3, 2, 1. Good morning. I'm Dr Bonnie Henry, BC's provincial health officer. And on the line in Vancouver today is Minister of Education Jennifer Whiteside who will be speaking after my remarks this morning. I want to start by acknowledging that today and the day after our day of reflection, I'm very grateful to be here on the traditional and unceded territories of the Lekongun speaking people. The traditional keepers of this land, now the Esquimalt and Songi's First Nation. And I hope that we will all continue the reflection that we started yesterday in our first official day of truth and reconciliation, a reconciliation and have meaningful progress towards reconciliation with indigenous peoples across this province. Over the last few weeks we have listened to parents, teachers, and others who have heard about the issue of the need for this school year. Knowing that we are in a very different position than we were last September with the highly effective vaccines that we have in place. That has made a huge difference in our schools across the province. But we also recognize we are facing a more infectious strain of the virus this year. And there are still many children who are not yet able to be protected. As we continue to recognize that we are protected. As we saw in the data I presented on Tuesday, we have seen a steady rise in COVID-19 diagnoses in school-age children, particularly those 5 to 11 years of age who are not yet eligible for vaccination. And particularly a rapid increase in the last two weeks. The majority of COVID transmission continues to occur in homes and through social networks. And we have seen that throughout this pandemic. But we are also seeing a significant increase in testing in school-age children. And I have showed those data as well this week. Nevertheless, increased diagnoses has led to increase in numbers of potential exposure events and several school outbreaks have also been detected and reported. COVID-19 continues to circulate in our communities. And schools reflect this. More cases, clusters and outbreaks are occurring in communities with the vaccination rates are lowest. And this has resulted in a number of additional regional orders, as we know, and regional interventions will continue to remain an important part of our approach in this phase of our pandemic. Our school teams are committed to ensuring we are taking all necessary measures to ensure schools can continue to provide that all important in school learning for children in BC. We know the absolute importance of the social, emotional and physical growth that occurs in schools and the importance of this to the health and well-being of children and families across BC. We have reviewed these data and the information we have from the first month returned to school. And today I am extending the PHO masking order in schools to cover all students and staff in K-12 across the province. This order will be in school learning and training for the rest of the school term. This order will be in place for the remainder of this school term, additional layer to help reduce risk of transmission in classrooms and schools. I want to extend my heart felt thanks to all of the school staff, educators, and families who have supported the return to school for over 600,000 children across BC. We know this is the best and safest place for them to be in the community or in the province. And this additional measure we are putting in place today is one more layer that will ensure we can continue to engage and support children through this ever-changing pandemic. We will continue to do this in a way that supports the positive aspects that children need to have to be able to wear masks effectively in these settings. I have been talking to a lot of people that they can adapt to this. They have been learning, we have had those first few weeks of school to help get used to it again. And I am so impressed by how resilient and adaptable children are.  It makes you a superhero. It means you are protecting yourself, but you are also looking out for your classmates in your school and your community. And I know that many of you in the school communities can do to protect children and youth, particularly those who are too young to be vaccinated yet. We are thankful that COVID remains mostly a mild disease in children, but we do not want any child to be ill. And we are taking measures to prevent as much illness as we can. I know that these measures will assist in stopping other respiratory illnesses that we are starting to see as well. We are also seeing things like enteroviruses and adenoviruses that cause those common colds. And we are also seeing a bit of para influenza and RSV, all things that can make children ill with respiratory illnesses that can look an awful lot like COVID. It remains critically important that we do those daily health checks and keep children out of the school environment if they are unwell. And I ask workplaces to continue to be flexible to support parents so that they can get through this next few months as we navigate this phase of our pandemic. We will also be making sure that all of those other important in-class and in-school measures that help reduce transmission of respiratory viruses are in place and optimized as we head into this respiratory season. Everything from reduced mixing of classes, staggering break times, reducing people in the school system, particularly if they are not vaccinated, and things like ventilation and increasing outdoor activities, all of these are important layers and adding masks is just one more. I also want to speak to parents. We know how important the social activities and extracurricular activities are for children, for their growth and well-being, whether it's sports or music, we know that these are important for many children in supporting their ability to learn. And we are committed to keeping these going as much as possible as well, and that's why these are so particularly important. If you are living in an area where transmission is increased, it's all the more important that everybody around you are vaccinated so that we can keep these things growing. We need to know for the next few months particularly, we need to keep the priority on the school. This might mean keeping other social activities outside of school and allowing these high rates of vaccination are so protective and are making the difference in allowing all of these other important social interactions to occur too. We have been committed to providing as much data as we can and as we have to our school communities and the team of BCCDC has been working with our education partners and schools to develop a more detailed school specific report. Our first report will be available in the middle of the next three months. We will be able to provide to parents, to school communities and to the public. We know school is an important part of a young person's life for their health and well-being and it is a safe place for many children. And we know that this has been a challenging time for all of our children as we navigate these ever-changing trials and tribulations of this pandemic. It is about learning, seeing friends, getting that around, emotional and mental health support and we need to do everything we can to safely continue this. These efforts are about supporting students, parents, educators and everyone who make our schools an even safer and more welcoming place to be. I will now turn it over to Minister Whiteside. Good morning, everyone. I am Jennifer Whiteside, BCCDC's Minister of Education and I am pleased to join you this morning from the story of the Squamish, Musqueam and Slewa-tooth people. That acknowledgement today does have particular meaning I think as we reflect on our collective experiences across our communities, our province and our country yesterday as we commemorate Orange Shirt Day and the first national day of Truth and Reconciliation. It is a pleasure to be here with you this morning. I wanted to say that we are now a month into the new school year and hundreds of thousands of children across BC are enjoying being back in school with their friends, learning in class with their teachers, playing outside, playing sports, we are taking part in band practice. As we have known since the beginning of the pandemic, in person learning is absolutely essential to students' emotional and mental well-being as well as for their intellectual development. From the beginning of the pandemic, our top priority has been the safety of all students, teachers and staff. We would not have gotten through this in the way we have without the incredible work and commitment and dedication of our educators, of school staff, school leadership, district leadership, trustees, rights holders, everyone working together across our education system to put kids at the center of all that we do. That is why we have worked so closely with the public health and safety guidelines that keep everyone safe while allowing that crucial full-time in-person learning to occur. A year and a half now into the pandemic, our experience tells us that COVID exposures in schools are indeed a reflection of what is happening in the surrounding community. That continues to be true. We have developed health and safety guidelines for all schools in BC that reflect the current situation with the COVID-19 pandemic. And in August, we announced that the mask mandate that was in place last school year would continue for all students in grades 4 to 12, along with the strong recommendation for mask wearing for students in kindergarten to grade 3. And I want to say that with respect to our school safety plans, we in fact maintained many of the measures that were in place last year to protect our school communities and to provide continuity. I don't want to take a long-term look at the guidelines in particular who have led their districts through a very challenging time and who continue to work closely with health authority school medical officers in their regions to support the school safety plans. And indeed, as Dr. Henry has noted, today we are in a much different place because this year we have vaccines. And we know that immunization protects communities and protects children.  We know the best protection for kids in our schools, especially for those who are too young to receive a vaccine, is for everyone who is eligible to be vaccinated. And I am asking you now, if you have not yet had your shot, now is your time. We also know that the Delta variant of COVID is more likely to go well, especially in areas with lower vaccination rates. And I, too, have had the opportunity to speak with many parents, educators, some kids as well, members of our school communities over the last few weeks. And I know that for many, the return to school is going well and in many cases, there has been minimal disruption from COVID. But for some, and particularly those communities experiencing high rates of COVID, there is a chance that people across the province will welcome these additional measures to keep our kids safe. So this additional step gives families and parents more reassurance, I think, about the safety of the school environment. We have also heard that parents want to be kept more up-to-date on what is happening in their child's school. And that is why public health is now providing regular updates on health authority websites about school and public health. And we have also announced that Dr. Henry has made with respect to the extension of the masking requirements in the public health order. We will, of course, update our education guidelines to reflect that, to reflect that all children in school, from all students in school and staff, from kindergarten to grade 12, must wear a mask while they are inside schools, including while at their desks and on school buses. And we have also announced that we will provide guidelines which already, as you know, require masks for students beginning and grade 4 in all public and independent schools. And again, with respect to notifications, I just want to reiterate that where there is a new, an exposure in a school, contact tracing continues to be in effect. And if your child has been, is at risk of an exposure from COVID, you will be notified. I think we will all welcome the report that Dr. Henry has spoken to with respect to a bit of a status update of what is happening in schools with respect to the virus. And look forward to seeing that in mid-October. So again, you know, as Dr. Henry outlined, these new measures extend our current health and safety guidelines. And there are many elements of that plan that are very crucial to ensure that we are, that the school communities are acting by every day. Doing the daily health check every day is very important. It is important that both students and staff stay home while they are sick. We have hand washing regimes. We have all of the strategies that are in place in our health and safety guidelines to reduce congestion and manage crowding in schools. We have school districts have been improving ventilation systems. And these measures, they were in place last year. They are in place this year. And just to remind folks that of course, public health officials continue to monitor what is happening in our schools very closely and continue to work with school districts. We continue to work at a provincial level with all of our education partners. And to respond to changes as they occur. And that is really what this is about today. Just by way of closing to say again, the most important tool in our toolbox right now is vaccination.  But we need to ensure we keep that going and I strongly encourage anyone who has not yet had an opportunity to get vaccinated to go and do so. Thank you so much. And I think Dr. Henry will start with questions on that side. And Dr. welcome everyone. A reminder to reporters on the line, please press star 1 to enter the queue. You may ask one question and one follow-up. A reminder as well since we are in two separate locations today. You are welcome to address your question to the spokesperson of your desire but we will probably start with Dr. Henry and Minister White-side may follow up. Please be patient with us as we work through this. Thank you. Thank you. I am just wondering what changed in the last three days we were talking about this very issue on Tuesday. Does this signify, like this move that you are making today, that you didn't have public confidence in your back-to-school plan? No, I don't believe that's it at all. We have been monitoring the data and I am not the only person who makes these decisions so it is important to look at both. It is in partnership with the school districts, the parent advisory committees and others. It was a matter of time once we had the data that we presented on Tuesday to look at what are the important measures that we need to do. I indicated, I thought quite clearly on Tuesday that these were things that we were looking at. We weren't at the place yet where we had all of the decisions made. I do. I know that this back-to-school plan was announced in late June, promising a school year that was as normal as possible. Maths are a small step here, but why not mandate vaccinations for all adults in the school system and bring in portable air filtration for each classroom as Toronto has done? I will let the minister talk to the ventilation question because I know a lot of work has been done on that. We strongly encourage everybody in the school system to be immunized. We knew that in June, we knew that when we updated in August, we have been following that of course with messages every day since that time. One of the things that we know is that we are not seeing a lot of transmission in the data I showed last week or on Tuesday, it shows that quite clearly that in that older age group in the 12 to 17, we were most started to see leveling off. We haven't seen transmission in the staff in school settings as much as we were seeing last year. So these tell us that the immunization program is working. And the challenge of course is that everything we need to do now is to make sure that we are keeping the younger kids from getting infected with COVID over this next period of time until vaccine is available for them. And the challenge is that the local MHOs are working with each school. And when we see people who are exposed or where there is outbreaks or clusters in the school, those who are not immunized are excluded from that environment, which is what we do for other infectious diseases as well. And that means that can be quite disruptive. So those are other incentives to make sure that people are immunized. And that is one of the ways that we are able to make sure that we are able to keep the rates of immunization in most school settings. And now we will go to Vancouver to hear from Minister Whiteside. Thank you. And with respect to ventilation, our government has invested $87.5 million over the last two years for districts to do the very important work of properly maintaining and upgrading their HVAC systems. And we will look at the fine details of how that work has unfolded. And to look at those particular areas where there may need to be particular mitigation efforts in place such as portable air filters. And those measures have been implemented by districts where warranted. For example, in Abbotsford, the school district has invested in portable air filtration systems for deployment in classrooms where they are unable to upgrade the mechanical HVAC systems. For the next question, we continue on the phone lines. We go to Camille Baines, Canadian press. Hi there, Dr. Henry. A few days ago you mentioned it would take some time to post information on exposures and cases. On average, how many days is it taking and if you could please walk me through the process, that would be great. Thank you very much. Depending on how many cases are taken? How stretched our public health resources are. And as much as we are trying to ramp up the public health resources, there is a finite pool of people to do that work. So what happens is public health is notified when a positive laboratory test comes in. So we get automatic notification from the lab. So somebody has to be a child, has some results, usually is within 24 hours. And we now have a process that parents or people who are tested themselves are automatically notified. Usually by text, but it could be by email as well. And so you are likely to know at the same time that public health receives that notification. And when we receive that notification, there is, as you know from looking at our numbers every day, there can be people that are tested positive every day. So public health has a system where the intake looks at the age of the person, the setting that they are in. And so we prioritize school-aged children for example to do that case follow-up. But it does mean that one of the public health team, the case and contact management team calls the parent and finds out the information about where the child was, what symptoms they have, where they were exposed to, because remember we are still trying to connect and look for clusters and outbreaks in our communities, in our schools, and also where they were during the period they were infectious. So it can take as short as 24 hours. That is our attempt is to make sure that once we get that positive lab report that we are trying to contact cases within 24 hours. But you can see that that may be a fact that the parent knows that their child is ill and when they get the test result back. And in some cases, particularly right now with a large number of cases that are occurring in the north and some parts of the interior, it can be a delay of two to three days. But our attempt is to try and get to most cases within 24 hours. So once that case investigation is done and there is a determination that the child is getting during their infectious period, and they had the type of contact that it might be transmitted to others. And so things like, was their mask wearing, what types of activities were they partaking in, et cetera. That is when we put the notification out and contact those who were potentially exposed directly. And that is when it gets posted on the website. So I think we all need to recognize that this does take time. And it is absolutely important for parents to know that if their child is sick and it does come back positive, you can share that information with those people that your child has had contact with. And I know there has been some reports of parents doing that. And I think that is great. We all need to support each other to do the best we can during this period of time. And public health is there to do our best to support you. And I think that is a great feature because we do those detailed case investigations and that is when we can tell whether there was an outbreak happening where there was transmission. And we can link it between different classes and sometimes it is related to siblings, sometimes it is related to things, social events that have happened outside of the school setting that we can actually see that bigger pattern as well. So it is all of us working together on this. And it is important for parents to know that if our child is sick, keeping them home and away from others until they are feeling better. Camille, do you have a follow-up? Yes, please. I am also hearing that for some schools, the information being posted is quote-unquote selective so that not all of the cases or exposures are being included and parents are therefore still having to rely on each other or another person to provide information on its website. Could you please address those concerns? Yes, so, you know, there is always, there are many reasons, as I have talked about, while a child may be or an adult in the school system may not have been a risk while in the school and parents can share that information about their child's illness, but public health will be posting when there is a risk in the school system. So, I think we are catching up with that now. And yes, sometimes parents will know and they will know the information from other parents prior to public health getting all of the pieces connected together. So, I think we have to work together on this. This is not about, it is not about saying that this is wrong, we will never be able to catch up to somebody passing that information together on this. It is not about us versus them and who is getting things right, it is about making sure we all have the information we need. Now, we will come to the room. The next question goes to Richard Zussman, Global News. Developmental Binder was asking, California has now announced their mandating vaccines in the entire school system that includes children as well, phasing in those under 12 when they are eligible for vaccine. So, why can't BC get ahead of this and get to this mandate which many may think is inevitable? And also, we are, I will leave it there. Thanks. We have talked about this many times. There are different ways that we can have conditions of employment that require immunization and there is a whole lot of different pieces that go with that. So, my responsibility under public health orders is to look at those highest risk environments that are in the health system. So, that is what I am focusing on from public health orders. We absolutely are supportive. There are many other higher risk environments where the virus can be transmitted between people and we think of group accommodations, industrial camps, prisons. There are many settings where an employer needs to have those policies and the employees. I do. There are wide exemptions for masks right now on the government website. Are those exemptions still going to exist and who is going to be in charge of enforcing them? And on a separate issue, there is a petition circulating around concern that at Whistler Black Home there is no vaccine certificate required to ski and ride is the province considering adding ski resorts as a place where the vaccine is. It is a place where the vaccine will apply. Okay, complex. I have forgotten your first question already, you got me too. Oh, mask exemptions. So, you know, there are some people who have challenges wearing masks. We know that and we have put in place exemptions that allow people not to wear masks in certain situations. And that goes for schools too. And we have been approaching it in schools as a very mask positive environment. And yes, there are some children that have difficulties with it. And we know that, especially younger children, it can be a challenge to keep it on and not play with it and it's irritating and some days you're not feeling. So we need to have that positive reinforcement in schools and I know educators and teachers are doing that in a really positive way and that's how it works. And I believe in masks that they are not entitled to have the same access to those indoor environments. Accommodation could mean that a grocery store can take your order online and have a drop-off at the door. So it does not mean just because you don't believe in masks that you can still do those same things in the same way because that could be putting others at risk. So if you are not able to wear a mask, could be online shopping, taking take-away, et cetera. And the Human Rights Commissioner has supported us in those restrictions and ability to accommodate but not necessarily doing everything that somebody who can wear a mask can do. In terms of the ski resorts, the vaccine card is in place for all of those activities that we have and all of those activities like restaurants, like the restaurant on the hill, et cetera. So the outdoor skiing environment we know was not the risky environment. However, I would encourage all of the ski resorts to put in place those measures that protect people as best possible. And now we will send it over to Vancouver to hear from Minister Whiteside. Thank you. I just wanted to weigh in on the enforcement and just to reiterate that I know how much effort educators and school communities have put into creating positive cultures around mask-wearing in schools, including at the younger grades, including in K-3. And I know that in many communities, this won't be a big shift because this is happening anyway. And we would expect that that positive encouragement to continue to be the way in which the way in which school communities approach this question. It is very much as they have been doing throughout the past year. And I think it has been quite remarkable to see the degree to which in many schools students have really picked up on this notion of caring for one another and doing everything that they can do as well to pitch in with the effort. And for the next question, we will ask the question to the CBC. Thank you very much. Doctor, are you tracking instances of vaccinated parents and grandparents, for instance, catching COVID from their unvaccinated school-aged children, or hearing from multiple vaccinated adults who have gotten COVID after classroom exposures? How big of a concern is that? So I'm not on an individual basis. We do know there have been some instances and sometimes it is very challenging to understand exactly who is vaccinated. And as we have seen in the numbers that we report, of course, there is a breakthrough transmission. But I will say how important it is because we know that people who are vaccinated are much less likely to get sick, much less likely to get severely ill or hospitalized, and we presented those data as well. And that holds. So even if a child brings it home, we know that if your parents are vaccinated, they are much less likely to get severe illness and less likely to pass it on to others. So it is a challenge sometimes to know exactly who is transmitting to who. But we know as well that there are communities, Fraser East, we know in much of the North, communities in the interior where vaccination rates are not high enough and we have a lot of transmission in the community that it is going to continue to spread. And that will help us curtail that so that we can continue the all important in-class learning that children need. Susan, do you have a follow-up? Yes, thank you. Just one quick thing first. If you could clarify as far as the timing, is this the renewed for K-3 ending in the spring break, December or spring break, rather, Christmas break? And then will you reevaluate it? And then also, is there a role for rapid testing in trying to help us in the respiratory season outside of the industrial business settings? Should rapid tests be made available to people, parents, for instance, we have seen it done in the UK who want to either rule COVID out quickly at home if they have symptoms or perhaps catch it rather than tying up resources at testing centres? Yes, really good question about that. Let me go back to the first one. This will be in place to the end of this term and we will be using the data to not to wonder when this is going to end. The mask order is in place until January, so that's at least until then, depending on what happens in the next little while. And of course, we're hopeful that there will be vaccination for younger children in the coming months as well. So that will factor into how long we'll need to keep this up in schools. Having said that, we know that this is respiratory season, which means there's a lot of people who are asking, does help to prevent other things as well. And this year, we're starting to see more circulation of other respiratory viruses than we saw last year. And influenza is likely to make much more of an appearance this year than last year. And we do have safe and effective influenza vaccines for children and especially school-aged children. We know that influenza, unlike COVID, can cause very serious illness more frequently in children. So that's something to pay attention to. And influenza vaccinations will be available very soon, too. In terms of rapid testing, the UK has a program where they're using take-home, at-home, lateral-flow tests, and we don't have those types of tests available yet in great numbers. There's been two that have recently been approved for use in Canada by Health Canada, but they're not yet available. And I think there's a role for that type of test for at-home testing. Right now, though, what we're doing is making available the gargle, the swish and gargle test, to school-aged kids around the province, making it more available so that you can pick up the kits through schools, pharmacies, and other places. It is a PCR-based test, so it's still a lab-based test. And the strategy moving into the fall has been to be able to test for multiple viruses at once. So depending on the symptoms of the person going in for testing, we'll be testing for all of those. So COVID, RSV influenza, and some of the para-influences as well. So that's what we've been ramping up over the last little while, one for surveillance, but also so that we can tell which are the viruses, which are the mandatory viruses that are causing the most illness in different parts of the province as we get through this next few months. For the next question, we go to Mary Griffin, Czech News. Thank you very much. Dr. Henry, I'm just wondering, is there a possibility that, because you've been asked, of course, many, many times about the mask mandate, and now it's implemented until the end of the school year, that there's a possibility that there's going to be a mandatory vaccination in the school system, because now we're hearing from the BCTA that they're not opposed to mandatory vaccination. Are they not, the staff and teachers also, members of those communities where the COVID-19 infection rates are rising? Absolutely. And, you know, we absolutely expect that all school staff take advantage of the prioritization that we gave to the community and the prioritization that we gave to school staff early on in the immunization program to take advantage of the protection that it offers, not just them, but their community, their own families, as well as the school community. And, as I mentioned earlier, my focus in terms of provincial health officer orders around vaccination is on those highest risk settings, where the risk to those who are exposed from workers is the greatest. And that, as you know, includes long-term care and assisted living, which is incredibly important. We know more and more, even with fully vaccinated residents, unvaccinated people introducing the virus into those settings is extremely dangerous and leads to unnecessary deaths. So, that is our focus. We also have put in a requirement for masking as a condition of employment for all healthcare workers, recognizing as well that those are high-risk environments for people who have underlying health conditions and are more vulnerable to infection to severe illness and to death. It is an employer-employee relationship in many other settings. And we are seeing increasingly that employers are requiring vaccination in many different settings. And school settings are no different. Do you have a follow-up, Mary? I do. Thanks very much. You just mentioned the vaccinations for younger children. Just wondering if there is any update on when parents could expect that for the under-12 group. And just following up, part two on Richard's question on the resorts and you suggested that you would encourage all those resorts to have their children. What was the first one again? And that stayed on the vaccination for younger children under 12. It has been a long week. So we know that Pfizer has submitted a part of their data package to the FDA. I know Health Canada is still waiting for that. We expect it to be. So what happens is they have done a number of press releases about their phase 3 trials and the effectiveness of the vaccine or the efficacy of the vaccine in stimulating a strong immune response in children. They need to submit that entire package which shows all of the safety data and how well it worked and the immunogenicity data. So it's what we call a bridging study. And then Health Canada reviews that. What we also know is that this is a new formulation. It's not a new one until the data package is submitted. But we understand it's a smaller dose. So 10 micrograms instead of 30 of the antigen. And that it's likely to be reformulated so it's a fridge stable project. Which is great news for us because that makes it a whole lot easier to distribute. And once the package is submitted to Health Canada, history has shown that it will be able to do all of the effectiveness data, all the effectiveness data, and they have to review the manufacturing, the safe manufacturing processes as well. So it may be as early as the end of October is what we're hearing, but it may take more time than that. But I am really hopeful that we will have vaccination for younger, the 5 to 11 age group anyway, before the end of this calendar year and hopefully as soon as possible. In terms of the vaccine card, so our vaccine card program is very specific to the BC vaccine card program is very specific to certain settings. So if you want to go to a bar or a pub or a restaurant or the restaurant on the hill, then you need to have your vaccine card. I would encourage all of the resorts to look at all of those settings where it might be prudent for them to have the vaccine card. The risk is less when you're outside. We know that in smaller groups and when you're wearing masks and goggles, et cetera. So for a short period of time on a gondola, the risk is probably not the same as if you're sitting down inside without a mask on, having a drink with a group of people. Next question goes to Robin Crawford, News 1130. So much for taking my question. What's the advice for families here in Metro Vancouver with getting together? You know what the advice is, get vaccinated right now so that you can get together safely with your family. This virus is still out there. If you're going to have older members of your family coming together, then you want to make sure that everybody who comes into your household is immunized. We know there are additional people in the community. And that means you can only have five other people or one other household together if they're not all fully vaccinated. The vaccine is our way to mitigate the risk across the board. So now is the time to start thinking about getting that vaccine so you can go home and visit with your granny or grumpy or your uncles or sisters who are immune compromised with those people in the community who are not vaccinated. Do you have a follow-up, Robin? I do, yes. And my second question is for minister Whiteside. You just spoke a little bit about keeping that positivity in the classrooms with the mask mandate. Is there any specific advice you have for the younger age teachers with having the kids not playing with their masks and taking them off while sitting at their desks? I think we have this now with COVID. This is the third school year that we are entering into with COVID and with our safety plans in place. And so there is considerable experience out there on the part of educators. And I think as Dr. Henry said earlier, it can sometimes be difficult for little kids. But I also think that there has been that many parents in many communities have worked very hard with their children to get them to see many little ones out there when they are shopping and such wearing their masks. So I think there can sometimes be challenges, but we have very skilled and compassionate and smart educators who have been working on this and who are going to continue to do that work with the little ones. And for our final question, we go to Colton Davies, radio and out. Colton, are you there? Hi, can you hear me? Yes. Bringing this up again as we heard concerns from parents in recent days about cohorts. Some parents around here wanting cohorts to be brought back as a way to limit exposure in elementary schools, particularly with the grades that aren't vaccinated up to grades 6 and 7. Is the province planning or even considering bringing back cohorts for elementary students and why or why not? I'll start and then maybe I'll turn it over to you. What were the things that impeded schools from having been able to cause more problems than benefit or impeded the working of the school? So we had the concept of cohorts last year or learning groups that were different sizes depending on the age of the children and the school system. And they, we found that they weren't a tool that was needed to prevent transmission and they caused significant challenges in operations of schools at all levels. So this year we've taken out that concept of the official cohort or learning group but what schools have done is on a school by school basis looked at the measures that are important and the important things were reducing the mixing of grades in particular, reducing the number of people in the school, reducing the grade of the school, reducing the group gatherings, whether it's assemblies and other things. So those are the things that they've looked at to try and make sure that we're having the effect that we want which is to prevent transmission between large groups in the school setting and not impeding the operations. And it made a big difference particularly in the older grades but also in the younger grades about which classes could be taught by schools. So it was not found to be helpful in terms of disease control and it was found to be impeding the operations of schools. So I think there's other measures that we're using now rather than having the official learning groups that we had put in place last year. And Minister, maybe you want to talk to that as well. Yes, thank you, Dr. Henry. And it's important to note that cohorts operated differently in schools. And there was, when public health determined in June, as part of our update in June, that it would not be, cohorts would not be, learning groups would not be required, there was really unanimity around our education sector table. That was a good thing because it posed very many challenges in many respects for learning, particularly for and timetabling, particularly for grades, for the high schools, for the high school grades. With respect to elementary schools, as Dr. Henry pointed out, there are many different mechanisms and ways that schools can use that are enumerated in or that are listed out in our safety guidelines around managing congestion and crowds in schools. And that has to do, that will be very much like how they operated last year. And it may be staggering time on the playground. It may be staggering recess times, staggering lunch break times, those kinds of things. So our school, our principals and school staff are very, very used to and adept at that. I think that there are, there is also great attention being paid right now to, you know, not having assemblies of many hundreds of kids together. I think that people are being very careful out there about respecting and respecting how quickly we move back to some of those kinds of activities. And again, these measures will be supported by our health authority school, medical health officials who work, our officers who work very closely with school districts. They track what is happening in particular communities and work with the districts and the schools to put in those and encourage those, in those particular recommendations around how to manage those issues. And the Interior Health Authority right now, we have a set of recommendations in place right now in Interior Health around limiting gatherings inside schools, limiting visitors to schools because of the particular conditions, the particular conditions there. So we still have those tools available. Cole, do you have a follow-up? Do you think, you know we've heard, and this would be for Henry, I know we've heard from you and you've heard from the people who are now with the unvaccinated and it was pointed out to me this week that includes anyone under 12 years old and most elementary school-aged kids anyways. And so I'm paraphrasing based on conversations I've had with parents in recent days. But what would you say to parents, what assurances might you have for parents who feel that their elementary school-aged kids might be more at risk right now than last year compared to so far through this school year compared to last year? I hear you, I know there's a lot of anxiety as this pandemic goes on and on and it changes. And we've had to change and adapt as we've learned more, as we've seen a more transmissible variant. But I think I can say with confidence that we are in a better place in our schools. That's because the adults in the school system have the ability to make sure that all of the adults and older siblings who are able to be vaccinated are, that protects the young kids, it protects the schools and keeps them open, but it also protects our family and our community. And that's what we need to do right now. We need to raise up all of our immunization levels because it is what makes us safer as a community. It means we're working together and it is that active altruism that is going to get us through this. So even if you have concerns, get those questions answered. We're here to help answer those questions. This is about all of us working together. And schools are an important reflection of how we're doing as a community working together. And there are many parts of this province where we need to do better. We need to support each other and get vaccinated. And for today, thank you very much. Have a great day. Thank you.


headline news update welcome folks we have the now industrial side trading up one eighty nasa gets down one thirty eight s&p's flat gold gold contract down eight dollars ten cents trading at eight at seventeen eighty eight an ounce we have silver down seventy two cents twenty three dollars fifty seven cents an ounce light sweet crude this is kind of intuitive this is pretty cool folks light sweet crude up about ninety seventy eight dollars sixty six cents and that's with the U.S. and about five other countries going to release lots of oil but guess what that demand has to be there man because that oil contract wants higher price notes and bonds a ten year note right now down seventy six trade in one twenty nine twenty five the thirty year up one full point at one fifty nine eleven and king dollar king dollars down sixty six six trade in ninety six four eighty two euro is at one twelve the end is at one fifteen and the British pound is trading at one thirty three to one U.S. dollar we get open we take a look at the markets out here you take a look at the spy first what you have out here you get a sideways moving the spy you rejected lower price at four sixty four you're at four sixty seven you've done forty nine million shares yesterday we hit a high with let's see what we did here hit a high with seventy three now when you hit a high with seventy three million folks okay that and you give it up on price most times you go right back top side so my take is we're going to go top side and test that level once again now the net the NBX you've got to check this out man because this is pretty cool so the NBX right now we got down it went to a higher high yesterday you got in sixteen thousand seven sixty four low today is at sixteen thousand one twenty one this little baby is a different animal that this little baby we'll see whether we get another a down day out here tomorrow and if you get another down day and the NBX with the same amount of space what you set up you just set up a nice candlestick charting pat and most times that patent that is set does retest also which is just a total mind blow but that patent itself is really bearish in a monster way it's very hard to set them up that's the real bottom line gold gold contract they got gold down into the swing well hasn't hit the swing point yet like this you know we get down to seventeen eighty four you're only seven dollars off of that level right now the swing is the top of the swing is seventeen ninety ninety one which you're into the bottom is seventeen sixty six say right there folks come right back


Hallo iedereen, mijn naam is Sander van Gelooven. Ik ben van stichting Z25.org van The Netherlands. Ik ga over de architectuur van digitisatie en ontwikkeling. En ik ga ernaar kiezen wat er is. Een kort introductie over mezelf. Ik heb een bepaalde achtergrond. Ik heb in het ICT gekozen over 20 jaar. Voor de laatste 10 jaar, een self-employed entreprenuer. Ik heb het vorig jaar gesproken over integratieve spel- en grammar-checking. En dit jaar, over het project met het stichting Z25.org, over de ontwikkeling van de ontwikkeling. En een aantal van deze andere ontwikkelingen, je kunt het op mijn github-account zien. Er zijn er veel dingen. Ik heb een bepaalde geïnteresse in veel verschillende dingen. En dus ik ben in het ontwikkeling van de ontwikkeling van de ontwikkeling. Oké, dus ik ben in het ontwikkeling van de ontwikkeling van de ontwikkeling. Dat heb ik nooit gedacht dat ik het in zou gaan.  Op een heel oud ontwikkeling. We hebben het geld voor het. Hoe we de projecten rondkomen. En wat soort open-source ontwikkelingen hebben we gebruikt om dit ontwikkeling te creëren. We zijn van de stad van Utrecht in Nederland.  En ze ontwikkelen het ongeveer 3 jaar geleden. Maar het is een publiek gebouw en het is een monument, een state monument. En het is gewoon een inspiratie voor een lange tijd, voor mij persoonlijk.  Die het kunnen weten. Oké. 400 mensen. Het is een prachtig overwelming atmosfair als je erin bent. De initiale ontwikkelingen zijn van de 20e. En het is een moderne gebouw. Maar het is volledig een soort... ...detail decoratie. Waarschijnlijk de meest belangrijkste zijn... ...numeren van statuën in de hoofdgrond. En deze zijn 5 of 6 statuën die hebben ladders op hun hoofdgrond. En over de jaren heb ik de idee van... ...maar het zou mooi zijn om die ladders te digitiseren... ...en te creëren van het fond. Maar ik heb veel van deze kleine ideeën... ...en dan om een hobbyproject te ontdekken. Dus waarom kunnen we dit niet in een meer serieus project... ...en het zo funderen om het te doen en het proper te doen? En ik weet niet of iedereen van jou ooit de fond ontwikkelt. Oké. Dus een fonddesign van zoveel vrienden van mij... ...die ik toen op de eerste stage van deze project... ...die zeiden, oh, je draait over de lijn en dat is het. En dan heb je het gedaan. Maar het is een beetje meer een beetje trickier dan dat. Sommige... ...maar ik ga naar dat lader, sorry. Ah, ik heb dat bepaald. Ja, oké. Een beetje achtergrond op de sculptuur, by the way, ...before I go into the design of the font. De guy was the third most influential sculpture in the Netherlands... ...for sculptures which are commissioned by buildings... ...that were built by the state. And you can find some of his work on the internet. And we didn't know much about buildings... ...oh sorry, sculptures for buildings. But back in the 20s and the 30s this was a big thing. And especially in the style he worked in, the Amsterdam school. There's many buildings in the Netherlands which have not just bricks... ...but also many decorative elements, many statues. Then this is a font about 100 years old. And we were walking around in Brussels the other day. So we thought like maybe there's some references... ...of current day usage of such a font as you saw on the statues. And there are plenty of examples you still find... ...of this really thick 100 year old font design. So even though it's old it's still relevant to useable... ...if you like something in this style. Then to go into the characters a bit more. So if you stand in the hall and you look up to the statues... ...this is what you actually see.  And there are many more aspects which make it not so easy to digitize this font. Such as the edges are pretty rough. They look smooth here but if you make a detailed photograph it's pretty messy. The letters are adjusted for height. En as you can see here the eye is sort of pushed together... ...in order to fit the whole word Australia. The proportions are also changed from statue to statue. So this little bar here from the E is in some statues a bit higher... ...and the other one is a bit lower. Some details differ and for example the K. The indentation on top sometimes has a little bit different shape.  Dus if you want to do edge detection on this, it's an extra challenge. What else? There's a whole list of stuff which doesn't make this easy. The original designs were made on gypsum... ...and they were even as maybe sometimes less accurate as the final result. So even if you have access to the design it doesn't make it that much easier. So we went there with my colleague Machiel... ...en took some pictures of this which was not easy. Specially you have to get to an elevated position to make the photographs. And even then if you zoom in in the photographs you'll see that... ...at the end of the picture already you're looking up... ...like if you're standing down and you get some distortions in the properties. So, that's the whole list actually. To get more acquainted with these letters I made some models of them... ...which was a fun project to get away from the computer once in a while. And you get a bit of a feeling. And it's not only for yourself as a study... ...but if you want to do such a project in a more serious way... ...and you've got some funding... ...it's very good to take that to the people you're talking to... ...and put it on the table and they can feel it... ...and then it speaks a bit more than just a photograph of some letters. So that was sort of a side effect which was very helpful. In order to get access to the designs that were made by this sculpture... ...which is already dead since before the Second World War... ...I requested access to a depot of a museum... ...and it took about five months to get the access... ...and it's a pretty heavy guarded place. En in there they searched for all the designs they had from this guy... ...and they put them on display for me... ...so I could study them and look at them... ...how he made those statues and all the works. And that was what became very clear pretty quickly was that... ...as you can see here maybe... ...is that the sides of the characters are not on a 90 degree angle. They are on a bigger angle. So if you have a statue in order to make it easier to look at... ...the sort of a beveled side to it... ...which doesn't make it easier if you're going to digitize it... ...because some details are smoothly going from the front surface to the back... ...and makes it challenge even bigger. But they had very nice designs. This one is from building in Amsterdam. It's a lobster. And it's about this big. So they pulled out all these gypsum models for me to look at for about two or three hours. I had the biggest fun with them. They had some sketches. This is also in the same post office made in tiles about three meters high. And some sketches. Those were most interesting to me. Here you can see how he created the characters in his sketches... ...but also in his statues. It helped me a lot in the digitization process and the design process. These statues only have 13 different characters. And for the alphabet you need 26. And you're still not there if you want to make a font for a wide range of applications. For some letters like from an E to an F in this kind of font it's pretty easy. But some characters you have no idea how to get started. So I'm looking at all these sketches and stuff. It gave me some ideas on how to construct these missing letters. But then you have the idea like 26 letters. Where do we stop? We can make a sharp S or we can make an IJ ligature... ...which is often used in Dutch. You can make numerals. I made a long list of about 400 different characters or glyphs... ...which I would like to design. If you grouped them together and draw the dependencies... ...for example if you have an E already and you want to go to an F... ...then it is a pretty easy step. This is the whole bridge made in one overview. All the black things. These are the characters which were on the statues. And if you want to start working with this then it's a bit tough. So I sort of grouped this together in a simple text file. And I prioritized my design. So for example the F could be derived from the E, the I from the T etc. Sometimes from multiple letters. En of course it's FOSDEM, so you want to see code. I processed the TSP file through Python. And with graph is I made some PNG files of prioritized dependencies of glyphs... ...in order for the design of this font. And then it became much more clear. In how I would go about designing this font. En also talking to people who were interested in financing this project. This would be more practical if you say well if you give us this much amount of money... ...we can do this work. Or maybe if you give a bit more we can design numerals. And if you have numerals we don't have only 10 extra glyphs. We have a whole bunch of stuff like superscript subscript. We changed this whole forest of glyphs into 10 different work packages. We were not able to see if we could find funding for this. So how do you find funding in these times? Anyone? Crowdfunding. We made a little video about this post office. And the statues and the idea we had. We set a target of 500, 200 euros. We came up with some ideas, some bags which could print stamps, books. People could adopt a letter. And they could choose a combination. Eventually we raised 5,820 euros. And by 500 or 5 people. And it created in our city a lot of attention. This post office is going to be designated for the library and some other re-usage. So a lot of people were already having a focus on what's going to happen on this building. So we sort of hitchhiked along with that. And well, sort of national online newspapers also wrote an article about it. En from that point we could also start working on co-funding. Because with these 5,820 euros we could do part of the 400 glyphs. And if you want to do more, we want to have more funding. And we also wrote applications to national and local state funding organizations. So this is a passion of the stuff we write. And we had a kick-off event during Bring Your Own Beamer. It's an event in Netherlands, in Belgium and also in other countries I believe. And you can bring your beamer to a specific venue. And you can project whatever you want. And what we did is we created an interactive installation. Where people could experience a concept version of this font. Here's the concept version, pretty crappy. This is a whole story altogether. But people could go there with a public transport card. And have their future predicted by one of these statues. And it would be projected on the wall in between the original statues. And at the same time you get a sticker. And you could put it on your clothes with a nice funny prediction of your hypothetical future. En we're going to speed up a bit. We used, of course, 0MQ to connect some parts of this installation. This is all the other technology we used in that. So finally, after the crowdfunding, we started with the digitization process. And you'll see a character, black on black, with edges. We made a pipeline to make it black and white. And for the colors it was edge detection. En you can do that with this simple line, image magic. Then from this we started in Inkscape designing characters. And after designing a big load of characters, we wanted to import these into font forge. And not manually, but with a script, of course. En dit is de laatste stuk van de code voor vandaag. In dit talk. Like the other file we had, we had a new TSV file, where we could import the characters, but also construct characters from an A and D-reses to get this one. We could horizontally flip, or vertically flip, glyphs in order to widen the number of glyphs supported in the final font. So, at the moment we have 173 glyphs designed. Some are alternative forms. We have some with an overshoot. If you use for horizontal typesetting, if you have vertical typesetting, you can disable this. And as of today, the better version of this font is available on GitHub. The plans are to also design some new rules. These are some of the numerals by the same sculpture. They are not in the same font, so they are going to work as an idea, starting points to work on that. So with numerals, not only 0 to 9 we can do, we can also do fractions, subscripts, superscripts. And this is sort of the wish list of what we are going to add in February. The open source design tools we used are these usual suspects. And these are the people who made it all possible. And last, I want to show you really quickly how this input process works in Fontforge. Who has ever worked with Fontforge? Good.  Oh, it's on my screen, sorry. I have to quit here. So, I didn't know if you see it, did you see it on the internet? So just before when I pressed this button, this got all filled up real time. All the glyphs got important, flipped or combined in order to make this font exportable to OTF, DTF, et cetera. That's the thing we did. Ah, and there was two people already requested to use it in the cover for their books. And they were pressing me to get it finished by Fontforge them. So I made them this afternoon that they can start with it. So it will be used in the next couple of months on some books. Ja, so I... We didn't repeat the question. So the question was the difference between automatically tracing the outlines of the images and drawing by hand. We drew everything by hands and used the images as a background to a starting point to see if it sort of matches up. Because as I said, many of the characters differ in size and aspect ratio. And we optimise all the glyphs that we build them up because it's a geometric font. So you just play around with circles and rectangles. So all is unified and minimised. So you have the least amount of notes in this in order to work with. And I spoke to other people who also did this before and they said, well, if you find an incomplete font, 100 years old, probably there is so much variation because it needs to fit between the ceiling and the floor so they mess up the letters all the time. Just start from scratch and don't fix yourself on the exact measurements. Yes? No, it's exactly the same. But these are references. So if we want to do a lower case, then we would fill them. But now they're references so that if people start using it and they're not aware that it's only uppercase, then it's like, ah, it doesn't work. So that's why we did it like that. Ah, we also got a funding from our local government, about 3.000 euros. My colleague, he went there to defend our application. And he was amazed how well known, for example, Inkscape and Open Source was in the local government finance department, which was a nice surprise for us. We thought we had to fight a big battle, but apparently from all the years of open source endorsement, it was pretty easy actually. Okay, thank you.


Can you hear me? Now yes, now better. It's everybody back? I don't know. Yeah. I will start. Hello to everybody again. For me it's a bit strange to look at the camera, but I will try to do it. Today we are going to continue talking about dimensional reduction. Let me start with a bit of reminder of what we have seen last day. It's that we are going to talk about unsupervised. In concrete last lecture and today we are going to talk about dimensional reduction. Reduction we mean that our data, our original data, that we can express as a vector for each data point, lives in a space in which we have big number of dimensions. What we try to do is to project this data in a different space. Why? For each data we have these small dimensions in such a way that this is usually much smaller than this. I explain to you how it is related with physics by making a comparison with a human-made dimensional reduction in the case of two free atoms, different with bonded atoms. In general what we explain to you is one of the possible methods for which you can do this transformation that is called PCA. If you remember the method, this method just tries to maximize the trace of the covariance matrix by applying a linear transformation to this data. So for using PCA the only thing that you need to do is to compute the covariance matrix in which each element is computed as this. Some for all the points each are centered. Decide in order to make a reduction of dimensionality. What I did not explain last time was how to decide what's big and what's small. That was a question from one of you. And now is the first thing I'm going to explain. But before that I just want you to ask me if there is any question. I can hear after this fast reminder. There are no questions. Let me explain to you how to decide the number of age and vectors. So you have age and values and you can sort it there if my data lies in an hyperplane. Let's put the simplest hyperplane that I can imagine. If I apply PCA here I would find a different basis. I would say, see is that age and vector, let's call it B1 would be associated with a different value of the variance that is the covariance of my data along this straight line. It's lambda 1 B1. Since I'm in an hyperplane this B0, strictly 0 if I'm in a line, this lambda 2 would be 0. So once I build this intuition, what would happen if I'm in approximately an hyperplane? If I'm in an approximately hyperplane and I plot lambda of the rank, the first one would be the bigger one, the second one would be here, the third one would be here. But at certain point, if I'm in something that is similar to an hyperplane, what I would see is that it would start to be, you would see a gap in your spectrum of age and values. If I see something like that, I can say, here I can just retain the first three age and values. So the first three components of my PCA, and those are the principal components, and ignore the other ones. This is something that happens when your data is nearly in an hyperplane. What happens if this is not the case? If this is not the case, what you will obtain, let's say it's something that is not necessarily gap. You will find a spectrum that is gap less. In this case, what you can do is, for instance, decide that you want to maintain a given percentage of the covariance explained. As we were saying last day, the fidelity of your reproduction is the sum of all the age and age values from one to this small, divided by the sum between 0 and 1. So one way that you can reduce your dimensionality in a gap less is the same spectrum. I want to have a fidelity that is nearly 0.9. You decide your D in such a way that f is equal to 0.9. This is a question in the chat. Let's explain again the case where there is a gap. If the data lies in an hyperplane, it would be a gap by definition because all the pure rotation will maintain only the significant variables and the other ones would be exactly 0 if you are in an hyperplane. If you are in something that is near to an hyperplane, you would see a gap but maybe, of course, if they are not in an hyperplane, they cannot be 0. So what you would have would be something like that. It's the difference between having an exact straight line and something like this, like that. In this case, the variance in this dimension would be small but would not be 0. But in any case, you would see a gap if your data is similar to an hyperplane. This is the best way of performing VCA. You check if there is a gap and if there is a gap, you are quite sure that your transformation is meaningful. Somebody asked what does fidelity imply for the VCA? The question is that, of course, the VCA what performs is a rotation. It's a rotation in which you maintain a priority as many components as you want. If you maintain all of them, you will have 100% fidelity, but you would just say, I just rotate my data. I'm not reducing my dimensionality. If I want to reduce my dimensionality, I want my data in the reduced space to be as similar as possible to the one in the original space. With the fidelity, you can quantify that. The fidelity is, we'll write it again, the sum of the agent values that you maintain in your representation divided by the total sum. If you look at this equation, if I do my fidelity with the one rotating, I'm not altering my data. A rotation is not a change in my data. If this, as it usually happens, is smaller than the, then I can have whatever number between 0 and 1. If I obtain one, it means that my data lives in an hyperplane whose real dimension is this, and it was embedded by rotation in this other one. The fidelity, it's a way to quantify how similar it's my projection to the original data. Talking about dimensional relaxation, the PCA consists in a linear transformation. Something that is my definition, because I take my transformation as a linear one, but it means that if my data is not linear, I cannot use PCA properly. Imagine that you have a data set that is like that in two dimensions. Whatever transformation I do with PCA, whatever rotation would not describe my data properly, right? Because even if this data is nearly approximately one dimensional, not embedded in an hyperplane, okay? You can see that this is a problem. In fact, the main fault in which my data lives is not linear. It's a bit twist. Maybe I can imagine even having something like that. Why not? Data are odd. The PCA cannot reduce the dimensionality, understood? I'm going to explain you in the next, let's say, 14 minutes are methods, well, at least the data allows you to the dimensionality that is to obtain this transformation in cases in which this transformation is not linear. I think that I have to explain things called multidimensional scaling. Multidimensional scaling is just a way, a different way to think about dimensional direction. What you try to do is imagine that you have in this space that we are talking about the Euclidean distance. This is nothing else than the square root, the sum. Clear this formula to everybody. This is just the distance, okay? Exactly the same. The idea that underlines multidimensional scaling is to choose y in such a way that these distances are as similar as possible to the original ones. This is what is called multidimensional scaling that allows you to do that. And the different methods, the difference between the different methods comes from how they define this comparison. By comparing two sets of distance, it depends on the distances, the original space, and the distances in the projected space. Excuse me, could you repeat what's the name of the S? Oh, stress, okay, thank you. Sorry, I know my spelling is not really good. Okay, so let me have some space. We can define it in many ways. Let's say the classical way of defining this stress, like let me check the questions because I don't remember them exactly. The sum, this is what it's called classical dimensional scaling. Let me put it like that. The dimensional scaling has the advantage. It can be solved when you compute there to minimize this quantity, because it's what you need to do, can be solved analytically. And when you minimize it, the solution is almost identical to a PCA. And it's almost identical to a PCA in the case that you use Euclidean uselessful. This result, you could say that it's useless, but it's not useless. Because linear distances are not the only way that we have for different configurations. So if you use a different kind of distances that are not Euclidean distances in this multi-dimensional scaling, and you will obtain something that would be similar with the same characteristics of PCA, but with a different set of distances. I think that you arrive always to a diagonalization, so it's something that is really similar to PCA. I'm not going to, because we don't have time. I'm not going to derive that. But you can think of a different kind of stress that it's what it's called metric stress, that it's metric. You do something, a different definition of S is equal to the sum. This is the rest. It's different, as you can see. And as opposite of the previous one, it has not an analytical solution. For solving that, you need to employ numerical initiation methods when you compare it with the classical dimensional scaling. And probably the most important difference is that it's not depends on the scales on the distances. You are, by dividing by this quantity, you are waiting less the sum of the distances. So a bit different. But it's an option that it's, let's say, not so commonly used. Mostly because it doesn't convert it necessarily to the same minima. Numerical minimization, would usually obtain local minima, not global ones, so it's not always convergent. In which we do a different thing and we use, for defining this scaling, function that is really similar to the one that I employ for the metric multi-dimensional scaling, functions, distances. Well, this is a really powerful method. You need to define this function. The idea is that, if you are wise, may I cancel that for multi-dimensional scaling many times with all the distances. But, for instance, only the ones that are close, the small distances. Because in this way, you can reproduce the local environment of your data caring about the long distances that would be far anyway, but you don't care so much if they are two, let's say, at one kilometer or ten kilometers. The multi-dimensional scaling is that this non-metric multi-dimensional scaling, it's like, for instance, in many, many cases, in many, many applications of multi-dimensional scaling on dimensional reduction, you are interested in your nearest neighbors. So, nearest neighbors are not so important. This is a problem of PCA, because PCA usually weights more long distances if you want to, if you express it in the terms of multi-dimensional scaling. So, when you apply this, what you can do is just to choose wisely these functions in such a way that small distances count normally while long distances are important because we want what is far, far but you don't care about how far are the things. For instance, you can apply an exponential care energy or other kind of functions. For sure, I mean, it means that your scaling will depend on the functions that you choose, so it's kind of a talk, it can be really useful in some cases. I don't know, I'm going to stop here for questions because we are half late. There are many questions. A question on what is the difference between multi-dimensional scaling and least squares. Well, in the case that you use the first one, it's a list of squares. You apply least squares to your distances. The idea is that you use the least squares equation but what you are optimizing, let me write again the question that we were talking about, what you optimize by minimizing this S is the set of Y. So it's a bit more complex because you are having this Y, this distance, it depends on this Y, this distance, it depends on this X. So what you value when you are optimizing this S is this. And you think a list of squares is a loss function. The sum over A and J means over every possible pair of different configurations. It always corresponds to the coordinates in the original space. It defines delta I, J. It's nothing else that my coordinates in the configuration space. In the Y, it's the same but in the projected space. So in order to get the small delta I, J, we need the Ys. We need the Ys. But do we first choose an ansatz function that maps the X and Ys? We just optimize directly depending on the stress. In the case of the metric stress, you can directly optimize it by taking the numbers directly. It's a diagonalization and you directly obtain the minimum of stress as a function of the Ys. In the other cases, what you have to do is to obtain the derivatives by applying the chain rule. You obtain the derivatives of this stress as a function of Ys. And then you starting from random Ys arrive to the local minimum. Okay, so there's it's not necessary for us to have an explicit form, explicit function that maps the Xs into the Ys. No, we don't have that. We obtain directly the Ys, by applying the directly minimizing the stress. Okay, thank you. No more questions. I'm going to try to guess. Let's say, mention some other methods that are those that are most used, but that we are not going to explain the maps behind. We are going to just say, let's say, the concepts the concepts that underline these methods. One thing that one method that is kind of pretty used yet is isomac. What do you do in isomac? What you do is to compute a multidimensional scaling in which the distances in the original space are not the Euclidean ones, but are what it's called the geodesic distance. What's the geodesic distance? I will explain to you just the concept without going too much, but imagine that you have I will... I'll just say that it's like that. Okay. You see that the meaningful here it's something... Let me just write it. Something like that. If you compute the Euclidean distance between these points you will obtain for instance from this to this it's okay, but you will also obtain this distance as Euclidean distance. In the geodesic distance what we try to do is to compute the distances within the manifold. Okay, I will play the other question later. Let me finish that. So what you try is to compute the distance between the manifold within the manifold. And for doing that it's what you do it's try to approximate from this point to this point as the sum of distances of neighbors. This way of computing depends on how many neighbors you consider or if you put a cutoff for instance you can put a cutoff then compute here the distances to this point then you put a cutoff here compute here the Euclidean distances but then at the end okay from here to here I find the path that gives me a minimum distance and this is my geodesic distance this way of doing that allows you a military course method using the geodesic distance what you are doing is unfolding your data unfolding your manifold and it would be something equivalent to having in this point here the distances are almost the same as the Euclidean but when you are going far in the manifold this point would be here right so by computing the geodesic distances you are computing the distances in the manifold in which the data allows and once you have these distances you try to reproduce them in the projected space multi-classic multi-dimensional scaling I don't know if it's clear let me try to reply these questions okay I didn't explain how to determine F and J what I said because it depends on many cases many different ways of determining them usually but what you try to do is to have functions that decrease when the distances are really big scaling as I explained you can just provide you the each of these things depending on your what you want to do for instance it's better to have a good projection than a bad one even if you cannot reproduce your projection for new data because sometimes if your data looks like that yes you can use PCA and obtain a good function that reproduces maybe it's not the optimal choice there is another question the distances between that you use to build the nearest neighbors usually are the Clidium ones but there is no restriction for that you can build the geodesic distance using whatever distances that are better to use data many for it's not a Clidium probably it would be better if you employ different distances questions they will continue because we are running out of time many many many methods either in PCA or on multidimensional scaling ok so the examples that I put you it's isomap but there are many ways of doing that I would mention there is something that it's called like I will put in the metrics some kind of reviews because we don't have time to look for all of them ok what is important what I just want to explain you now is what makes dimensional reduction powerful it makes dimensional reduction powerful it's that the data the real data usually lies in many forms of relatively low dimensionality and that's because in interesting data there are the correlations as I explained you yesterday I mean also in physics the interactions between atoms the interactions between the Hamiltonian of the distance determines a lot of correlations and these correlations lead to spaces where the dimensionality is low but it's not trivial to check ok so there are methods that are oriented not only not to project your data in a given manifold but just to know which is the dimensionality of the manifold in which your data lies ok the idea of these methods is usually these methods are called intrinsic but these methods try to do is directly from your data estimate the dimension of the manifold in which your data lies in many cases this corresponds to the minimum number of coordinates of features that you need to project your data ok in the case of PCA when we are deciding that looking at the spectrum after a gap I have enough with these three dimensions what we are saying is that the intrinsic dimension of my manifold is three to determine this quantity I will just give you a really really fast idea and it's that the number of points within a radius of a given point the density of points to the deep imagine that I'm in one dimension points in just one dimension if I look at this point the number of points within a given radius let's put it within this radius would be proportional this radius to the one in two dimensions my data uniformly is that the number of points within a given radius would be proportional to the area of the circle right would be proportional to a response if I'm in dimension three so on so the methods that many methods that try to estimate this being just take the distances and use the distances and use how to the distances from one point to its neighbors is case in such a way that you can see for instance in this case you would have that the logarithm of the number of neighbors of that would be proportional by using the slope of this dimension excuse me tell me the dimension is not the capital letter D related to the original data no it's the D it's the one in which you want to project so we should define the small letter D first and then come to this intrinsic dimension yeah this one is not the it's the one that you want to compute this is the intrinsic dimension it's what you want to compute I see here you are using the distances in another space okay and then you are computing which is the dimension of the manifold in which they live and then if you have a good projection method you can try to project in this D but projecting in a D that is smaller than this one would give you some error because you are you would not be able to fully express the manifold in which your data live I have a question finally what is the relation with the PCA for example and the D in this formula there is a relation yes let's say if your PCA is well done the result of for instance it's not that you are going to employ this method but this method is probably the the share one but this method would give you a value of this if your data do not live in an interplay is that you would need more components that this D because this D let's say it's the minimum value of variables that you need for project if your data live in a manifold in an interplay then this D would be the one that gives you the gap if not probably you would need more principal components that the ones that you have ok thank you if there are no more questions we can leave it here next day I will start with clustering methods ok I will change the format I will do the lectures from my house with a PowerPoint with some slides so thank you very much and see you on next day