This episode was prerecorded as part of a live continuing education webinar. On-demand CEUs are still available for this presentation through all CEUs. Register at allceus.com slash counselor toolbox. I'd like to welcome everybody to today's presentation Disaster Planning and Ethical Obligation. Doesn't that make it sound like it's going to be a really important presentation? We're going to talk about the rationale and process for disaster planning, preparing for disaster, continuity planning, managing prescription medications, which is important and testing the plan. Now you might be thinking right off, you know, well, I'm in individual practice or I'm just a clinician. I'm not an agency administrator. Why does this matter to me? And, you know, we don't have that many natural disasters, hurricanes, tornadoes, whatever in my area. Well, disaster planning covers a whole wide range of things. When we went through our last, which was it, maybe it was a JCO audit, could have been car. Anyway, we had to really up our level of preparation for a variety of disasters. And we'll talk about how you figure out what you need to plan for in your area. And the hint is there's a list at your health department, but we'll go on from that. And even if you don't prescribe prescription medications, which most of you probably don't, being able to make sure your clients know where they can go to access to get refills to access physicians who can and will write a prescription refill. Maybe it's only a 30 day refill. But in the event of an emergency in which hospitals are overloaded and stuff happens, we need to make sure that we know how to get our clients to the resources they need.  If you think back to Hurricane Katrina, people staying in Texas and one of the shelters, not having access to their medication for, you know, a week, let alone a month or two months. So we want to make sure that we know how to do all this and test it. Disaster planning can save lives, minimize injury, emotional trauma, protect property and operational capability, and prevent or reduce interruptions in treatment. This is why I think it's an ethical issue when we start thinking about non malfeasance, you know, above all, do no harm and beneficence, making sure we're proactively thinking in terms of protecting and assisting the client. Disaster planning really comes in there. Behavioral health treatment programs have a special obligation to prepare for disasters because we provide essential services, you know, sometimes you may feel not as essential to certain things. But we really are essential in a disaster situation in which, you know, some people may be getting hurt but there's often a lot more people who are experiencing traumatic reactions from the disaster. By their very nature, disasters have an impact on behavioral health. Most people who experience disaster, whether it's a victim or a responder, and this is important, responders have reactions to. And sometimes they have to stuff those down because they can't deal with them right then and do their job. So it's important to make sure that we reach out to those people and provide some stabilization services. We'll have some type of psychological, physical, cognitive and or emotional response to the event. Most reactions are very normal responses to severely abnormal circumstances. And that's one of the ones that I really harp on when I'm doing stress response training for law enforcement emergency medical services is the fact that, you know, talking about these things having some depression being stressed out, being really freaked out by something, you know, whatever word they want to use for it, that's normal. It doesn't mean that they are mentally ill or they're impaired or they're risking losing their job because of said perceived impairment. Most of the time it's a transient, you know, short term normal reaction to the abnormal circumstances. So, you know, I say that a lot in order to get them to kind of hear it and embrace it. Disaster planning can prepare the program for continuing to provide services to its existing clientele in order to prevent relapse. So if you've got people that are coming maybe they've stepped down they're only seeing you once a month. They may need to up their services. You may also have clients who have recently discharged disaster happens, and they need access to services. Medical and psychological consequences for prematurely discontinuing medically managed detox or crisis stabilization. So if you run a or work on a detox or crisis stabilization unit. There's a major disaster there's a flood there's something and you've got to evacuate. You can't just open the doors and go well good luck. It's been real. There has to be a plan in place. That's not kosher. If clients are at a residential facility, if they are again in detox in CSU or in residential treatment, they may not have a place that they lay their head at night. So, ideally when they go through their assessment process they identify somewhere that they would be able to go should an emergency arise or should they discharge AMA. So if you want to start and all insurance companies require this start discharge planning at the time of admission sound like a broken record with that. And this is one of those reasons if for some reason they have to leave the facility. Where are they going to go we don't want to just turn them turn them out and go well. Nice knowing you good luck there's probably opening at a shelter downtown somewhere that doesn't work. We also want to prevent client destabilization due to lack of lack of access to medications prescribed and or administered by the agency. And I put that a little bit more broadly, because those of us in private practice, you know, we don't prescribe we don't administer and most of us don't have a psychiatrist on staff. The client is seeing a an independent psychiatrist, but in order to exercise due diligence, in my opinion, it's good practice to make sure that clients know and we know where they can go. Should something happen, a tornado or hurricane a flood a fire, something where they can't get to their psychiatrist and all of the typical walk in emergency clinics are closed. Where do they go to get their prescription refilled some places don't want to deal with prescribing psychotropic medication refills for someone who hasn't been a historical patient. There are also other places or some of the same places who will not or do not want to prescribe opiate based medications pain medications or methadone, buprenorphine suboxone to people for whom they are not current clients and some of those things like suboxone and buprenorphine and methadone have to come from a specifically licensed clinic. So, make sure you know what meds your clients are on make sure you know where they can access them in an emergency. And we also don't want to, or we want to prevent exacerbation of problems and at risk populations, as the result of lack of access to support. So we're talking about those typically what they consider your high risk populations, people who use injectable drugs, pregnant and postpartum mothers the elderly children, making sure that we have resources that we can refer out to. We may not be even even be in our offices at this point so we need to make sure that we know what the plan is. Disaster planning can help mitigate psychological issues in the community by providing services to new clients, either through aiding other programs who have had to shut down but you're still operating so you say, you know we can take on some of your clients temporarily. And having groups services available and individual services and crisis services available to people who may not have been a client anywhere before, but all of a sudden this hit and their world was turned topsy turvy or they're freaked out. And they need to talk to somebody just to deal with that before it becomes an issue. We recently had a major fire down in Gatlin Burke, and the same thing was true there. I mean, there are a lot of people who had never had diagnosable mental health issues never seen a mental condition, but that was a really stressful horrific experience, and it was a normal reaction to abnormal events and they needed help figuring out how to make sense of it. So, by making sure that we know how we can best reach out to the community to prevent problems that will prove prevent later over utilization of treatment services so there are a bunch of disasters and there are a bunch but just some to think about. If your facility is incapacitated or destroyed due to fire building floods sinkhole, but other facilities remain open and clients are in their own homes. One example of this one of the places I worked we had, and we had several buildings. The main building where we provided outpatient services was remodeled. Gorgeous, look beautiful. Unfortunately, the plumbers did not do a good job. And in the middle of the night, one of the main water mains broke and flooded the entire building. And this we didn't have electronic medical records at this point we had paper medical records, all of them were soaked. I mean it was, it was a disaster. Obviously we couldn't see clients in there for quite a while, because we had to dry the whole place out and, you know, put in new drywall and flooring and all kinds of stuff. So there are times when you're working in an individual setting or in a small clinic, where you may have to shut down and you need to prepare for that. The city and others are incapacitated and clients are in shelters, such as Hurricane Katrina, or during some of the blizzards they've had up north recently. The fire like the one in Gatlinburg. I mean, there was nothing in Gatlinburg that was able to be accessed people were having to go out to Knoxville and other places so where are you going to refer people to, and your clinicians. And continue seeing clients or if you're in private practice, and you want to be able to continue to see clients. Do you have a memorandum of understanding with someone in a nearby county where you could go and, you know, see your clients, you know, office share do something. Another thing would be if your facility is functional in the aftermath of a natural disaster in which your patients are in shelters. So a citywide flood would be one, you may be on a high ridge somewhere where most of the city got wiped out. Nashville back in 2010 had a flood that leveled a ton of stuff, but in the outlying counties like where I am, you know, they weren't affected that much. So, where do your clients go. When the program must and patients had to go in shelters during the Nashville floods because they were flooded out of their homes to I mean the entire city in large parts of the city, we're just totally underwater. When your program must cease provision of non essential services do us due to a sudden reduction in resources infrastructure or available personnel, due to illness or diversion of resources, which, you know, is if in an emergency, if your staff has to go and instead of doing normal billing stuff. Whether they're triaging phone calls or whatever, or if there's a pandemic illness such as influenza, and evidently now you're required by many accrediting bodies if you're accredited by Jacob or car to have a plan if there is like an influenza pandemic. So I alluded to this earlier health departments will provide you a copy of the local hazard identification risk assessment or hyra. You can call them ask them for it. If you're getting accredited. That's what you're you're going to have to use and those are the hazards you're going to have to plan for. Could you be going through the accreditation process. If you're not bothering to get accredited you're an independent practitioner and Jacob accreditation isn't something you're worried about. It's still a good idea to have it to be aware of things that might happen in your area so you can look over it and go is this something I need to plan for with my population. Continuity planning requires a program's personnel to consider the threats that could adversely affect essential functions. Determine the personnel and vital information and other resources required to continue those essential functions. So looking at your program. You know, as an independent practitioner, I provide individual and group counseling and obviously training. If something happened, you know, what would I need in order to continue to provide those functions and Internet connection something that's that's for sure. You know, I could probably downgrade and not have the video available just do audio so there was less drain and use a lower bandwidth. But I'd have to know where to access that and have to have a place where I could meet with clients. Other than that, there's not a lot of essential functions. Now when I worked at a community behavioral health center, we had crisis stabilization detox we had residential units.  There were a lot of things in order for our clients to be served efficiently and effectively. There were a lot of things that had to happen. So we had to look and say, okay, what can be kind of cut back on during this period, we still need to maintain some sort of records management. Once we went over to electronic health records that was easier because we didn't have so much filing to do. But that's an essential function. Whether we want to embrace it or not, you don't write it down. It didn't happen. You don't get paid, and you can be sued. And in this time of chaos and everything, there is a significant chance that there may be an increased risk for liability, or, you know, lawsuits, not necessarily that you did anything wrong. But people can get agitated and frustrated and and look for somebody to direct their their frustrations out on to feel a sense of control again. You want to develop a plan for providing those essential functions either on site or at alternate locations, like I said, be creative. You know you may not be able to get a time share with another mental health practice if you are an independent practitioner. Where else might you be able to find office space. I mean the nice thing about what we do is the fact that we don't, we're not like medical doctors where we have to have equipment and stuff we pretty much have to have ourselves and a confidential room so is there are their local community centers are their rooms at libraries you could access if they're still open. Make advanced arrangements for obtaining the resources necessary to support essential functions throughout the disaster and recovery phases. Again, if you're in, if you have a residential program, or a program, well, especially residential, you need to make sure you have enough food, water, batteries, flashlights, blankets, that kind of stuff, squirreled away to handle your daily number of clients. We tend to err on the high end, not go with the average but save the average plus 10%. In order to, you know, hopefully make sure we had enough. And we also need to plan for the safety of personnel during these periods. If there is a hurricane, well, hurricanes you can plan for. You usually have pretty good forewarning of that. There's a huge storm cell that's coming in that eventually is going to produce a flood. You don't know that ahead of time but you see this storm cell coming in. You don't want to be calling your staff to come in so they have to drive through that in order to maintain facility staffing. So what do you need to do who's going to be responsible for monitoring weather conditions. At what point do people need to be called in to prevent them from having to travel in hazardous situations. In initial work, the disaster planning team conducts or gathers from partner agencies in the community, a hazard identification and risk assessment. Again, this is usually the health department, but you can also talk with other agencies and or other providers about what they've experienced in terms of disasters that have caused them to shut down for a week or two weeks. If you're creating this you're going to create something called a hazard specific index. So you're going to have a general hazard plan with your decision tree of who decides when you're going into emergency protocols and who decides who's going to be called in and all that kind of stuff, who is coordinated with. And then you're going to have a hazard specific index. So if it is an explosion at a factory in your town, you're going to institute these procedures. If it is a hurricane, you're going to institute these procedures. It's much more specific types of clients you're going to see current clients. Well, they're pretty easy to deal with because you've already got their charts open current clients who are destabilizing. You know, again, you've got their chart charts open if they're destabilizing and need additional services at a time when your services are being stretched really thin. What are you going to have available. We've offered in the past have been crisis hotlines. We've also offered ongoing support groups where clients who are destabilizing could come in and there was a safe place. If they're in a shelter if transportation is not possible to the facility for some reason, then obviously the telephone hotlines are better than nothing. You may have guest clients from other agencies. How are you going to handle that you're going to need to be able to get hold of their medical records in order to be able to provide continuity of care. This is all done through what we're going to talk about in a little while called an MOU or memory that memorandum of understanding where they say yeah if we become incapacitated. You will take will refer 20% of our clients to you and we will make sure that you're able to get the bare minimum information in that that you need to provide treatment through this method. With E electronic health records. I'm not even going to try to do the abbreviation. That's much easier than it was before but you do have to have somebody on the tech end that can open the switch that gives clinician Jane from the new facility access to your electronic health record. So everybody's going to get involved in this. You'll have prior clients whose recoveries are threatened because of the stress individuals who've never been treated before who need to have treatment in order to prevent further deterioration. Family members of clients who need assistance to support their loved ones. Again hotline online support groups. Those are also great if the people can access an internet connection. The beauty with mobile devices is that it's often possible for them to log in and participate in online support groups. Even from a shelter because there's generally Wi Fi, it may be overloaded so there could be some other problems with that but trying to provide as many creative options as possible. Patients who need prescription refills written somebody may come to your facility and say you're you know Jane and private practice and they're like I need a new prescription for this antidepressant. And you look at them and you're like well I'm sorry but I don't have prescribing privileges. You can't. Well you could but ethically you shouldn't just say well not my thing. Good luck try down the road. So who are you going to refer to. And patients on an opioid pain medication, not necessarily methadone, buprenorphine or or suboxone but somebody who has a pain condition who's being pain managed, who can't access their physician. Where can they go. If they're your client. And you know we have clients who have chronic pain. Who handle them where can you refer them. Theoretically, they're treating physician is going to have a similar plan in place and it's going to be able to refer them. That would be where I would first start when I'm making my disaster plan is to call, you know, the pain management clinic in town, or the one that my clients are seeing and say, if there's an emergency what's your disaster plan where do you refer to. So clients don't destabilize generally they already have one in place, you just fill it in with that information and you're good to go. So the plan, the introduction is the purpose of the plan and the objectives generally what we stated on the first slide. The concept of operations, who what when and how are going to activate and deactivate this process are you going to send out a text message to all your staff are you going to call everybody staff meeting. What's going to happen. So consider doing broadcast message on your local TV and radio station. If you need to institute emergency procedures, just like they do when they close schools for a snow day, if your facility needs to be closed for, you know, even for a snow day. It is nice for people to be able to go to their local web, their local television channel and or the website there in and see which businesses are closed so they don't think well do I need to try to make that appointment. You need to have which staff are responsible for what in the disaster, you know, who organizes the clients who monitors the weather station, who gets out the flashlights and batteries. Etc. List the personnel positions authorized to make requests for outside aid or assistance if you can't handle something. If it, you determine that you need to evacuate clients and you need emergency medical services assistance doing so. Who's able to make that call at the places I've worked with it's always been a senior vice president or higher. In a smaller organization. There may be a different person, but you need to know who you can call if things start getting bad, and you need to assist request assistance. The conditions under which to request aid. Yeah, if it's really bad weather outside and it's kind of scary. You know, maybe debris is flying everywhere and a window broke. Or in a big 15,000 square foot facility, probably not a reason to call out the Calvary in the middle of the storm. But if part of your roof blows off, then that might be different so you may need to take different procedures. The procedures for managing requests to give aid.  Who's authorized to say sure we can take will activate that memorandum of understanding and we will take 20% of your clients right now. Direct them to call this number in order to get an appointment or whatever your procedure is. There's a list of resources that can be used in those efforts. Well if the roof blows off the building and you need everybody evacuated and you're standing there twiddling your thumbs going well. Who do I call law enforcement EMS. That needs to be decided ahead of time. So in each appendix for each type of disaster you're going to have a list of the types of people you may need to contact and their phone numbers and a contact name if you have that. So there's no guessing you're not flipping through the book trying to figure out who to call. So these specific indexes are called functional and annexes and they are by specific hazard. So hazardous weather tornado fire flood facility flood hurricane or a blizzard, you know, hurricanes and blizzards you have a lot more time to plan for then tornadoes or hazardous weather coming in so you know some of these maybe seem similar, but they may be separated based on the amount of time you have to plan for them. So implementation instructions checklist and materials necessary to perform disaster related tasks and things that can be included in this appendix would be scripts to respond to the media, the public or consumers if they're calling and going. You know where can I get help or when are you going to be open again or whatever the case that way you have a consistent message to put out floor plans. And you know if everybody's been evacuated ideally emergency medical emergency response will also have a copy of your floor plans in their response plan, because if there's a fire, they need to know what the floor plan is the facility and community maps. So if you're trying to tell somebody to get from point A to point B and the internet's down so you can't pull up Google. So the fashion community map is going to be really helpful. Safety related policies and procedures will also go in here. You know what to do in the case of a slip and fall what to do, you know, all of those other things, and your memoranda of agreement or understanding depending on where you are it's the same thing, including the address of each facility phone number and a contact person. So if I were, you know, here, for example, if I was going to refer patients up to Centennial Hospital, I would have the name of the person that I would need to contact to see if they were going to accept our activation of the MOU, the phone number, the address of the facility and you know, whatever procedures, I needed to undertake to make sure that they were prepared to handle my clients. The basic plan should address general procedures, contain a general decision and notification tree and plans for monitoring where clients go. So if you've got a big facility and 300 clients coming in, you're not going to refer all of them to one place. What you're going to do is, you know, kind of probably break them up between two or three different facilities. So you need to know where you're referring. Avoid having staff need to refer to multiple sections of the plan. You don't want staff flipping back and forth going, okay, I need to refer here and then I need to contact this person. That's not going to work. If your agency has multiple locations or types of programs, each program type needs its own addendum to each functional annex. In a hurricane warning, for example. When I worked at Community Mental Health, we had a detox facility, which, you know, obviously we couldn't just open the doors and go good luck. We had a residential program. The clients in there were a lot more stable. Ideally, we would keep them in residential, but that wasn't necessarily mandatory. There were situations where some clients, maybe not all of them, could be referred back home and then they would come back to us as soon as the crisis had passed. If you have an adolescent facility or an adolescent outpatient program, your outpatient programs are going to close sooner than your residential programs. You just kind of need to plan for that. Supervisory staff should maintain a paper copy and each building unit should maintain a paper copy in an accessible location. I know this sounds antiquated, but in the event of a major power outage and you can't access the internet or the online intranet or anything like that, you need to have something to which you can refer, which unfortunately is still paper. Administrative and clinical staff must all be adequately trained, including scenario training. So they need to know what they're supposed to do in the event of any sort of disaster. Your MOUs, memorandums should include hospitals and health departments. So, because they're probably going to be good referral sources and you might be able to help. They may need additional counselors coming in. Your behavioral health disaster response team, which is usually coordinated by the health department. You want to have one with emergency management for the evacuation of patients in the event of an emergency. Even if you're an outpatient program, if you've got 30 people and at your clinic and there happens to be a major emergency and you need to have them evacuated. Now, you got to think about whether that, how likely that is to really happen. But if it is possible, then you may want to have a MOU with emergency management. Other clinics for mutual referral or staff borrowing. So if other clinics shut down, you're taking on the brunt of a lot of different agencies caseload, you may need additional staff. So they may be able to let you borrow their clinicians. And there's got to be policies and procedures for getting all of their, you know, human resources information, as well as who pays them and how does billing work. And sober homes for patients in addiction recovery. If you've got, for example, a residential facility or an IOP facility and patients can't go back to their homes.  If you can send them to sober homes. Yeah, they may have to sleep on the couch. But it would be better in a disaster for them to be in a safe, clean environment than on the streets, obviously. SAMHSA's Disaster Technical Assistance Center can help you link with disaster behavioral health coordinator for your state and answer questions about accessing state and federal funding in a disaster. You know, obviously we're talking wide scale, not your plumbing bursts. But if there's a natural disaster of some sort. Oftentimes you can access funding to support additional staff on duty and the functions that you need to do. Health departments must coordinate disaster planning with the community's behavioral health treatment systems. So the health departments, if you're in an agency, not necessarily if you're an independent practitioner, you may have to reach out to them. But if you're in an agency, health department should have already reached out to you and said, okay, you're part of this big conglomerate now. So let's all get on the same page for disaster planning. The health department engages and coordinates with emergency management, healthcare organizations, both private and community based and behavioral health providers and community and faith based partners. I've been in many locations where the churches served as temporary shelters and were able to provide a place where clinicians could go meet with clients who were able to get to that location because sometimes you can get in a 10 square mile area and not any farther, but then people can come to that location. So faith based partners and community organizations, even your community centers are great. Health departments support the development of public health medical and behavioral health systems that support recovery. So theoretically they're supposed to be making sure that we're all on the same page. They participate in awareness training with community and faith based partners on how to prevent, respond to and recover from public health incidents. Now if, and I don't know if any of you run recovery homes, your agency runs a recovery home. You know, it's really good for them to be in the same conglomerate that way health departments can use them as a resource in the event of a disaster. We want to make sure the health department promotes awareness of an access to medical and behavioral health resources that help protect the community's health and address the functional needs of at risk individuals. So again back to prevention instead of waiting until after the disaster, the disasters over and people have been compensated. And they receive and or integrate health needs of populations who have been displaced due to incidents that have occurred in their own distant communities. Think again thinking back to Katrina. I was able to manage the Katrina grant for the 13 Northern counties of Florida. There were a lot of people in that came to Florida, who were from Mississippi and Alabama, who had been displaced. The DEA, yep, they get their fingers in it to monitors and reviews actions the program takes in a disaster regarding controlled substances. If your agency has controlled substances if your sober living facility happens to have controlled medications on the premises and it doesn't have medication assisted therapy, then the DEA is going to want to know, how do you transport those in the event of an emergency to make sure your clients get them and nobody else does. Inform the local DEA agent about the use of controlled substances that are prescribed or dispensed to patients and stored at the facility.  So you're the DEA is going to be interested in how you're handling that the state opioid treatment authority can assist in making contact with the local DEA official, even if you're not talking about opiate medications, that person's going to know who to contact. So reach out to them instead of trying to go through the decision tree of the phone numbers. The media can assist in the coordination of services. So be request being included in local TV and radio emergency listings. So everybody's aware of the operating status of the program and where to go with its closed if they were planning on coming to you for detox or if they're, you're in a community crisis stabilization unit and you're closed. Where are they supposed to go generally is to the next county over but you know which county and who do they contact pre disaster preparedness, educate partners to destigmatize and ensure continuity of care at guest agencies or in shelters. So we're talking Katrina and other disasters I'm sure but there's a lot more research on Katrina because it was so long. There were people who were on methadone and suboxone who were not able to get access to their medication or not allowed into certain hospitals because they were on that medication. So we want to educate partners, including the ones that are going to operate the emergency shelters and facilities about these different medications, how to store them what they're used for yada yada. So they don't discriminate against our clients. Schizophrenia is another one where agencies are people who are running the shelters may be less inclined to open them with welcome them with open arms and may say they need to go to over to this specialized facility. Well, if that specialized facility is locked down, full up, whatever, we need to make sure we can get someone who is relatively stable on their medications, but who has schizophrenia into this other facility with their meds. Educate the public about the importance and availability of behavioral health services in in an emergency, you know, going out doing outreach doing stress management, going to some of the shelters where people may be residing and doing preemptive stress management outreach kind of activities, not group therapy, but education, helping parents understand why their kids are acting why they are helping parents understand why they're feeling why they are, and what to do about it, giving them practical tools to help them, all those sorts of things are great in an emergency. We also want to provide them as much as possible beforehand. So if a local elementary school is going to be a shelter, maybe looking at who's going to staff that shelter and can we provide pre disaster training. So the people who are staffing it have a few tools to hand out and maybe some handouts about stress reactions. Again, make sure your memorandum of understanding are signed and in place before the problem. Educate local emergency response organizations about the characteristics of your patients.  If you've got clients who run the gamut from severe substance abuse to severe and persistent mental illness. Let's educate them so they know how they can best serve those clients and what they can do in a disaster to help the clients instead of further stigmatize them or traumatize them. We need to know the needs of patients during and after transport, and the most appropriate settings for relocation, you know, maybe it's not one of the special needs shelters, maybe it is a general shelter that has the ability to dispense medications. So specific locations that have through MOU agreed to accept your patients. So if you have clients for example on methadone maintenance, and there is a shelter who's agreed to accept all of your clients, then you want to have an MOU with them and educate the local emergency response. So they're not going well this person's on methadone I have no idea where to take them. Let me just dump them off at the local emergency room. I want to make sure that they know that they can take them over to the church at the corner of fifth and third, which is, they've agreed to accept all of the methadone maintenance patients, and that's where your physicians are going to end up going. Right to expect from general population emergency shelters support services that provide access to medications to maintain their mental health and their health refrigeration for medications and assistance that may be required due to cognitive and intellectual disabilities. So this is not your special needs shelter. This is your general purposes shelter. We need to make sure that they under the shelters and the shelter staff understand that so they're not thrown for a loop. This, this is a time of stress people are, you know, typically very nice and very open minded. But when they get stressed out and they're flooded with intakes and stress levels are high and it's chaotic. They may not, you know, think or respond in the way that they would normally. So we want to make sure there's a plan want to make sure that they know what's what's happening, you know, and the same is true for emergency response. They try to do the best by the clients. So they're going to take them to whatever makes the most sense based on their knowledge to care for the patient, which, you know, for methadone clients that are maintained on methadone may be a hospital. Not saying that they're trying to be ugly. We need to make sure that they they know that we've already prepared for that.  And they're not going to give you a hard time because emergency response needs to be able to do their job and get free as quickly as possible. So try your essential functions to maintain the safety of clients and visitors. You may have a bad storm cell suddenly come in or a tornado warning go off, and it's a visitation. You know, you've got 20 visitors and 37 clients that you've got to figure out what to do with and how to handle them. Behavioral health emergency services, including right crisis and relapse prevention. What are you going to be able to provide and how are you going to do it. How are you going to track your clients who've been evacuated maybe even to a different state to make sure that they're getting their needs met. How can you assist clients in accessing needed medications. We talked about that already. If there are clients who have man court mandated drug testing for some reason. You may need to figure out how you're going to conduct those mandated drug tests now where I've been in the past that has fallen to a secondary sort of thing and a probation officers want to test that bad they come out and get it. But that is a decision your agency has to make. How are you going to adhere to applicable state licensing standards, you know, HIPAA high tech, all that stuff. Maintain treatment and billing records in accordance with regulatory requirements. Yeah, the paperwork just doesn't even go away in the middle of a disaster. Partly to ensure continuity of care to prevent clients from falling through the cracks and to make sure that your agency gets reimbursed because if they go two weeks or a month providing all these great services and can't get reimbursed for a one of them. You know, you're going to take a big hit going back to risk management on cash flow. You want to be able to protect client rights and privacy, including the integrity of their PHI.  How can you maintain that client's confidentiality when you're trying to manage things if you're having a face to face conversation. If you're able to go to a facility and provide counseling services, where's a secure place that you can provide that counseling where you can protect their confidentiality. As resources are available and based on mandates, you need to be able to provide disaster mental health services in the community, including prevention specific guidance and crisis intervention. So this goes down to your prevention people, your behavioral health techs, you know, not just your licensed clinicians. There is a lot of stuff. Your unlicensed staff can do to help free up your licensed staff in order so they can focus on the clients who are destabilizing or who are in active crisis. Become aware of funding sources and how to access them. Like I said, state and federal funds become available in a natural disaster. Crisis counseling, assistance and training program grants are funded by FEMA. So if FEMA is activated, you're probably going to have access to these. And your SAMHSA emergency response grants also would be available in the case of a declared emergency. That won't apply if you're having a locally, you know, it's just your building, something happened, but it could apply in these situations. Mid of the gate risk by improving your facility's ability to withstand a disaster. If you live in a place that has hurricanes, make sure you have hurricane window coverings, backup generators. Backup generators are good anywhere because the power can go out and you need to make sure that medications stay refrigerated. Sometimes food may need to stay refrigerated if you're providing food at your facility. There's a lot of reasons for that. Prepare shelter in place for when evacuation is unsafe. For example, there's a semi going down the street right outside your facility and it gets into a wreck and there is a huge noxious chemical spill.  You've got a river on one side and you just it's not even possible to walk out.  Stockpile supplies, including cots, linen, soap, toothpaste, non perishables for a 72 hour period for as many clients and staff as you expect to be on the premises. This is not something you can plan for a week in advance. So you want to stockpile it and then audit it every six months or so. Prepare personal go kits one per client with a water bottle flashlight batteries toiletries and consider adding a t shirt and shorts, a towel, a high energy food bar. Some of these things if you're running a residential program or it's a sober living facility, you can have clients bring these added mission so they have their own personal go bag in the event of an emergency. You know, that's up to whatever funding your agency have an inventory and replace supplies at least quarterly. We all know batteries explode. So, enough said there. Have real time data backup of electronic health records at remote local access in an emergency. Keep coolers on site for transportation of refrigerated medications. Make sure an electric water pump, if any, you know, if you have pump water instead of city water, make sure it's connected to the backup generator. Train all staff. This includes your front desk staff, your texts in emergency psychological first aid, so they can become aware of the signs of somebody who's who is starting to head into crisis. And they know what to do to get them referred out and help stabilize the situation. There's a psychiatric advanced directive in the file for any patient who may destabilize in an emergency, which includes helpful interventions about legal representatives, helpful interventions and info about legal representatives should they become incapacitated. We do this at admission. When we go through the process I have a whole sheet that's dedicated to okay, you know, in the past when you've gotten into crisis and you've just, you know, really been. Unable to function or really been angry or stressed out whatever the case is for that client. What things help what things help you deescalate what can we do that is going to be useful. And what could we do that might be harmful or might make the situation worse that way we know ahead of time what not to do. And then the event that you can't speak for yourself you've going to a full psychotic episode or something if you're dealing with that kind of patient. Who could we contact in order to make decisions on your behalf, prepare for financial resiliency and this kind of goes back to risk management. So enroll clients in emergency Medicaid, if you've got clients who are paying, and all of a sudden there's the disaster and they can't pay you may lose a big portion of your client population. So if you can get them enrolled in an emergency Medicaid, that might help. Likewise, again with Katrina, we had people coming in from other states they weren't on our state Medicaid, but in order to get paid for providing them services. We had to get them on emergency Medicaid so they could get services and the agencies could get paid. Educate payers about modified counseling services to facilitate reimbursement. We'll talk about that on Tuesday with technology based counseling, but some payers are still not okay with reimbursing for any sort of tele mental health video or otherwise. So if you think that's something you're going to use, educate the payers ahead of time and say if we're in an emergency, and we have no other way. We will use this. Are you going to pay for it or what do we need to do in order to get it paid for to see if you can come to some sort of an understanding for an emergency situation. Some agencies may have a reduction in cash flow due to relocation of community residents, you know all your patients have gone over to another state. So you need to figure out how are you going to maintain payroll and get through that situation. Staff members might be shared with programs or other agencies experiencing an influx of clients to reduce your payroll load. So they may basically work PRN at another facility during the disaster in order to help them with their increased client load and take the burden off of your agency. Consider how to support client retention through active outreach following a disaster. When things like this turn the apple cart topsy-turvy a lot of clients will drop off they'll just kind of forget about counseling it will seem less important. So what can you do during and after a disaster to continue to reach out make sure those clients know that they're important to you and their welfare is important to you. Disaster planning prepares for client safety and continuity of care and financial solvency for organizations in the event of a disaster. It is largely about client safety and making sure that we do no harm and you know all that stuff. But we also want to make sure our staff is safe and they're able to keep their jobs and you know all that kind of stuff and that our agency is able to maintain payroll and resume functioning as soon as possible. Providing those services that we have promised our clients we're going to provide. Get memoranda of understanding with local agencies the health department and emergency services this is vital to preparation. You want to make sure that you've already gone out and shook hands and agreed upon in writing what each agency is going to do so there's no question.   There are a lot of things that you would do.  Have a list of identified risks for your area by contacting the local health department and getting that just handed to you they've already got it you might as well save yourself some work. And make sure all staff is trained in the disaster procedure and scenario training that reinforces this periodically. It's great to write it down and talk about it. But as we all know when it comes to crunch time and in a crisis and when people are kind of in an adrenaline fog, we might not think as clearly. And if you go through the scenarios, it's really easy to put something down on paper and go yeah that looks great. You know let's let's file that away. But then when you actually operationalize it, you get to places and you're like oh wait a second. We want went on a hike yesterday and we got to this one point it was supposed to be just you know, an out and then a loop kind of like a kind of like a balloon. But there were a couple different places we had to make decisions about which ways to turn. And then that wasn't something we had really planned for thankfully we had the map, but you want to make sure that you actually walk through it at least once. Obviously you're not going to, you know, transport clients, but you would get to the point of calling emergency services to transport clients and talk about what would you do, and may even have someone act like emergency services. So you make sure the handoff goes smoothly. Okay, that is what I've got as a really brief rundown for disaster planning. Whether you are a single practitioner, a sober living facility or a full scale multi program community mental health facility. It's a good idea to plan ahead to make sure that those people that you are responsible for serving are going to be taken care of in the event of, you know, weird things that you know knock on wood. They'll never happen, but it's better to be safe. I'm sorry. Any questions. So on Tuesday we're going to talk about technology based techniques for the use and counseling, and there are a lot of them out there and a lot more research than I really realized. There's actually like 196 clinical trials going on right now with technology based mental health treatment. So that's really exciting stuff that's coming up and it segues in with this disaster planning and the ability to provide services to clients who are at a distance who can't get to your facility and you need to use remote procedures. Everybody have an amazing weekend and I will see you on Tuesday. This episode has been brought to you in part by AllCEUs.com providing 24-7 multimedia continuing education and pre-certification training to counselors, therapists and nurses since 2006.


Check your own pronunciation. Do you pronounce these words over here with a sharp initial S and say safari, sex, single, and software? Or is your version a pretty German one and you say something like safari, sex, single, and software? Well, if the latter is the case, I think I can do something for you. The problem is a distributional one. Both English and German have a voiceless alveolar fricative as an alofone of the phoneme S, as an English kiss and its German equivalent kuss. English words like sex, however, where we have an initial S are realized with a voiced alofone in German and thus often come out as sex, so the initial S in German is generally voiced. How can we solve that problem and achieve a voiceless variant even in this position? Well, the trick is quite simple. We use those initial S contexts where even Germans use a voiceless S and such contexts exist, namely those where a consonant follows the S. Here are two parallel examples, skeleton and German skillet and Slovenia and the German counterpart Slovenian. In these cases, even Germans use an initial voiceless alveolar fricative. So once we are aware of this fact, present-day English words like snake, slope or swallow must be considered relatively uncomplicated as far as the initial S is concerned. The only thing is we have to transfer this awareness to contexts where the initial S is followed by a vowel. And if this still doesn't help, well, in such cases I suggest to put a short glottal stop, which is of course voiceless in front of each word when you practice it in isolation. So you get a safari, a sex, a single software. Well, and that's almost identical with the English counterpart. Okay, I hope this helps and you will no longer find it difficult to produce present-day English words with an initial S.


Who has made it to the list is Heimant Malik, ITC Limited With 30 years of experience under his wing Heimant has spearheaded lifestyle retail operations, FMCG sales and shown a demonstrable ability to launch products according to changing trends Brands such as Ashirwad, Pingo, Sunfeast, Minto, under his leadership have leveraged digital mediums to successfully evangelize their messaging Thank you very much, Exchange for Media for featuring me in this list of marketing leaders and to actually be given the top slot I'm really humbled Thank you Anurag and Nabil and the editorial team that you felt I think your list, which you've restarted after a gap of a few years is extremely relevant I think it's going to become an extremely popular list based upon the number of compliments I have received and I'm sure that people will all want to be part of this list So thank you once again I think as far as digital itself is concerned for this recognition, I think the recognition is due to my team We have all taken very aggressively to this format for all across our brands We've believed in trying and testing out newer solutions We've believed in failing fast We believe that this is the new world and I think it's a recognition for the great work that my team has done and I'm sure digital is a new way of marketing There are new learnings that are coming in and your platform and your channel has been trying to keep all of us abreast about it So thank you once again and wish you all the very best


I would like to thank Ivan for the introduction, for the invitations, for Frank and the other organizers. So it's great to be here. It's my first time here. So the topic of my talk is actually parabolic equations, so not really connected with wave phenomenon. However, what I will discuss is blow up phenomenon. So that, of course, as it has been deeply studied already, it has a lot of parallels with singularity formation in parabolic problems, except that here the mechanism that triggers it is diffusion. So I will mention next three problems that have rather similar features. Of course, with a lot of technical differences, one with respect to each other, but with a common flavor. I will only have time to speak about one of them. So I prefer to say a little bit more about one of them specifically. So one of the examples, actually, of the type of phenomenon I would like to see, where perhaps it is easier to explain what happens is, say, the three problems that I'm going to mention are actually have been studied a lot. They are quite standard in the literature. So one of them is that reaction diffusion equation with this special power, which is the critical solar exponent. Say we can consider, for instance, the problem of finding positive solutions in the domain, maybe with boundary conditions, and define up to some time capital T that could even be infinity. So a second problem, which is the one I will really talk about, is the harmonic map flow into S2 from R2 into S2. This is a special case, of course, the flow of harmonic maps, the evolution problem for harmonic maps. But in the case of values in S2, it takes a particularly simple form, which is this semi-linear equation, where the non-linearity carries this gradient squared term. And some special feature that is actually preserved along the flow is the fact that the absolute value of u is 1. So u really has values into S2. So we will consider this problem in a bounded domain, omega, although most of what I will mention is valid also in the space, or certain classes of bounded domains, but doesn't really matter. And up to finite time T. I will consider this problem with a given boundary condition and corresponding initial data. So a third problem of this type is the Taylor-Siegel equation. The Taylor-Siegel equation is an unlocal equation, if you want, or a system. So this is simply the heat equation, the standard heat equation, modified by a drift operator that depends on u and on this v. And what is this v? This v is inverse Laplacian of u, which by definition for me will be simply the convolution of u with the fundamental solution. This is a two-dimensional problem, which you can also write this problem in divergence form like this. OK, what do these problems have in common? One of them, one very important that makes the problems somehow nice, is the fact that they all have Lyapunov functionals. Actually, this is valid not just for the critical power, but for any power you wish, formally. Say this functional, defined like this, is a Lyapunov functional. In fact, it is strictly decreasing unless we are at steady states. At this we are standing at steady states. And more precisely, it's just a computation, formal computation tells us that the derivative in time of this guy is going to be minus integral of u t square. So it's negative. So a similar feature we have for the harmonium flow, harmonium flow by definition actually, is the two-gradient flow, or the two-negative gradient flow for the Dirichlet integral. For here, I insist u has values into s2. And again, we have the same characteristic for e2. So e2 is strictly decreasing along smooth solutions of it, non-trivial solutions, non-static solutions. And well, perhaps a little bit more complicated, but still similar, is the Taylor-Siegel system, the Taylor-Siegel equation, the Taylor-Siegel non-local equation, which can be written in this form, as I mentioned. And it turns out that the Lyapunov functional is given by this quantity, which is a little bit different. Now the derivative of this guy along smooth solutions is negative. But now the right-hand side is given by this. OK, so this is one feature. This is one feature, the fact that they have this structure, this variational structure. But another one that they share that is very special for these problems is the following. It's the presence of a special family of steady states. As a matter of fact, a continuum of steady states, but a continuum of steady states depending on the scaling parameter, the three problems have special scaling variances. And that asymptotically becomes singular. Say, what do I mean? I mean, let us consider this, which is a special solution of this space. Well, in fact, all solutions of this can be written as a translation and a scaling of this function. So they are all given by this formula. This is known, the positive solutions, I mean. And a characteristic they have is that they all have the same energy, the same energy that I wrote before. So it's actually constant along this scaling. So we have energy invariant family, an energy invariant continuum of steady states, which as the parameter takes to the limit to lambda going to 0. Say, this function becomes singular. Of course, away from the origin, this goes to 0, but exactly at the origin. This is 1 over lambda raised to the power. It goes to infinity. So it has spike form, so like that. OK, so what is the corresponding object that I will consider? Because it's not the only one, unlike the critical exponent equation. Say, an object that seems to play a similar role is the following. This is a harmonic map. This function is a harmonic map. A harmonic map is, by definition, steady state of the harmonic flow. And this function indeed solves this elliptic equation with absolute value 1. We call it the one co-rotational harmonic map or the standard one co-rotational harmonic map. Again, we have a same type of translation invariance. We also have a dilation invariance. If you simply scale the argument of it, the energy is preserved. The energy, meaning the Dirichlet integral is time. No lambdas in front, of course, because you have values in each one. But there is an extra invariance that is this. If you rotate, u is a vector. So it's an element in S2. If you rotate it by an orthogonal transformation of R3, then you still get a solution of the equation. And they all have the same energy once more. And as lambda goes to 0, this, of course, does not blow up itself. It has absolute value 1. But what blows up here is its gradient. The gradient of u is actually going to infinity. Now, what is the corresponding object in the Keller-Siegel system? In the Keller-Siegel system, say, in the Keller-Siegel equation in R2, well, a natural object to refer here is this function. And this function has, again, the characteristic that if you scale it now this way, you still get a solution. And this scaling preserves, again, the energy. This funny energy rose at the beginning. That is. Ah, they have an additional feature that they all have mass 8 pi. So what is the topic of this talk? The topic of this talk, or actually the issue that I would like to analyze for the three problems, but in reality, it will refer only to the second one now, is the construction of solutions that have blow-up phenomenon, the exhibit blow-up phenomenon as the approaches a finite time or even infinite time. And what is the special pattern of blow-up that these equations exhibit, or that is already more or less known, that there is blow-up arising in this way, is precisely like this. Say it's precisely in the form of blow-up around the finite number of points, maybe one or maybe more, where the profile of blow-up near each of the blow-up points is scaling asymptotically singular, or resembles the scaling, an asymptotically singular scaling of a steady state of one of these energy preserving steady states. This is not so crazy, because since the energy is preserved, say the energy of an object like I am picturing here actually gets stabilized, because the scaling doesn't change the energy. So this is what is special in these problems. That's a feature sometimes called criticality, as a matter of fact, in this setting. OK, so now I would like to refer to the harmonic map flow from R2 into S2. Then I consider this problem, which from now on I will call HMF. So I consider this parabolic equation up to some given finite time capital T in a bounded domain, or in entire R2. But if omega is not the whole space, I consider boundary conditions and an initial condition. So of course, both the initial and the boundary condition have to go into S2. If that's the case, that property of having absolute value one is indeed preserving along the flow. OK, so there is a lot of literature around this problem. In fact, I would like to make a sort of review of known results. A lot of people have worked on this since long ago. Well, the harmonic map flow was introduced, not just in the setting, the two-dimensional setting, but as, say, as the L2 gradient flow, or L2 negative gradient flow for the Dirichlet integral for maps between two more general remaining manifolds. Yeah. And it was introduced as a way to build harmonic maps in reality. So these flows was introduced by Ilson and Samson many years ago, 50 years ago. And concerning, for instance, the problem of existence, local existence in time of classical solutions, this was first seen by Ilson and Samson themselves. Then Struve, and then for the case of compact manifolds, and for the case of the boundary value problem by KC Chang, more or less in 85. OK, so I repeat what I said before. Say the Dirichlet integral is actually strictly decreasing along non-trivial trajectory, non-steady trajectories, non-trivial trajectories of the flow, and we have this identity. So the energy is decreasing along the flow, along the flow, as long as the solution remains smooth. But something that has become, that became known, is that, in general, we don't expect global existence, global existence of a smooth solution. That's typically not the case. Not typically, but it may not be the case. Say that the solutions remain smooth at all times, while this didn't really become known up to much later. However, Struve, in 84, say this is an important result of the theory, actually, proved the following. Proved that even though the solution may develop singularities, those singularities can more or less be understood. And it can be understood enough in the case so that the solution can actually be continued in a natural way. In fact, it can be continued in a way, continued as a weak solution. It can be continued as an H1 weak solution, where the energy has discontinuities. The energy still decreases, but it has jumps. This is what happens with the definition of Struve. Well, as a matter of fact, it turns out that only at the finite number of points in space time, so only up to only for finite number of times, and for each of those times at the finite number of points, we can have blow up. And at those points, at those times, jumps down in the energy take place. There is this resolve by Freyr in 2002. He actually proved that for a certain class of solutions, where energy is decreasing even if it has jumps, this solution is unique. So that means that the definition of Struve is, in a way, a good definition. More recently, I don't remember exactly the reference, but very recently, a student of Struve proved that if the jumps say, the solution may not have decreasing jumps. Say, even if you have a weak solution with jumps in the energy that could even go a little bit up, but not too much, the solution is still unique. What I mean is that the jumps, as I will try to argue a little bit later, the jumps in the energy are quantized. In fact, in all examples known, this jump cannot be less than 4 pi. And I think this is a general fact indeed. So this is Struve's solution, the energy in Struve's solution when you reach a singularity. OK, so as I mentioned, say, you itself does not blow up, has absolute value 1, but the gradient blows up when we have blow up. So in fact, if I call capital T the first time at which regularity is lost, which is strictly positive, as we know, we must have that the gradient goes to infinity as T goes from below to the blow up to the time capital T. Well, I will mention, although maybe the statement is not completely precise, I will state the property that is a summary of results by several people who work on this in the 80s and 90s, starting with Struve and several other authors, as I mentioned here. So the question is, how does the solution looks like when it blows up? And it turns out that quite a bit of it can be set. The solution actually does blow up if it does. If it blows up, it blows up in the form that I mentioned before, namely, as scaling around a finite number of points of steady states, steady states, steady states Ui, which are not necessarily the U that I wrote before. So more precisely, the statement is a little bit weaker, but still quite a strong assumption. If we approach capital T along a sequence, then I can extract a subsequence such that for a finite number of points Q1 up to Qk, the following holds. U along that sequence resembles an h1 function plus the sum of these bubbles. This is the subtraction of the value of infinity of the bubble, which makes sense. And say where this guy, say this is just a normalization, where this actually goes to 0. This difference, say, pointwise. Pointwise away from the points Qi. Qin is approaching each of the Qis. And these lambda ins go to 0. In fact, a little bit of important information can be obtained about the relation between the scaling parameters and the mutual distances of the points, which is this fact. These numbers here, for i different from j, go to infinity. What does this mean? What happens is that if the points, for instance, Qi are all well separated, one from each other, say this is automatically satisfied. It doesn't matter what this is. This goes to infinity, because this goes to 0. But it could be the case at all points, Qi, or a finite number of them coincide. What this says is that if they coincide, if they coincide, for instance, then this goes to infinity, which means that the rates are not comparable. One of the rates is much smaller than the other. So if we scale around the point, that means that you see just a single object. Say, if you use lambda i or lambda j, you will just see one object. So this is what that property means. So the UIs, as I mentioned, are harmonic maps. So harmonic maps with finite energy in entire ones. So what I mean is the UIs add entire solutions of this equation with values in S2 and with finite energy, with finite energy, which is natural. I mean, we are starting with a finite energy configuration. So in the limit, we should see something with finite energy. This is also a standard fact. Is that U is a function that goes from R2 into S2. But I could regard it after stereographic projection as a function from R2 into R2, or from the complex numbers into the complex numbers, or with the composition in the other way, from S2 into S2. I can regard it as a function from complex to complex, or from S2 into S2. So this is known. This is a known fact. These maps are, say, conformal and in S2. And that makes, well, in fact, when it is lifted to S2, it becomes a smooth function. So that, in particular, the value U at infinity, say infinity is one of the poles in S2, is well-defined. Some fact that is known is that using correspondence in the complex numbers with a rational function. And in fact, this also holds. So if we compute again by conformality in S2, say the integral of gradient squared turns out to be a multiple of 4 pi. Say, 4 pi is the area of S1, of S2. So it's an integer times the area of S2. And this fact holds for some m in the national numbers. So in particular, the least energy, non-trivial harmonic maps, non-constant harmonic maps, have energy 4 pi. So this is the reason of the 4 pi I mentioned before. So in particular, say, what are we going to have? We are going to have that this U along Tn goes weakly to U star in H1. And the energy, say, the defect with respect to the gradient of U star squared are precisely asymptotic for the Dirichlet measure is given by this asymptotically. Simply integer multiples of 4 pi times direct delta set, the corresponding lower points. So this is a way to visualize quickly what the statement says. OK, so of course, there are many questions around it. This is a very interesting phenomenon. By the time of Struve's results or many others that I mentioned, it was not really much known, so much known about existence, for instance, of such patterns or further properties of it. Stopping in 2004 proved this very interesting fact. Proved that the rates at which the lambda is, remember, are these blow-up rates around each of the bubbles in this decomposition. This is what I mean. So what Topping proved is, say, along subsequences, but I mean it doesn't matter, he proved that these blow-up rates have to be of this form. So they go to 0 faster than t minus t to power 1 half. In fact, the estimate he finds, I think, is a little bit better, say, with the log in the denominator. But what this says in the language of these type of geometric problems, or actually of many singularity formation phenomena, what this says is that the singularities developed must necessarily be of type 2. Type 2 means a singularity that cannot be captured with a sub-similar form. This is more or less what it means. And the right rate for that in the harmonium flow is this 1 half. So lambda i actually goes to 0 faster than that. This is also valid in more general targets, not just in S2. In fact, Topping finds examples that show that this estimate is, in fact, optimal, or approximately optimal. There are examples of manifolds for which you can get blow-up rates as t minus t to 1 half plus delta for any arbitrarily small delta. OK. So what are the, let me consider now the function u that I am calling from now 1u0, this standard harmonic map. This standard harmonic map, actually, when you is just lifting, say, this is a function from R2 into S2. But if you take it from R2 into R2, this is the identity. So this just comes from a stereographic projection. So these guys have exactly energy given by 4 pi, degree 1, if you want. And the valued infinity of them, of course, as you quickly see, is 0, 0, 1. So let me now mention what is it known concerning existence of blow-up patterns. In fact, there are very few examples known. And in fact, the examples known concern single blow-up points where the profile is like this. But more than that, the examples concern radially symmetric corrotational, actually more precisely, radially symmetric settings of which this is the only steady state. Let me be more precise. One corrotational solution of the harmonic map flow is a solution that has this form. This is, of course, the spherical coordinates is a way to represent a vector, say, in S2, a point in S2. And I assume that this angular variable is always e to the i theta in polar coordinates, where r and theta are the polar coordinates. And these functions are radial, radially symmetric. So what is very nice is that with these ansatz, the harmonic map flow reduces to scalar equation. And this scalar parabolic equation is actually very simple. It's vt equal to d Laplacian, modified by this guy, which is sort of, by the way, an encant type non-linearity. But I will not really elaborate on all that. But something that can be observed is that this guy has the following steady state, the only monotone or finite energy or whatever steady state is given by decreasing, say. It's given by this function. This is explicit solution of, stationary solution of the equation. And if we evaluate it with this v, say we obtain exactly the u0 that I mentioned before, the standard power. OK, so concerning the literature. In fact, it had been, as I saw in their paper, it had been actually previously conjectured that it may be the case that no blow-up exists at all, but there's no blow-up in this 2D harmonic map flow. But Changding and Ye in 1991 found a very nice example within the one-corrotational class. In fact, what they are able to find is a solution of the scalar equation, v, which looks like the steady state, w, scaled this way, scaled by some small number lambda of t. Or equivalently, say, for the actual original harmonic map flow, the solution you associated looks like the u0 at x over lambda of t. Where this lambda of t goes to 0 as t approaches capital T. So what they do is they, it's very, very nice arguments. They capture the blow-up using barriers. So they prove that there is blow-up using some special barriers. And those barriers are very sensitive to what the boundary conditions are. So it is necessary to take the boundary conditions in certain range in order to observe the phenomenon. They take initial conditions 0 and boundary values, say, bigger than pi or less than pi. And they observe this phenomenon. Well, for the one-corrotational solution, this was proven many years later, 2009, Angen and Hulshoff and Matano found a much stronger estimate for this setting, for these special solutions, for this special harmonic map flow into S2 and one corrotational, the rate turns out to be much smaller than t minus t to 1 half. It turns out to be little order of capital T minus This is what they proved in 2009. Actually, before them, Wanderberg-Hulshoff and King in 2003 made a very, very beautiful paper, formal paper, in which they describe a lot of phenomena around the one-corrotational blow-up, the blow-up in the one-corrotational case. And when they discovered, formally, is that the blow-up rate, here is a mistake, important. Here is squared. There is a 2 there, not the one. It's a very different life with the 2 than with the 1 in these rates, by the way. So what they discovered is that lambda of t is of disorder. So it's not just little order of t minus t, but actually modified with the log square in the denominator. So the result of Angenin, Matano, and Hulshoff is weaker than this statement, but of course it is a rigorous result. And a result that is much more recent. In fact, I think the year is 2013. It's due to Raphael and Schweger. They prove a very important fact. They succeeded to make a construction of an actual solution, one-corrotational solution, that blows up exactly with this rate. So the construction is very explicit. It's not based on barriers. It's actually machinery closer to dispersive equations to analysis of blow-up in dispersive problems. And they found a very, very, very nice description of their solution with the right blow-up. And they were able also to establish this very interesting fact. They proved that this rate, say, in the formal language of these authors, they say that they find the, quote, generic rate. So they say the generic rate is should be this, with the two. So what Raphael and Schweger proved sort of that, but, well, not exactly. What they proved is that for the solution they constructed, if they take small perturbations of the initial condition for that special solution, then they still see the same phenomenon. I mean, they see steel blow-up with the same rate, of course, at a slightly different time. This is, I insist, in the one-corrotational radial symmetric class. So these are the examples now for the flow from R2 into S2, as far as we know. Now there are, of course, a natural question now is to investigate what happens in the non-radial situation. Or in a situation where there are boundary conditions. In the case of the result I just mentioned, the setting was entire space. So the question is, natural question is, well, are there solutions that are in non-radial symmetric settings? For instance, is it possible to have more elements, like in Struber's, the composition, the bubbling resolution, like several bubbles in different places? Can you have towers of bubbles or bubble trees? I mean, et cetera, there are many questions around. And of course, the question of their stability, because it might perfectly be the case that the solution is stable within the radial symmetric class, but when you make perturbations, which get off the radial symmetric class, perhaps the stability is destroyed. And our result, just as a summary, is the following. Say we prove that if we take any finite number of points of omega, in fact, I should say the following. Yeah, it's roughly this. You fix k points arbitrarily. Then you can cook up initial conditions and boundary conditions, boundary conditions independent of time, so that a blow-up solution with exactly those k given points exists. This is essentially the result. And the profile is like Raphael and Schwerer scaling, or Schenckding and Gehr. It's a scaling of the u0 with rates that can be computed explicitly. And they coincide with the one formally derived and rigorously found by later. And this is also a kind of result that supports the quote's geneticity statement. At least the bubbling at one point, at exactly one point, is stable. This, in fact, very connected with some work by Frank Merlin and Hatem Zag in the subcritical heat flow, where solutions with finite number of points were found, arbitrary points in the domain. So it results shares the flavor. OK, so very quickly, let me say how, yes? When you had the initial cartoon of the multiple points, it looked like there was a hole in the domain. Oh, yeah, yeah, yeah. No, no, but there's no need of the hole. No, no, in fact, if you are looking for this type of phenomenon in elliptic problems, where the bubbling is triggered by parameters, many times you need topology. So I actually borrowed the picture from an elliptic setting. But many times, you need some topological assumption to get multiple blow-up. But here, we don't need anything. A way to put it is that here, we put all the blame in the initial condition. Say, all topology needed, say, is in the initial condition, which I don't say what it is. If the question is whether there's any numerics that shows this or not yet. Actually, the only numerical result that we are aware of, in fact, provided evidence opposite to one of our claims that was the stability. In fact, there is a paper by Wanderberg, I think, and Williams, that I learned from Peter, actually, that conjecture, numerically, that if you destroy the symmetry, then the solution may blow up. Sorry, the blow-up may be destroyed, exactly the opposite. But say, OK, so as I mentioned, the energies of all these guys is for pi. Let me consider not just arbitrary rotations, arbitrary orthogonal transformations. I will consider special ones that correspond simply to rotate this vector around the y3 axis, which means if you write it in complex form, simply multiply the first two components written in complex numbers, a complex number by e to the i alpha. OK, so this is our more precise statement. What we are able to prove is the following. Given k points, the distinct points, there exists initial among the conditions, such that the solution of harmonic map flow for those data blows up at exactly those k points. And the profile at those k points is given by, say, by a convergence to 0 like this in H1, and uniform senses, H1 and uniform, where the bubbling takes the form of simply suitable rotation around the axis times the corresponding scaling around qi, where now we put correctly the two where the blow up parameters are like this. So we have, in particular, this energy formula. The uniform convergence, by the way, is a property in the bubbling decomposition. Let me mention something very quickly. When the time goes to infinity, so if you go, actually, along a palet-smale sequence for the flow, or for the, if you go along the solution, but for time going to infinity, in fact, other properties are known. For instance, this convergence to 0 uniformly is sometimes called non-neck property. So it is not known if this goes in general in the finite blow up thing. Well, of course, when time goes to infinity, this guy sees the harmonic map. There is a paper by Peter Topic where it is proven that if towers are formed at infinity, then all the elements of the tower, except the first one, must be either holomorphic or conjugates of holomorphic at the same time, not holomorphic. I think that's the, is that what you proved? No. OK. So anyway. So Raphael and Schwed, as I mentioned, proved the stability within the one corrotational class. And here I mentioned this numerical work by van der Weyden-Williams. Ah, and actually, let me mention the stability. The stability statement is a little bit more precise. It's a little bit more precise. Say, well, the single blow up is stable in this sense. If you perturb the initial data, then you observe exactly the same phenomenon where, of course, these numbers, alpha i star, this cap i star, some of the time capital T and the points qi, are slightly modified, as it is natural. And if you consider the blow up point at exactly k points, that phenomenon is not stable, which is, I mean, no wonder.  This is what it means. But if you insist that the blow up takes place in exactly those k points, you can choose the initial data in a co-dimension k minus 1 manifold around the initial condition. OK, so let me mention another issue that we find quite interesting. That is also addressed in the formal paper by Vanderberg and Hulshof and King. And in rigorous work by Peter, which is continuation after blow up by a mechanism called reverse bubbling. I will say very quickly what that is. Say, what happens is that the definition of Struve, say, has this unpleasant fissure that the energy jumps. But the energy jumps means, say, a change in the homotopy class. I mean, actually, it turns out that that means a change in the homotopy class of the image of you. A change of degree, if you want, not just a change of degree, a change of homotopy class. So the question is, are there other type of continuations after blow up that are nicer in the sense that they possibly preserve some of the topology of the original manifold. And a topping proposes a way to do this and prove that there is a continuation with this fissure in the one-corrotational case. He proved that Chang, Ding, and Ye solution can be continued with a profile very similar. However, with one difference, it's not the one-corrotational standard bubble, what you see after the blow up time. But after the blow up time, you see the same thing, but in reverse orientation, the conjugate, if you want. And that is this map. So asymptotically, it's the same, so this is 0, 1, like the other. But around the origin, it winds in the opposite direction. So this type of procedure is what is called reverse bubbling. So in the reverse bubbling has, in the energy, a feature that is different from Struve. In fact, it's nicer in a way, because the energy, in fact, continues continuously, except exactly at time T when it goes down, goes down and up. Remember that decreasing implies unique. But if you leave the decreasing, but you allow that there is fixable discontinuity of the energy, then this solution does it. What we proved is that this continuation is possible for the solutions we built. And the solutions we built can be continued with exactly the same profile, except that after, when you go from above the blow up time, say the solution is defined up to T plus some delta.  So concerning the construction, something that may be reasonable to think is that this type of profiles that we built may actually be quite general. Say, may even be generic, really. Say, in the way blow up takes place. Why do we say this? It's not obvious at all. It's not obvious at all. But the question is, is it possible to have bubbles other than those induced by 0 or its conjugate? Because there are other harmonic maps. There are k-corotational harmonic maps with higher degree. So is it possible that there are profiles like that? And it turns out that in the k-corotational class, which also leads to some similar scalar equation, it turns out that for high, in the high-corotational class, these authors, Juan, Gustavsson, and Tsai, prove that this is not possible. In fact, they prove that this was not possible for high-corotational number, but they conjecture that it is true also for lower ones. Say, there is, I think it's Wanderberg or Wanderhout, the author. Sorry, I didn't include it. Actually, there are no bubble trees in finite time, so no towers. This is another thing. But just in the one-corotational class. In the infinite time, Topping found them. In the infinite time, bubbling, there exists bubble trees, at least with some special right-hand sides. I mean target manifolds. And all the rights are also possible. They have been found by Raphael and Schwerer in the one-corotational class, but they are non-generic. They come with different powers of t minus t. Sorry. This shouldn't be here. Anyway, no, just let me, in one second, let me say how the solution we find is made. In fact, I don't have time to discuss it, unfortunately. Yeah, it was like for two talks. No, OK, the solution is made in the following way, OK? The solution is made as the bubble and actually this whole thing that I had written in the previous pages was to attempt to justify how the scaling parameter is chosen. And the way it is chosen is connected with the following. The initial condition is made in the following way, by the bubble, but plus some remainders. And these remainders are crucial. And I will not say, I mean, what this does is to correct the error, what this term does is to correct the error due to the lambda far away.  And this just corrected far away. But this guy is less obvious. This is a function projected in the tangent space of the sphere, say, the orthogonal to u. And this c star is a solution to hit equation. And this is a lower order term. That is explicit, but doesn't matter. And this guy has to have the following properties. It has to have, it's a vector field in R2, actually. With two components are 0, c star tilde is some c star, and with 0, third component. And we need divergence positive, currently equal to 0, and value equal to 0. So you cannot put c star equal to 0. This is what I mean. You really need this guy. You really need the perturbation of this type in order to find a reasonable equation for lambda. And that reasonable equation for lambda is an equation like this. It's an equation, it's a non-local equation. It's a non-local equation like this. At this non-local equation, when this guy is negative, it's actually something that we cannot solve exactly, but we can solve approximately at a very high precision. It looks like we cannot really solve it exactly. And this leads us to, I mean, this is not difficult to see. An equation like this leads, it's a non-local equation, but it leads us to a solution of this type where k is exactly proportional to the divergence of c star. So this is what, yeah, I'm sorry, it was the first time I tried to give you this talk, so it was too long. Okay, thank you very much. Thank you very much. Questions, comments? The continuation with the Rebels bubble. Yes. Does it come as a limit or something? Some parameter goes to 0 or whatever, or you just throw it out? The construction is actually explicit. Say, let me put it this way. In the limit, you see the bubble, which exactly at time capital T, you drop. Then you get a new function there, right? It's kind of smooth, yeah? Yes, it's a point. Let me precise your question. When you look at another P which do not blow up and approximate that, what is the rate? I think that's a very good question. No, we have asked ourselves that question. Now I understood the question. Yes, we have asked is... One question is... Is this the right continuation? I know what you mean, yeah. Guess what, with this, it's very much. Do you or will they focus right away, so we are... I think, in fact, I think it's a very good question. I mean, we have asked that question ourselves. I'm sorry, what is the question? No, the question is this. Say you regularize your flow. Say you put gradient U to power 2 minus epsilon or something like that. I don't know if that's the right thing. So, say, and then you analyze what is happening around that blow up time for same initial conditions when you let epsilon go to zero. Say, presumably the solution will blow up. But the question exists also after blow up. So, is the solution we are constructing the right limit? It's a good question. In fact, my opinion is yes, but my co-authors' opinion is the opposite. But we don't really have a clear evidence to that. No, no, it's impossible to guess. You have to learn the truth. No, absolutely, absolutely. No, we don't know. This is somehow the choice that seems to make the energy more continuous. On the other hand, you know, if you... The convergence is not so nice in a way. Okay, because you have the bubble in one, with one rotation up to the blow up time, but then the rotation changes, changes direction. So, you go from degree one to minus one. So, there is a sort of discontinuity, even though the topology is preserved, yeah? Same degree, you just rotate more, 180. Yeah, yeah, yeah, this is... I'm sorry, this is what I mean. It's same degree, this is why the homotopy class is preserved. But if you see what is happening immediately after, immediately before, say, there is no uniform convergence. Say, the difference between time t plus epsilon and time t minus epsilon, it's not something that goes to zero. The chemistry has it. Yes, yeah. The first effect, you have this change, I think it's similar to what Merle did, his configuration in the NLS, that it comes in and opens up. Yes, so you have this change of the class one to minus and everything else. Ah, no, I didn't think those terms could be. You think so? So, it's unstable. Yeah, but what is missing here, right? Is something should be lost in the single level, after the single level, maybe. And in your continuation, I didn't see anything get lost. No, there's nothing lost, actually. Say, the energy is sort of continuous nicely. No, there's nothing else. This is, yeah, but this is a diffusion phenomenon, so maybe slightly different. I'm thinking, okay, but anyway, okay, I don't know. But it is a geometric equation, so you have some constraints coming from the geometry, so it could, that's the reason why probably there is only original way of continuation. It is possible, I don't know if you have, do you have that opinion? Do you, for example, have different speed of de-focusing activity, so how can each one increase? Ah, let me, this is a mention. When you construct the reverse bubbling, in fact, there are many reverse bubbling rates that you can get. In fact, the genetic one is not this one. If you go from positive time to zero, you can construct a blow-up solution, but you can get all the rates, and the typical rate is not with log square, but with log. So it's not... It depends of your approximation. You choose just one rate. Yes, so the rate you choose may depend on it, I don't know. Yeah, what do you say? It depends on the approximation of your equation. The, you don't have the freedom of the rate. This way to do it is just approximate. Yes, you do an approximation. Yes, of course, and I'll get right around it, yeah. You differ. Many of them do not appear, but they're... Yeah, yeah, yeah, yeah, yeah. So it may actually not... Okay, so this has bearing on the stability that you're talking about, which I don't understand, but it may be, you're not approximating the equation, but just approximating the initial data. So it will be a reasonable way to construct a continuation by taking approximations of the initial data flow, maybe with smoothness and take a limit, but... Somehow the claim you're making about the stability has bearing on this, and I must say I don't understand that. So in general, this finite time singularity can't be stable because you can smoothly perform. Is the only example... Finite time singularity to a harmonic map, which has no singularity. So unless the singular time is going back to infinity, which is... The singular time? No, you're not... You can perturb, in the case of one bubble, you seem to be claiming you can perturb the initial data. And you still get that. But not in full generality though, right? Because you can take an initial data which generates a finite time singularity just to give it to a harmonic map. This is absolutely... Well, our construction is something extremely local. Say this function C star has an isolated zero, non-degenerate, positive, diverse... There are a lot of constraints in it. If you perturb slightly from it, the stability is not lost. Okay, so you're saying you construct a solution and then in a neighborhood? In a neighborhood of that special solution, I get it. Yeah, in general, maybe who knows what could happen. If there are some degeneracy involved, maybe the singularities could escape. I mean, it's possible. But then do you include the Chang-Ding and Ye, for example, in your examples? Does the Chang-Ding and Ye is actually... Absolutely. In fact, they are boundary condition, is consistent with our divergence negative assumption. Say, we analyze that. In fact, it is consistent with it. Last question, maybe? Well, we got a lot of answers to some of the things I wanted to ask. But one is that every blow up you give is somehow isotropic. You have one target, one queue, and there's no non-isotropic blow up, so you don't get elongated bubbles. It's kind of a question of uniqueness. Right. Here, say... Yeah, I mean, we are really standing at the standard bubble. And the standard bubble is sort of isolated. In fact, the key element in the proof is the non-degeneracy of the standard bubble. Say, if you analyze the linearized equation for the harmonium flow around it, you can invert it with flat-home alternative where the kernel of the linearized operator just is due to rigid motions. So there's nothing bifurcating from it, if you wish. So non-isotropic, I don't know... Other type of shapes I don't know if you can get. But not nearby, at least. Not nearby, at least, yes, yes. Thank you again. Thank you.