that's a reality.  But costs continue to escalate for anything and everything that you buy out there. And so, you know, people got to make sure that you budget what you can, right? And the fact is that I also saw something this last couple of weeks is that, you know, people are using their credit cards a lot more because, you know, you are tapping into your credit lines. So that's the economy that we are at.  And restaurants are no exception. Yes, Victor. I hear daily I have restaurant tours calling me and the restaurant tours that, especially in our tourist areas that used to depend on the Asian market tourist, you know, they reported back to me that after the holidays, their numbers were not as good as 2019 because we don't have that Asian visitor here. We're lucky that we have the West Coast as well as mainland visitors. But the Asian visitors, we're probably doing about 10, 15% of what we used to do. And right now, you know, even though China is opening up, but the pandemic, you know, the amount of COVID cases that they have, people are very concerned that what's going to happen. And the other thing, you know, some of the given examples, one of the issues that I've been working on right now is that, you know, unemployment insurance rate, you know, during the pandemic, 2020 and 2021, 22, we were at their D rate on this D schedule on what business pay for unemployment insurance. In 23, we are looking at going from D, jumping from D to an F schedule, which means that all the businesses are going to continue to pay at a higher unemployment insurance on top of, you know, all the other courses that you see. So we're going to see what we can do, maybe try to nudge some people that maybe we can slow it down some, you know, I mean, anything that we can do to make life easy for the small businesses, we're all for it. That's what we're here for. And Victor, you have always been the voice of the Hawaii Restaurant Association, especially when we speak to our government officials, and you're right, this unemployment insurance has everybody, you know, with big ears trying to hear what's going to happen next. So as you mentioned, you know, we're going to try our best to explain the process and why we need to slow it down. Because it's going to affect their bottom line, Victor. It's going to affect everybody, you know, and of course, you know, like any other insurance, right? I mean, your experience level, your business experience level will affect your insurance rate, and unemployment insurance is no different. However, because of the, we work very hard with the legislator as well as the previous administration to make sure that during the pandemic, you know, people were on an unemployment roll, not because of business creating debt, people on an unemployment roll, but it's a pandemic that causes businesses to shut down, causes business to lay off and has nothing to do with our business community. And we were able to do that. But right now, I think we need to make sure that they understand and they continue to soften and make the rates reasonable for the community. Thank you, Victor. Now, is there any other bills or any other legislation that we need to discuss today, Victor, that we should be aware of?  So, you know, at McDonald's, you know, our employees are not tipped. But many of the mid-tier and fine dining restaurants, the employee, part of the employee compensation is having tips. And the businesses have a small break in terms of what we call tip credit for those people. And every year we have legislation. And I understand that right now, we are looking at, there are some senators that are trying to introduce a bill that's going to eliminate the tip credit. And there will be a further pressure on our mid-tier and fine dining restaurants. And the tip employees is more than just restaurants, you know, in the hotels where you do valet parking and things like that. All those people are compensated. The wage is only a small part of, you know, the paid wage is only a small part of it. But they get 20, 30 percentile increases with a tip, you know. And if you eliminate that, those businesses and those employees will get hurt even more. And so that's one of the issues that we will face and we expect to face every year. Thank you, Victor.  When we were in the pandemic, well, I'm sorry, Victor, it was before the pandemic, we knew it was coming. And we went to meet with Governor E. Gay. And it was Victor who really said, you know, can you please, Governor, consider cocktails to go? And it was Victor who, you know, as he mentioned, he's in a fast food restaurant, has no benefit, but he's the one who put his name on that card that day and asked the governor. And we were all present when you did that. Victor is out there even fighting for tip credit. And as he mentioned, his restaurant doesn't have that type of employee, but yet he'll go out there and fight for the industry regarding tip credit or whatever the issue is. So thank you, Victor. Thank you so a lot. At the Hawaii Restaurants Association is the restaurants have namthip restaurants to fine dining restaurants and anything and everything in between. And our job is to be advocate for the industry. And the fact is that, you know, many of our elected officials, even though that the intention is good, they do not understand our business. We understand our business better than they do.  And then if you look at it during the pandemic, whether it's with Mayor Blangerie or Mayor Caldwell to Governor E. Gay, we have some heart to heart dialogue, right?  And they don't understand that unless, you know, we provide that with them. But, you know, we were very fortunate that, you know, all the different mayors in all the counties, you know, Governor E. Gay and his staff, they always have a room to return our calls. And I want to say, you know, we're very thankful that they allow us having a voice. And we don't win all the time.  Because if we don't, we are in a whole lot of hurt. And you're so right, Victor, how many numerous calls we had with Governor E. Gay, with all the mayors and the relationship that the Hawaii Restaurant Association has built. And even more so, I think, Victor, during the pandemic, right? Where there was way more conversations than prior to the pandemic has really built really, really solid, strong relationships with our government officials. And that's because, you know, we follow the philosophy. It's always being honest. You know, we do not exaggerate. We provide them with facts that they don't know about. We share with them what some of the consequences of their decision might be. And they appreciate that. And that's part of the reason why, you know, when you talk to them and what we call, they always return our calls, you know? I mean, that's a relationship that we want to continue to build and nurture. And that's also with all the legislatures. And that's why we think this meet and greet that, you know, we have scheduled for on the 30th Monday. It's one of the many steps that we do to make sure that we encourage that relationship and build on that foundation that we have built up. And Victor, this year we have some new legislators. So my, you know, request is to anybody who is able to attend, the tickets are only $25, but to come and meet, especially the new legislators, right, Victor? Yeah, we have a lot of, we have a lot of new legislators and we have a lot of new committee chairs this year on both the House as well as the Senate. So the players that you think that was doing looking after, you know, a certain area of the economy before the players have changed. And so it's important that, you know, we come and meet the new ones, talk to them and, you know, share with them what you do. And the reason that we're having our government relations committee meeting on the 26th prior to the 30th event is so that we can discuss these kind of things, right? Victor, prepare for when you attend the 30th and you're face to face with these government officials that make these decisions. You know, the relationship we need to keep continuing this great relationship where they do return our calls and they do return my Texas and they reply right away, especially when they know that, you know, we have a very urgent question. Yeah. So really, you know, the name of the game is to get engagement. Yeah. And the thing that I tell a lot of the restaurant people when I meet them is that when you see a politician, whether it's a council member or representative or state senator that comes into your restaurant, don't be afraid to go and introduce yourself. You know, they are there as your customer, but it's also, you know, a good way to start the relationship at the grassroots level where you said, hey, thank you for coming to my establishment.   They might not be aware that some of those bills that they passed in a, you know, two, three years ago, that's not make sense. And maybe we can find a way to rectify that later on, you know, but these are the kind of things that they need to hear. They're good, they're better than ugly, but always be called Joe. Yes. And get to know your representatives, not only your home, where you live and where you vote, but also where your business is. Knowing your representative in your business district is also so important because as you mentioned, Victor, you know, getting to know them so when they do call and say, you know, we have a question and we have a comment that they will answer the call and your business is right in their district. That's exactly, you know, make them more than a customer, make them a friend. And anytime you need to reach out, they will return your calls, you know? Yes. And Victor, you do so much work. I tell you, during the legislative session, I think Victor works more for Hawaii Restaurant Association than he does for McDonald's because my phone is going off at four o'clock in the morning and we're talking at late at night, right, Victor, making strategy for the next day. So thank you. But thank goodness for technology, you know? We have Wi-Fi, connectivity, cell phones, so no matter where I'm at, you know, things can still get engaged. You can, it's easy to get engaged, you know? And Victor, I don't know if you saw my email yesterday. It's been dizzy because obviously yesterday was Monday and everybody's back. And then today we're at the hiring event here at the Doe Canary. The National Restaurant Association, Michael, will be flying in for this event. And yes, I sent you an email yesterday saying, sorry, Victor, I'm trying to help Michael schedule a hotel room and get him down here. And when he is here, the National Restaurant Association representative, Michael, he is attending our event and he will be able to also make a few visits and we will be having a government relations meeting when he is here also, Victor. So I'm still waiting for his flight information. So he'll be here for the 30th at least, okay? And then we'll hook up from there. Yes. I didn't get a chance to catch an email from you yet. So, yes, yes. And so it's been kind of busy. I mean, they see all my emails. So they know what's happening here at the Hawaii Restaurant Association and they all want to know, you know, when they can assist us and we will hear from him because, Victor, we want to know at the national level what the NRA, the National Restaurant Association is also watching. They're watching all the states and as they watch all states and they can let us know some of the things that may come here to Hawaii eventually, hit our shores. I'm very familiar with that because I'm also very engaged on the national side, all the states. So yes, you know, I cover for McDonald's, not just Hawaii, but the whole country. Yes, Victor is our National Restaurant Association liaison for their government relations committee also. Jai, Victor does so much. So, Victor, is there anything else before we close our show that you would like to make any closing comments?  You know, if you don't get engaged, you know, you might end up being on the menu instead of, you don't want to be eating up alive. So you don't want to be on a menu. Okay, so you got to stay engaged. Really, it's not that difficult. Our elected officials are people like you and I, they mean well, but many times they hear one side of the story and they don't hear the business side of the story. And I want to encourage everybody to get engaged. You know me, my phone is always available. People can call me, email me, and I'm always working with my fellow restaurant tours to make sure that anything I can do to help because I believe that rising tide raise all ships. So everybody, we work for everybody. So, thank you. Well, I just want to again thank Victor for all of his time.  He just constantly is going all of that effort. So he does all of his energy and supporting the food service industry. Victor, thank you for all that you do. It's my pleasure. And we'll see everybody on the 30th. As I mentioned, tickets are already on sale. Again, my name is Cheryl Matsuoka, the executive director of the Hawaii Restaurant Association. The Hawaii Restaurant Association is the voice of Hawaii's restaurants and food service industry. Thank you, everyone. Take care and see you soon. Thank you so much for watching Think Tech Hawaii. If you like what we do, please like us and click the subscribe button on YouTube and the follow button on Vimeo. You can also follow us on Facebook, Instagram, and LinkedIn, and donate to us at thinktechhawaii.com. Mahalo.


Welcome to non-linear control. So, where we were last time was at the Frobenius theorem we had started discussing the Frobenius theorem. We are going to continue to actually discuss and talk about the actual theorem itself. In order to talk about the Frobenius theorem we first introduce the notion of a distribution which is basically you take all these generating vector fields and you take a span. So, basically at every point P in the state space or whatever set you are working with you get a subspace. At every point P you get a subspace. So, that is what is the distribution itself. Obviously, we do not want the distribution to lose rank or change rank. So, therefore, we talk about non-singular distributions which do not alter in rank as you change the point P. So, we will always work with non-singular distributions and then we stated and proved this lemma which is saying that if delta is a non-singular distribution then involutivity is exactly identical to the Liebrakhet being in delta. So, actually I forgot we also defined involutivity which is saying that if there are two vector fields in the distribution. If fg belong to the distribution then the Liebrakhet also belongs to the distribution. Now, we also discussed this that it will lead us if you want to actually check this in reality you will have to do all these iterated Liebrakhet. So, many iterated Liebrakhet. So, we came up with a single simpler condition which is this lemma 1.3 which says that if you have k generating vector fields for delta then involutivity is identical to just verifying that pair wise they belong to delta. That is it, pair wise you have to check that fifj belong to delta. We also proved this I am not going to go into the proof of this. We also sort of I mean anyway did this example on feedback linearization, this system and anyway we just this is again going back to the previous material. We just took an output which was given to us and then computed the relative degree of the system. After computing the relative degree of the system we saw that it was 2 and the state space was 3 dimensional. So, obviously I need one more additional coordinate and we saw what we were thinking how to choose it. The simple obvious choice does not work. Like if I choose z1 is x1 the derivative of x1 contains the control which we do not like because in the normal form the control appears only in the linear part and not in the non-linear part. So, we do not like this choice. So, obviously in order to come up with this good choice we use the definition itself that is you know we want to choose this phi function such that L g phi is equal to 0 and that gives us a bunch of basically gives us just one partial differential equation. Just one partial differential equation which is looking like this. As you can see this is not completely specifying the function, but we are just going to guess one possible choice that satisfies this relationship and we guessed it. I would say I guessed it. If you can come up with a more smarter way of doing this sure. In fact, we can go later and see how to maybe I do not know maybe it is possible to do better than this. But as of now no we just have this we are basically guessing this function based on the PDE that we have. So, it is not like a completely out in the blue sort of a guess, but it is more like you have a PDE and it is not easy to solve this. So, you will sort of try to do something better. I mean actually you can do something, but I am not going to I mean it is going to be very complicated. Guessing is way easier here. You just trying to cancel appropriate terms and so on and we discussed this last time. This I left for you to sort of look at because this is part of the exercise that was given, but I have it looks like I have already done something on it. So, I leave it to you folks to sort of verify this ok. Now, we actually move on to the statement of the Frobenius theorem itself. Why do we care about the Frobenius theorem? Because we are trying to answer that original question. When is it possible to feedback linearize a system completely feedback linearize system? Until now we have been looking at relative degree something right which is less than n of course the Frobenius theorem is useful even then, but it becomes especially useful to figure out when your relative degree can be made n ok which means that you essentially have the entire system to look like a linear system right after suitable state transformation ok. So, that is the question we are trying to answer. So, Frobenius theorem is what lets you answer that question. So, that is why we are moving towards the Frobenius theorem alright. So, we make a couple of couple of one definition and one theorem right. So, the non-singular distribution delta which is generated by these k vector fields is said to be completely integrable on some open set in the state space if there exist n minus k annihilators ok. If you remember your vector space course annihilators are essentially what annihilate the elements of the vector space vector field or vector space itself ok. In this case and and remember that the annihilator always has dimension n minus the yeah the vector space of annihilators is always n minus the dimension of the vector space itself that is how it works. So, in this case you have k vector fields distribution is non-singular which means delta is of dimension k at every point p at every point p delta is going to have dimension k right because it is a non-singular distribution ok. Therefore, we have n minus k functions ok. So, what are these n minus k functions these are h notice that these are real valued by these are scalar functions ok these are scalar functions and what how do we define them they have to satisfy that L F I H J which is this del H J del X F I is exactly equal to 0 ok this is actually like an annihilator ok. So, here it is not h itself, but you are taking the it is not the h is not the annihilator vector the annihilator vector is the partial of h or dh ok because h is a scalar field or this real valued function yeah, but when I take its partial with respect to x I now get a rho vector right it is it is 1 by n dimension ok. So, this is the annihilating vector field vector ok. So, and further you want that these dh dh is of course this guy itself we have already defined this notation dh is this these dh are supposed to be linearly independent ok ok. So, if this if these conditions are satisfied then the vector field or the sorry or the distribution is said to be completely integrable ok this is just a definition. So, just keep this in mind we do not want to go into too much more detail than this yeah. So, distribution generated by k vector fields I want the existence of n minus k functions such that their dh multiplied by f i is 0 for all i and all j yeah i is ranging from 1 to k j from n 1 to n minus k ok. And of course, these dh have to be linearly independent as soon as I said this dh has to be linearly independent you should be reminded of this lemma 0.2 yeah. If you remember we I mean I will scroll back what was lemma 0.2 yeah we started saying that some row vectors are linearly independent ok. So, exactly like this as soon as I say that these dh are linearly independent you should be reminded of that yeah. So, you are already it looks like there is a connection between what we are saying here or what we want here and what we were looking for there ok all right great. Then we talk about I mean in order to actually verify this result the Frobenius theorem we need the inverse function theorem, but the inverse function theorem is such a inverse function and implicit function theorem. These two theorems are such powerful the results that all of you who are doing anything in systems and control just read and understand this theorem, these two theorems the implicit function theorem and the inverse function theorem ok. Implicit function theorem is an out by product of the inverse function theorem, it's very straightforward what does the inverse function theorem say it just says that if you have a continuously differentiable function from an open set in R n to R n and if the total derivative that is d t of p is invertible ok at some point p. So, d t of p is invertible then the function is not just invertible at p, but in a neighborhood of p ok. So, so all these result both the implicit and inverse function theorem results remember I connected if you remember when I talked about the diffeomorphism right and I said that it is essentially like the equivalent of a similarity transformation for non-linear systems right. So, when I talked about the diffeomorphism how did I verify something is a diffeomorphism I took its Jacobian and the Jacobian has to be invertible right. So, this is where it all that comes from because if the Jacobian is invertible that is the d t is invertible at a particular point then there exists a neighborhood around p in which the entire function is invertible ok. So, it is almost like what we do with linearization in you know in controls also we do this right we take a non-linear system and we linearize around then some equilibrium point and then we look at the linearization the a b matrices and if they have some nice property like if a is a Hurwitz matrix we say that the system is locally exponentially stable or locally asymptotically stable. So, this is almost like that the derivative of a map or the Jacobian of a map actually gives you something about the invertibility of the map ok and this is why these results are rather powerful and applicable in so many different places yeah. So, that is what this is saying is just saying that if you have a continuously differentiable function from one open set in R n to another and the derivative or the Jacobian is invertible at some point p you just have to check at one point then there exists a neighborhood around p in which the entire function is invertible yeah not talking about Jacobian Jacobian was already invertible yeah the function itself is invertible in this entire set ok. So, that is the inverse function theorem and not only invertible it is in fact the inverse is also continuously differentiable ok. So, similarly if you started with a smooth map then the inverse will also be smooth this is exactly what we use to define a diffeomorphism ok. So, whenever you have to check that a map is a diffeomorphism by the way the map t can be is a d t can be invertible only if it is going from the same dimension to the same dimension right. So, therefore, we are always talking about R n to R n same in diffeomorphism right it is a state transformation. So, the number of states here in the left has to be same as the number of states on the right right. How do you check it is a diffeomorphism just compute the Jacobian of the map and the Jacobian is invertible you are good to go it is a diffeomorphism ok and these are admissible transformations state transformations like similarity transformations yeah ok excellent great. Now, we are ready to state the Frobenius theorem ok. Before I state the theorem itself I will tell you that I am not going to do the proof extensively the proof is written here yeah if we actually end up having time I might just do a session separately just for the proof yeah proof is quite involved and but I will encourage you to re-retain you. So, I will just give you a short sketch we do not expect you to do the proof itself. So, I am not going to actually cover it, but later on if there is extra time I will just do a separate session on just the proof ok alright. It is very actually this Vivek's notes is done a very good job because usually it is not easy to find the proof of Frobenius theorem in Euclidean space yeah typically whenever if you remember I told you that the reference was Astolfi Alessandro Astolfi's book. So, most of the notes and everything out there whenever we talk of Frobenius theorem they are working on manifolds not Rn and then there is lot more notation and you know careful bookkeeping there yeah. So, here everything is proved in Rn which is rather nice. So, the proof is very nice please go through it ok if you get a chance. So, let us look at the statement the statement is actually just two pieces one it says that if you of course, you start with a non-singular distribution of dimension k ok always I mean that is what we have been doing then in what this entire thing says is two things one involutivity and complete integrability are equivalent ok. There is two pieces here although it has long statement here involutivity is equivalent to complete integrability that is the one statement and the other statement is that other piece is that if you have involutivity then your there exist some transformation such that your delta looks like a span of unit vectors ok I do not know if you can appreciate it yet. So, I started with what I started with yeah that is what I started with that delta is what it is a span of this guy right some k vector fields evaluated at particular point what are we saying we are saying that something rather powerful we are saying that if delta is involutive in the state space then it is equivalent to saying that this delta is in fact the span of identity vector fields or the unit vector fields what is the unit vector field E i is this E 1 is this. So, obviously it is not affected by point p or anything everywhere it is the same. So, it is pretty powerful it says that there exist some smooth change of coordinates ok such that all these vector fields that you have f 1 to f k looks exactly like E 1 E 2 E 3 and E k ok alright I hope you can appreciate the power of the result ok. And if you remember what are these vector fields there is a right hand sides of differential equation right if you mean that is how we have been if you think about the control vector field is something like x dot is u i summation of u i f i ok that is how we have been looking at right and it basically gives you what directions of movement at every point at every point a distribution test tells you that what are the directions where you can move using this particular control ok. So, if I now say that this span f 1 to f k which is some complex nonlinear function became just span of E 1 to E k.  So, it essentially you immediately can say that at every point in the state space I can move in a k dimensional subspace of that state space yeah that is pretty powerful ok. Also if you replace f 1 by E 1 f 2 by E 2 f 3 by E 3 what is the dynamics come out to somehow looks like some integrators are happening right x 1 dot is x 2 x 2 dot is x 3 no is it look like it is happening maybe not exactly ok that may be not that no no no it is not the integrator is not happening very well let us not worry about that. But the point is the key point is you are reducing this rather complicated nonlinear you know at every point p you get a different subspace different shape of the subspace to a very nice hyper plane ok. So, this is the power of the Frobenius theorem 1 if you have invulitivity of this delta then you get this very nice hyper plane at every point yeah which is the r k dimensional subspace in r n ok and 2 invulitivity and complete integrability are identical yeah if you have a non singular delta yeah and that is pretty cool because invulitivity was some kind of an algebraic computation you know whatever I mean you are just doing Leigh brackets yeah and you just do it is easy to verify yeah and by doing that you actually get that you have complete integrability and when we actually say it is completely integrable you actually got these functions h 1 to h n minus k yeah that is what it means right complete integrability means I actually get these functions h 1 to h n minus k which the derivatives of which act as annihilators ok alright. So, these are what will become a new coordinates right. So, alright proof I will just sketch it for you proof goes in 3 steps in the first step in step 1 what is being done is just this proof that if you start with invulitivity any such f 1 to f k will become even 2 e k ok that is what this step 1 is doing ok it does it in a rather nice cool way ok, but I mean it does not do it ok it does not do it in completeness, but it more or less does that ok that you are if you see these f 1 to f k's you started with f 1 to f k these are and then you ended up with something like even 2 e k, but with something more here yeah with something more here not even 2 e k itself, but up to the kth element this is consistent right it is just the unit vectors first unit vector second unit vector and so on, but there is some terms here ok that is what this does in the first step yeah it all the other thing it also does is it shows that this new vector fields commute what are the new vector fields these guys ok and when we say vector fields commute we mean that the Leigh brackets are 0 ok that is how you define commuting vector fields it is like in the matrix case also right you a b minus b a equal to 0 that is actually the same exactly this for the matrix case yeah if you say linear system case x dot is a x x dot is b x this is the Leigh bracket it is easy to commute easy to compute if I say f 1 is a x f 2 is b x Leigh bracket is exactly a b minus b a ok not difficult you can think about it in fact just a thought experiment. So, f i f j commute ok so earlier when you started with f 1 to f k it was not evident, but once you do this transformation it is evident that the vector fields commute ok alright what do we do in the second step hmm second step is the complicated step actually sorry I apologize here all you show is that the vector fields commute that is all you do not show that it becomes equivalent to e 1 to e k that is done at the in the second step you look at just the last line of second step you can see f 1 to f k are mapped to the constant distribution e 1 to e k ok and what the second step does is it actually comes up with the transformation the state transformation you need a state transformation right to go from the f 1 to f k vector fields to the e 1 to e k vector fields that is what the second step does it is rather complicated because it uses flows and things like that I have actually not introduced this terminology too much again if time permits we will do a separate session on this, but not right now yeah all I am telling you is what each step is moving alright the final step ok once you know that your f 1 to f k's are smoothly mapped to e 1 to e k's ok you try to come up with the h functions for the e 1 to e k system ok what did we do we went from the f 1 to f k vector fields to the e 1 to e k vector fields alright and now in order to prove complete integrability what do I need I need to come up with the h h 1 to h n minus k that will annihilate this guy and it is this is much easier to do right because even annihilating e 1 to e k is much easier right what do I say all I do is I pick this annihilating functions as x j plus k for j starting from 1 to n minus k ok I hope this is not getting already too complicated ok just look at this x 1 x 2 x k x k plus 1 I am going to write this as x k plus n minus k yeah you see this vector yeah let us go back to what we are doing in feedback linearization let us forget this annihilator business what were we doing in feedback linearization whatever was the relative degree of the system we were choosing the rest of the coordinates right if relative degree was r we were choosing n minus r coordinates on our own so that the entire thing becomes a difumorphism right and in the normal form of course l g phi is 0 right it is almost like that almost exactly like that yeah if you look at this this almost looks like l g phi does not it yeah because the g it is the flipped version the g is this guy the vector field and the phi is this guy right exactly looks like even if I if I go back here l f h right exactly looks like l g phi this is how I was choosing the new coordinates right so that the control does not appear that is all this this looks exactly similar to that you make something 0 some l g phi to be 0 it is exactly like that in this case the g is this vector field and phi is this function ok so that is all we are doing if you notice I am choosing the g in a smart way so that this partial multiplied by E i is 0 now I ranges from what 1 to k right so E i has 1 in what position in the ith position right E i has 1 in the ith position and 0 everywhere else and this i is maximum k cannot be more than k now if I choose my this guy is j plus k ok then where will it have its if I take a partial with respect to x this row vector where will it have 1 where will it have 1 in the j plus kth position right it will have 1 in j plus kth position and 0 everywhere else right so definitely I will in so this guy will definitely have 1 in the j plus kth position this will have 1 in the ith position and i is less than or equal to k therefore they do not have this is a dot product right so they do not have 1 in the same position can never have that is how I chose it right this E i will have 1 say here E 2 will have 1 in the second position ok this will have 1 in the j plus 2th position ok so therefore they are not going to be have 1 in the same position so the dot product has to be 0 ok that is it I am just making the smart choice ok why why do I do it in the E i in the E 1 E 2 E k frame coordinates because it is easier it is just unit vectors yeah much easier to construct this ok now once I have constructed this ni highlighter in the E coordinates E i coordinates I can take it back to the original coordinates that is the f 1 to f k system yeah just by doing a transformation that transformation comes from here yeah that transformation comes from here which is why this thing is a bit complicated and it is pretty easy to show that once I make this backward transformation this will also have the same property that del h j del q f i q will be 0 because I moved back and forth with the same coordinate change right I got a very nice coordinate change ok and I constructed a annihilator in the new coordinates then I went back I took that annihilator back in the original coordinates that is it ok yeah the process is simple notation is complicated alright and so what have I done I started with involutivity ok and I proved that I have integrity complete integrity ok.


Final day of the section 8-3-8 finals at the Preserves. Jack Evans on the first, long distance. Overshoots the hole, but on the fringe of the green, he'll be a tap in for him. Brainer a little closer towards a possible team sectional title. How about some Gavin Metz? Same hole where he chipped it in last week. Almost gets this one to go as well, missing by only inches from the cup. Not the performance Brainer boys want today. Alexandria had a winning sectional title. Girls goes to Buffalo, though Metz does qualify for state along with Bemidji's Matt Allen. If you've enjoyed this segment of Lakeland News, please consider making a tax deductible contribution to Lakeland Public Television.


Good day, fellow investors! Yesterday we discussed how one of the reasons why the stock market is so volatile now is that we might be closed to the end of the current economic cycle. And that is something huge, because the end of the cycle means there will be a recession soon. And the recession is not good for stocks. So let's dig into economic data to see how the economy is doing, whether there will be a recession or not, see what are the risks of the current economic cycle turning into a recession and see what does that mean for stocks and what are the likely scenarios. Let's go! Let's start with economic news. The economic news is relatively good. Jobless claims have reached the lowest level in history, very very good, because more employment, more spending, more purchasing, more taxes, more everything, good good numbers. The unemployment rate is expected to fall even further which means more jobs and even a stronger economy. And inflation is slowly reaching the Fed's target of 2% which shows healthy demand for goods and services. To sum it all up, even the Fed has increased their economic growth projections. Things haven't been this good in the past eight years. Why is the market jittery and why is the market nervous? Let's see further. To explain why the market is nervous, you have to see things from a long-term investing perspective, from a cyclical investing perspective. Each economy, whatever economy you look at, is cyclical. That's human nature, that's the nature of the economies we are creating because each transaction that we make is the economy. So we are the economy and we are cyclical. And after eight years of economic growth it might be a good time for the economy to consolidate, slow down, eradicate the weeds, let the good businesses prosper and continue higher after deleveraging and making the growth more sustainable. However, nobody likes that and it would definitely hit stocks. So there are three major components of economic growth. Productivity, the short-term debt cycle and the long-term debt cycle. Today I'll focus on the short-term debt cycle first, mention the long-term to show what can happen and we will touch on productivity some other time as the credit is the most important thing now from a shorter term perspective. If an economy is driven by credit the more credit there is the better the economy will do, the more there will be spending, the more production, the more hiring, the more employment and the credit cycle revs up and things are good. However, at some point that going up reverts and starts going down. If we look at total US consumer credit it is up 45% in the last 10 years. So consumer credit is up 45% since the terrible 2008 and we all know how terrible was 2008 and 2009 and how worried was the financial system for consumer credit and all other credits and now consumer credit is 45% higher. From a long-term perspective this is unsustainable and this also shows that the economy has been driven by credit. So 45% credit growth is much bigger than what the economy grew in the last eight years. If we go back to the unemployment chart we can see that the current unemployment level isn't far from what it was in 2008. This means the following at some point people will reach their credit maximum, higher interest rates will increase debt payments and defaults, demand for cars, trips, pools, houses will drop, a recession is inevitable. The question is only when. So the recession is inevitable. Ray Dalio said and I would say that the probability of a recession in prior to the next presidential election would be relatively high. What would I say? I don't know 70% or something like that and that's huge and that's something the market might start to price in and if the market really starts to price in that probability of a recession you will see it drop to levels of I don't know 1500, 2000, 1500 points etc. That's a very very big possibility. Let's see the long-term credit cycle. This is the long-term consumer credit line and you can see that it is 10 times higher now than it was 45 years ago. This simply means that whatever happened in the last 45 years is thanks to lower interest rates and higher consumer credit. So the good scenario in this case is one where we have a normal small recession, two quarters, three quarters and then a lot of companies go bankrupt but there is enough movement, there is enough productivity to stimulate further growth, growth new companies, changing in models etc. and the economy continues to grow. The bad scenario is one that says okay this piling up of debt over the last 75 years the long-term credit cycle is over and then we might see another 1930s great depression scenario. So those are two possibilities that one should keep in mind and hedge yourself accordingly especially now that hedging yourself isn't that expensive because nobody expects a great depression scenario. What does this mean for stocks? Well the first scenario recession would mean valuations drop, bad businesses are going bankrupt or are being re-bought or whatever. Good businesses drop in valuations, represent great buying opportunities and then you invest and you make a lot of money in the next leg up and that's what everybody expects. So that's the let's say short-term easy recession scenario. However if there is the long-term recession scenario the long-term credit cycle reverts and as everybody has reached their debt ceilings then we are in trouble. Let me show you what I mean by showing your chart. This is the interest on US debt as a percentage of federal revenue. Now it is around what 7, 6, 7% but if we see higher interest rates if we see a slower economic growth projections from the Wall Street Journal are that interest payments of federal revenue will be above 20% in the next what 10 years. That is huge and that would put a huge burden on the US economy, on the US government, on US deficits, on whatever and if this has to be deleveraged from a long-term credit cycle then the whole world is in for a big big depression. I think we are in for a wild ride over the next 10 years and what to do? There are various scenarios. Small recession, big recession, the market continues to go on like it is for the next five years. All possibilities. What is the best thing to do? Always look for low-risk, high-potential return investments or hedges for each of those scenarios. Growth companies that okay those will survive if there is a recession and then they have give you a lot of upside if there is no recession. If there is the Great Depression, stagflation, hard assets, precious metals, hedges with a part of your portfolio that can really reward you exponentially but there is limited risk if the hedges don't work. There is a normal recession then you buy good businesses with good yields, good business modes that will do fine whatever happens. So when you invest, when you position your portfolio, when you diversify, think in those categories. There are more sophisticated ways by those go beyond this video. Thank you for watching and looking forward to your comments. I'll see you in the next video.


Hello and welcome to the session. In this session we discuss the following question which says which term of the AP 26, 24, 22, 20 and so on is the first negative term. So we are given an AP and we need to find its first negative term. First let's see what is the nth term of an AP it is given by tn and this is equal to a plus n minus 1 into d where this a is the first term of the given AP then d is the common difference. So this is the key idea that we use in this question. Let's proceed with the solution now. The given AP is 26, 24, 22, 20 and so on. So this is the AP given to us. Let's see what is the first term of this AP that is given by a and this is 26. Now the common difference d is given by subtracting this first term from the next negative term that is 24. So 24 minus 26 so this is equal to minus 2. So minus 2 is our common difference. Now we need to find the first negative term of this AP. So we assume let the nth term of the given AP be the first negative term. Now the nth term is given by tn so since we have assumed that this tn is the first negative term so obviously this tn would be less than 0. Now let's see what is tn. tn is equal to a plus n minus 1 into d. Now we put the values for a and d so we get tn is equal to 26 plus n minus 1 into minus 2. So this would be equal to 26 plus minus 2n plus 2 that is equal to 26 minus 2n plus 2. So therefore we get tn is equal to 28 minus 2n. Now that we have tn is less than 0 so this means 28 minus 2n would be less than 0. This would further mean 28 is less than 2n or you can say 2n is greater than 28 so from here we have n is greater than 28 upon 2 which means that n is greater than 14. Now that we have n is greater than 14 so this means that n is equal to 15. Now we had assumed that the nth term would be the first negative term of the given AP thus we have that the 15th term is the first negative term of the given AP. So this is our final answer that the 15th term is the first negative term of the given AP so with this we complete the session hope you have understood the solution of this question.