The news we are about to share with you is about cancer, an intruder that is very personal to all of us. It impacts our families and friends in greater numbers here in New Jersey, where we also face a higher cancer death rate than the national average. Today, we are proud to announce that Memorial Sloan Kettering and Hackensack Meridian Health are creating an extraordinary strategic partnership to change the course of cancer. This new partnership with Memorial Sloan Kettering Cancer Center takes us to a new level that is simply unparalleled. We will be better serving all of our patients throughout an extended area in New York and New Jersey, and we will help eradicate cancer. We look forward to opening a number of really important cancer discoveries as well as new cancer therapies that we can introduce to patients here. First in New Jersey, but ultimately to set a model for the rest of the world with this collaboration. Our existing cancer centers will not only bear each other's name, but they will operate with a single standard of care. There are more award-winning doctors in the two institutions dedicated to cancer than probably anywhere, and you can find the two. Collectively, the strengths of the two systems that we have is absolutely amazing. Together, our mission will be based on two core principles, improving and speeding up the progress in discovery in cancer while at the same time developing value-based care. What's the quickest way to get to the moon? You put the two most powerful and smartest rockets together and you launch. Today is blast-off. This is probably in my 25 years in the United States Congress, and in the last 12 years in the United States Senate, the singular most important moment in healthcare in our state. It is an extraordinary moment. There's no doubt in my mind that this partnership will be a game-changer for cancer patients in New Jersey, New York, and all over the place. We are at a big deal here. This is an historic moment, and I'm so honored and proud to be part of it. We will build new sites together as true partners to bring world-class care to new communities throughout our region and ultimately across the nation.


My last deployment here was in November of 1990 in the United States Army Reserve out of Evansville, Indiana with the 766 Transportation Battalion stationed in Saudi Arabia right there on the Kuwaiti-Iraqi border. My name is Master Sergeant Sherry Bishop. I work in the Commander Support Staff for the 136th Operations Group out of Fort Worth, Texas. I've been doing this job for probably 30 years. I was what they referred to as the Battalion Postal Clerk. My job was to gather all of the outgoing mail, sort it. It was a four-hour drive to what they referred to as KKMC, take all the mail there, and then pick up all of the incoming mail for all of the individuals. We actually had a Patriot Missile launch squad that was probably not even a mile from us that was there basically to protect us. After a while, you just get used to it. Stuff being blown up or the ground shaking because you knew something got blown up, it just became part of your everyday life. You just learned how to cope with it.  When someone says, did I get mail today? Their face kind of lights up if you tell them yes, but if you have to say, I didn't see anything for you, you know, it's like their whole facial expression. I've seen a few people have like, no, you didn't get any mail today and they'll be like but mail definitely just from looking at people's facial expressions I think is a morale booster. It does affect the war effort in itself because if someone else is having a bad day or anything like that, that can contribute over into one, how do they fix the planes? How do they transport the equipment? Are they safe? Are they looking out for what they should be or are they thinking about what's going on at home? Why haven't I heard from home? 30 years later, it's easy, I mean, everybody has cell phones. 30 years ago, you stood in line at a tent for a five minute conversation with home. If you don't have the ground troops doing what they need to do on the ground, it makes it more difficult for the Air Force to do what they need to do in the air. Use the crews and stuff, be able to plan their missions and do them a little bit more safely.


Hello, everyone and welcome. This is Melissa Armel of the Stocks. We'll show you in the spy. Nice calling here. I made it to the market. I've been anticipating this drop. Kind of came out of nowhere here this morning, but I really felt that this was the week. So I guess the question is, where do we go from here? There is a potential that this drop could have some follow-through because really today is only Tuesday and it's 2.36. So there could be some follow-through here, but then again, there might not be the immediate follow-through. So again, nice drop in here called the puts last week into this. And then more this morning, a nice sell off here in the market. We're selling off actually in the spy. We are selling off in the cues and we are selling off in the diamonds. So we are just selling off here. So very, very, very, very, very nice move for the market and we will see exactly where we go from here. I have to see where we close today and then where we end up gapping tomorrow morning. But if we don't collapse, I mean absolutely tank here the next hour and a half of the day, which we might, if we don't, though, then we could see follow-through tomorrow. We could gap down tomorrow morning. We could be neutral. It's hard to imagine we could gap up tomorrow if we fall here into the close hard like this. I mean, I'm really, really, really seeing the weakness here in this market finally, which I've been waiting for. Because really, we didn't see any big, fat, massive green bar rallies at all here. And the last two weeks, even though we lifted higher, where was the full-on institutional money? Where was the buyers? Where was the, you know, like the, gosh, the meat and potatoes. The meat and potatoes wasn't there. It's the best way I can describe it. Yes, we gradually moved higher, but it wasn't like what I would call the meat and potatoes to hold everything up. So nice drop off here. Great shorts on today, and we'll see where we go. So good luck, everyone, and congratulations to everyone in the Gap Options newsletter who did these puts, and if we're still in, you can ride them on out. Ride these puppies out into the close, and we'll see where we end up going. Have a great day, everyone. If you're interested in the Golden Gap course, email me at melissathestockswish.com next class on July 13th and 14th.


Hi, my name is Shalu Kulkani. I'm a partner with Hydric Consulting. Increasingly, we see the CHRO as being more involved as top voices in the table because we are seeing organizations recognize human capital as a core and key strategic asset. So we see CHRO as being a lot more involved in strategic decision making that boards make, that leadership teams make much earlier in the process than we may have observed in the past. Looking ahead, CHROs we would say are looking at about two or three key challenges. The first being dealing with a hybrid workforce in every definition of the word. So whether it's an intergenerational workforce that they have to deal with or from a physical perspective a partially remote workforce equally with the introduction of automation, robotics, etc. a lot more about exploring where the human automation angle starts to work closely together. The other one would be to look in terms of data. So data, analytics, AI, these are aspects that they would have to deal with both from a broader organization perspective but also what this means from an employee experience perspective. And the third one is again probably linked to the pandemic but certainly a big topic and brought to the fore now is the psychological well-being and safety of the employees. How do you manage and take care of them and what's your duty of care towards them? So at Hydric we constantly research what the leaders of the future look like and we also work with clients. We are continuously learning from them, advising and guiding them. What we see are sort of two or three key attributes for leaders of the future particularly CHROs. One is agility, so continuing to sort of flex to a rapidly changing and disrupting environment. The second is to be a lot more leading in terms of inspiring and influencing with empathy, bringing that aspect into your organization. And the third one, which we see a lot more relevant in today's times is digital dexterity, being very, very comfortable with data, with analytics, with information at your fingertips. Change is a constant. We recognize that business disruption is going to be a continuous in the times that we work in. For any aspiring new young CHROs, our guidance would be firstly, keep building towards your learning skill sets. Keep looking at agility, building upon your understanding of where the organization is going and where the markets are going. The second one is to keep networking. The more you engage with your colleagues and peers, the more you can share stories with them and the more you can support. And the third one is to constantly challenge yourself in the way you approach problems and problem solving. So how you sort of process data and information, the processes you make, the prioritization approaches that you apply, the more you can constantly adjust and adapt the more successful you'll be.


Touch and pin prick and this is my knee hammer. What does do I need? And for the time being, I'll do with this. And if I need to do it, I need to do it. You may have to remove your document. Okay. You can come even closer. Paul, can you see from there? You can't see anything. Just stand on top of the chair. No problems. Today we are very democratic. You can stand on top of the table also. Okay. So we'll start the photo system. You'll be asked to do a quick examination. So one I'll demonstrate here. Another one I'll demonstrate here. And we'll just keep switching so that all of you can see. The photo system, you have to look for just involuntary movements. Hang on. He does not. Oh, I'm sorry. We have to do the basic protocols. I'll just do it once. Hello? My name is Dr. Sanya. I'm your physician for today. You are Mr. Abbott, the Badger. So how would you like me to address you? Mr. Dabajah. And you are... How would you like me to address you? Chanel or Ms. Fernandez? Chanel's fine. Wonderful. So, okay, I did that only once. But you'll be graded for all these points, okay? So assume you have washed your hands, you have knocked on the door, and you have addressed yourself with your title and your last name. You have asked how you want the patient to be addressed and they have all confirmed. Mr. Dabajah and Chanel. Okay, then you start. Motor system. Involuntary movements. Just watch. Just watch the patient sitting quietly. No involuntary movements. Thank God. Look at the bulk of the muscle on corresponding sides. Equal. Bulk of the muscle corresponding sides. Fine. The next one is stone. Please sit down here. Stone? I definitely don't have that. Stone for the upper limb, stone for the lower limb. Can you sit down here? Oh, yeah. I don't have dads. Just keep falling there also. For the upper limb. Support the elbow. And just passively move the fingers. Passively move the wrist. Passively move the elbow. And passively move the shoulder. Remember, I'll be watching you. You should be doing both sides. You lose points because you do only one side and you forget about it. So you have to do the other side also. Support the elbow. Passively move the fingers. Passively move the wrist. Passively. Tell the patient, relax please. Passively move the wrist, the elbow, and put the shoulder through a moderate range of movement. Same thing on the leg. But I have to go through that, please. Can you go? There's a lot to do. Oh, I've not seen my laptop. Passively move the knee. It's all shown there. Just look at the pictures. And again, do the other side. Passively. You don't do anything? I just do nothing. Because there's any excess resistance or excess mobility. If there is decreased tone, it'll be like a rag doll. It'll be like a rag doll. Another way to do it is to hold both the wrists up and just let the wrists fall down. See? This is normal. If there is decreased tone, that side wrist will be lower down. And move the joints and see. It's normal. So this is tone. Examination of tone of the upper limb. Examination of tone of the lower limb. The next item. Next slide, please. Examination of muscle strength. Again, let's start with the upper leg. You have to turn the shoulder. You have to do the elbow. You have to do the wrist. And you have to do the fingers. So shoulder strength, bicep strength, tricep strength, wrist, dorsiflexion, grip strength. Then I'm going to go to the muscle in the leg. So please extend your hand against my resistance. Give resistance. This is how you test for shoulder. I'm weak, sir. Good. That's fine. That's fine. So you're tested for deltoid. Similarly, again, I'm repeating, don't forget to test the opposite side. Many of you do forget and you lose points. Next, I'll ask you to flex your elbow. And I'll give resistance. So flex it tightly. Pull off a desk. Against resistance.  Try to straighten your hand against resistance. Keep it flexed. Keep it flexed. Flex it. Now try to straighten it. Give resistance. So biceps, triceps. Next, dorsiflexion of the wrist. Look at the picture very carefully. Next slide. Dorsiflexion should be with the hand closed. Why? Because we don't want them to use the extensor digitorum. So wrist should be in the flex position. And so please make a fist. And try to straighten the wrist against resistance. So this test for dorsiflexion of the wrist. Oh, by the way, can you just rush down and call the doctor? Call them also. He's supposed to be here. He's forgotten. So you're supposed to ask the patient to make a fist. Move it up. Move it up. And don't let me bring you down. This is dorsiflexion of the wrist.  So we will watch you, whether you've asked the patient to make a fist and whether you're giving resistance. Don't keep it open because otherwise he'll use the extensor digitorum also. So here you're testing for the extensor carbaryteal as long as braves and ulnaris. Similarly on the other side, please make a fist. Yes, and you try to give resistance. Last one, grip strength. Now watch very carefully. Don't keep your fingers straight next to each other. Why? Sometimes a patient is so strong that they will crush your finger. Always keep one finger over the other finger. We will watch this. Please try to hold my fingers as tightly as you can. You can do both simultaneously. And watch for strength. With your thumb, just keep holding it.  This is testing for grip strength. Everybody watch me. Okay, so this is for the upper limb. Now for the lower limb. Now I'm going to use you. You'll have to go a little back. What is this? I'm going to tell you the screen. First, test for adduction, abduction. It's better to do it on him. I mean, I do more. So for adduction, keep both your fists slightly separate. Try to bring my hands together. Testing for adduction. Adductors, okay? Abduction. Try to move my hands out. Abduction. Next, put your hand behind the thigh. Press down on my hand. This is extension of the hip. Gluteus medius and gluteus minimus. This is extension. Flexion. This is, no, iliosaurus. Flexion. You can do both simultaneously. There's the quickest way to do. Next, flexion of the knee. Give resistance. Yes. Patient is trying to flex. I'm trying to extend. Do the same on the opposite side. Resistance. Now try to straighten your knee. Straighten it. Try to straighten it. Straighten your knee. Yes, give resistance. Straighten. This is extension. So flexion extension. Both sides. Next, try to put your foot up. Give resistance. L5. Try to do only with a great toe. L5. Push down on my hand. S1. Just a great toe. S2. So we have tested with all the muscle strength. Grading of muscle strength. Can you go back to the slides? You have to know that they will. You'll be asked. Zero. No movement at all. One. Later. Two. Again, with gravity eliminated. It's already there in your slide. It's already eliminated means the gravity is eliminated and the pain is moving like this. Grade three against gravity. Grade four against gravity and with a little resistance provided by you and grade five normal strength. So you'll be asked the strength. Of course, the subject you'll be having will be normal. Okay. So this is about the motor system. Now next, we have tested for all. Now we come to the Cerebellar. It's all here in a simplified form. We have done the motor system. We have done the upper limb. We have done the lower limb. Upper limb. Lower limb. Now we are going to test for the cerebellum. Cerebellum basically, is he coming? Cerebellum basically tests for coordination. So we have four groups of tests. They are headed under four headings. One is called the rapid alternating movement. Ram. I'm going to show you both in the upper limb and the lower limb. Then you have the point to point test. Then you have the stance and then you have the gate. So let's start with the ramp. Rapid alternating. Can you do this on one arm? Morally fast. Maybe not. Can you do it the other way? So the absence of this is called this data book. You know that. This is an example of a ramp. Rapidly alternating movement test. There's another one for this. You can do it on this also. This is rapid alternating movement. It's shown there. There is yet one more way of doing it. There is yet one more way of doing it. Ask the patient to tap his or her thumb with the index finger. It's shown there in that picture, in the lower picture. Ask the patient to tap his or her thumb. So these are the two ramps for the upper limb. Now let's do the ramp for the lower limb. No, you can keep your leg hanging now. Ask the patient to tap your hand with his foot. You can do it simultaneously. Please, no. Tap my hand. Good job, Abit. So this is the ramp for the leg. Rapid alternating movements. Next one. Point to point. Point to point, you do basically the finger nose test. So I'll do one finger nose test with her. Both are very similar. One is to test for dysmetria, the other is to test for pass point. Dysmetria. So you have to look at me first. Extend your hand out. Your right hand out with your forefinger.  And then touch your nose. Again, touch my forefinger and bring it out. Bring it out. Do it a few times. No, no. You touch my finger. Your nose. Again, my finger back. So easy. No. Take that. Back my finger. His finger is down. Woo! What do I have to do? I'm testing for this. Build the test. This is the first one. You're moving your finger out but the patient has got his eyes open. I'm not good at coordination, sir. Doesn't matter. Okay.  Touch the finger. Finger. That's my finger. Okay. So this is the finger nose test. You're testing for dysmetria. If the person is persistently overshooting, you're testing for dysmetria. That means when I'm moving, she's overshooting. She's overshooting. Now I'll do the other one which is also very similar. Keep your eyes open first. Do the same thing. Touch your nose. Again, back. My finger. Your nose. Again, my finger. Back. Again, my finger. See, he's saying it to him. Now. Close your eyes and do it. Okay. See. This is testing for the other one. Passpointing. It's so good. Dysmetria is overshooting. Passpointing is consistent deviation to one side. Suppose he had a right cerebellar lesion. He would have consistently deviated to the right. So both are very similar. In your exam, we will be testing only the passpointing. That is dysmetria. Not the passpointing. We won't ask the first subject to close his eyes. But these are the two point-to-point tests. Dysmetria and passpointing. Now for the leg. This was with a hand. With a lower limb. I'll use him. When you were college, now you weren't really charged. Yes, because this was the eye open. With eyes open. But when you're doing for the passpointing, you keep the hand in one position.  And then ask him to close his eyes and remain. Keep your hand in the same position. Because now close his eyes. Because now you're moving up.  So you have to keep your hand in the same place. No, I understand that. But you still instruct him to do each step. I told him to do it a few times, right? So he got the habit. Then I asked him to close his eyes. My finger was still in the same place. In her case, since her eyes are open, I was moving my hand. So in this case, her eyes are already open. So I was moving my hand to see whether she has got that ability or not. So what's the order of that? You have to touch my finger. Your nose. Again, my finger. Your nose. And eyes open. After a few eyes open, keep it closed and keep your hand in the same place. Dismetria pass pointing. Overshooting versus tendivation to one side. It's all clearly illustrated. Now with a leg. With a leg, first you show the patient. This is the simple heel sheen test. Which all of you know. First demonstrate to the patient what I'd like you to do is with your heel, start from your knee and go all the way down to your ankle. Similarly, the other side. With your heel, go all the way. First show him. Next, ask him to close his eyes and do it. Can you close your eyes and do it please? Yes. Another headache. This is it. If the person has got a cerebellar problem, the person will do all those funny things and we try to look where he is doing all those things. So you asked him to do it once. He got the hang of it. Then he should do it. Both sides. So this is the heel sheen test. This is also a point-to-point test but with a lower leg. This was a point-to-point test with a hand. This was a point-to-point test with a lower leg. We are good. Next one, next slide please. The gate. I can use you for the gate. Would you like to walk this way or this way? Just walk normally. Go all the way up to the whiteboard and come back to me. Thank God she can do this way. This is the catwalk, isn't it? No, I can do that. I am walking normally. Just walk. Go all the way to a particular distance and then turn. So watch for the stance, the gate, the movement, the rhythm, the equilibrium, the hand motion, everything. Just a standard walking. How the person turns. Whether the person turns in one shot or whether the person turns in multiple blocks. I will be teaching all those things in Parkinson's. They will have what is called a-block turn stance and all those things. They will have magnetic gate and all those things. So her gate is fine. The next one will be tandem gate or heel to toe walking. Like you do when you are being tested for alcohol by the police, isn't it? So this is a straight line. So you have to walk in a straight line. Yes. Oh my God! She is drunk. Please turn around and come back. Wow! One smooth turn. Yes. Oh my God! So, blood alcohol is zero by zero. This is the tandem walking. Next, I can use you now. You have to walk on your heel. You can walk up and down. My socks hurt. Okay, just doesn't matter. Walk on your heel and then turn around and walk on your toes. This, walking on heel. So this is heel walk and toe walk. In corticospinal tract lesion also they allow difficulty in heel walking. It also tests for cerebral lymph. Next one, I think I'll use him. That is, you have to hop in one place first with one leg and then the other leg. Hop in one place. And down. Then with the other leg. And then with both the legs, shallow. Appreciate that. So this test for both proximal and distal muscles. Heel walking and toe walking tested only the distal musculature. The next one I'll ask you to do that. One leg, shallow knee bends. First with one leg, shallow knee bends. And then with the other leg, shallow knee bends. He's changed your tie here. And then back then both the legs. Just do it. This also test for both the legs. Thank you. So this is, this is... Abil, test the hip. Test the hip. Test the hip. You know how to do that. Okay. So this also, this also test for the proximal and distal muscles. Hop in one place. One leg at a time. Shallow knee bends. One leg at a time. Both the legs. And then finally the next one. From a sitting position. I can use you. From a sitting position, I want you to stand up. This test for the gluteus maximus muscle. The proximal muscle. Try to see whether he takes support from somewhere or not. Because again this is deficient in many conditions. So this is for the proximal muscle. So these are all the tests for gait. Next slide please. The stance. We have two tests for the stance. So I'm going to use you for one and one for the other one. So please you have to come here so that everybody can see. This is the typical long box sign which you have been taught about. We'll show you exactly how it is done. First I'll demonstrate to you. Both the legs together. Both the legs together. As a patient to stretch out both the hands. As far as possible out. Close the eyes. And remains to be for about 20 to 30 seconds. So please do that. So you'll be asking your subject to do that. So I'm letting everybody see that what you're being asked to do. 20 to 30 seconds. What do we watch? Whether the person is swaying with his eyes open. And whether the person is swaying with her. These are her eyes closed. So she's not swaying with her eyes closed. Now you can open your eyes. The person is not swaying with her eyes open either. Thank you very much. So what have we tested? We have tested. If the person sways with the eyes open. Obviously the person will sway with the eyes closed also. That indicates cerebral recognition. On the other hand, if the person does not sway with the eyes open. But starts swaying when you ask the person to close his eyes. That indicates cerebral recognition. That is wrong box sign positive. Are we clear? Because the visual cue is lost. So we have done that. Sorry. Yeah. So that is actually a combination of both. We can accept the cerebellar problem. And there is a dorsal problem problem. So you will get, actually you can't say it's dorsal. Purely dorsal problem. They have sensory. You see, a taxa can be sensory taxa. Due to dorsal condition, a taxa can be cerebellar taxa. We have learned all that. So we have tested for both actually. The next one is the pronator drip. Watch this carefully. I'll use you for this pronator drip. It's closed. I'll demonstrate to you. With the patient's eyes, legs together. Both the hands, palm up. Keep it up. And eyes closed. And watch for two things. Please do that. Palm up. Eyes closed for about 20 to 30 seconds. What do we look for? First thing. Whether the hand remains steady in its place or not. What is this pronator drip? If there is a corticospinal tract lesion on his left side, let's say. Left corticospinal tract. His right hand will do something. Or if he's got a cerebellar lesion on the right side, his right hand will do something. What will it do? I'll show you. You can open there so that you can see. Suppose I have a lesion on my corticospinal tract on the left side or my cerebellum on the left side. When I'm asked to do this, my hand will slowly pronate. And it may even flex at the wrist and at the elbow. And it will drift away. So this I'm just showing you. So when you ask the person to do this, if there's a lesion, it might go. Sometimes it may go even up. So this is called pronator drift. The second part, yes. Are they conscious of it? No, they're not aware of it. That's why there's a lesion. The hand is automatically unable to remain like that. The other component of this test is the next component, yes. We will just see how you're asking the patient to do it and what you're watching for. Okay, are you going to ask this, like, is this corticospinal tract? I usually don't, some of you. I don't like to hear your questions and practicals. I just watch for the procedures, whether you've done all the protocols, steps currently or not. That's a practical example. The next component of this test is, after you have observed this person for a few seconds to see whether the hand is deviating or not, the next component of the test continues through the same thing. You gently tap the hand down. Both the hands. You'll find that a normal person, it swings back again. Keep your hand eyes closed. If you do that, because the hand has got a certain amount of tone and it is remaining like that, it will come back to its automatic position. On the other hand, if it's a cerebellar lesion, the hand will bounce and it will do all sorts of funny things. So this is the second component of the pro-inter drift. So we have done the stance. What did we do? We did the rhombus test, rhombus sign, eyes closed, stretched out, and we watched for swing and we watched the pro-inter drift and the bouncing of the hand. So we have finished the cerebellar tests. So this stance gate and the cerebellar done. So we have finished with the motor system. We have finished with the cerebellar. Next slide, please. You will be given during the lab. The next one, sensory system. So again, we will start. This is actually the lumbar function needle which you are going to be using in our last lab. We are not going to do pain, but pain is done in the tip of safety pin. So we are not going to do the pain. Temperature, again, we won't do it. But you are supposed to do it with the test tube of hot and cold water. Which nucleus? Spinal. I'm still hopping mad. Light touch is true touch. That is done with a wisp of cotton. You will be given a cotton. You will be testing for light touch, crude touch. And fine touch is, again, with the tip of a pin. With the tip of a pin, but you don't press so hard so as to produce a pain. But we won't do that. But you will be given a light touch. You will be given a wisp of cotton. And you will do light touch. When you do the sensation, I'm just assuming that I'm holding a piece of cotton. You have to do corresponding areas. Always go from an anesthetized area to a normal area. Suppose the patient says I don't have any sensation on my wrist or wherever. So start from that area and keep going approximately till the person feels sensation. Compare with the opposite side. Again, the same area. One very important point here. You have to ask the patient to close his or her eyes. I'll be watching for these two things. Whether you are doing both the sides simultaneously or invariably you lose points on these two points. Issues. Otherwise the person sees he or she will definitely say yes, of course I'm feeling the touch. So we have to ask the patient to close their eyes. So that is how you test for. You'll be the cotton ball. Let me demonstrate the other one. The vibration and the joint position of the dorsal column sensations. This is actually 256 hertz. For vibration, you're supposed to use 120 at the low frequency one. This is used for hearing. I'm using this. How do you use the unique fork? Never touch the prongs. Always hold the step. And many of you will do all sorts of funny things to make it vibrate. Give it a sharp tap over the heel of your hand. Can you hear the whining sound? Do not hit on the table. Do not hit a hard surface. All those are wrong. Because if you hit here, see it produces two different harmonics. Did you notice? It's acceptable. We will watch this whether you're doing it the right way or not. So best is to hit the heel of your hand. If you touch here now, again, the vibrations will stop. So once you've set it in vibration, can I start by testing on the dorsum of the thumb? You can do this on the dorsum of the other digits also. This is where we start from. If this is abnormal, then you can go approximately to other bony areas. Like for example, you can do it on the Oligrenum process. You can do it on the chromium. You can simulate on the foot. I'm not asking to remove your shoes. You start on the dorsum of the great toe. If it is abnormal, then you can go to the medial valueless. Then you can go to the medial epicondyne. You can go to the iliac rest and all the rest of it. So start with the dorsum of the great toe and dorsum of the thumb. This is what we're going to be watching for. How you strike the dune fork, how you set it in motion, whether you're touching this or not, and one more point here. Many patients do not know the difference because patients are not as intellectual as you. Patients do not know the difference between pressure and vibration. Because you're holding it here, they might interpret the pressure itself as vibration. So what do we do? When you're thinking that perhaps the patient is confusing pressure with vibration, stop it.  And then ask him, are you feeling the vibration or not? If he says, yes, I'm still feeling the vibration, then you know he's guessing. Because that means it is the pressure which is confusing as vibration. So these are small tricks of trade actually for doing this procedure. So that is the testing for vibration. So this is the dorsal column sensation. Now we come to the other one, the joint position. So can I use you now? For this, you'll have to remove your socks and you'll have to sit down. Where did this one come from? Okay. So here, because joint position of the great toe is a very important test. Remember in vitamin B12 deficiency this is the first sensation to be lost. In many B12 deficiency, many dorsal column lesions you have learned joint position is lost. And the best way to test for it is the great toe. First, again we will do it on both the sides. Don't forget. First you'll have to demonstrate to the patient what exactly you are doing and explain. So you want Mr. Tabajan. Yes. Mr. Tabajan, what I'm going to do is please look carefully. When you feel your great toe going up, you will say it's up. No, not now. I'm just telling you what I'm going to do. This is, when it is here, you'll say it's down. And when I do like this, you'll say it's going around. Next point. Separate the great toe away from the other toes. Why? Because he should not get the feeling from the other toes and tell you what his position is. I'll be watching this. Move the great toe away from the other toes, demonstrate to him what you are going to do and then please close your eyes Mr. Tabajan. What is the position of your great toe? Wonderful. What is the position of your great toe? What is the position now? Going around. So this is how you do. If you let it touch the other toes, I did that points. Because when you touch the other toes, he will use the sensation of the other toes to tell you his position, right? So I'll watch whether you have removed it from the other toes, whether you have clearly explained to the patient and again, patient's eyes should be closed. Don't forget, you lose points on that. You forget to tell the patient to close his or her eyes. Again, do it on the other side corresponding. You forget to do that. Again, you lose points. So please close your eyes. Which is the position of your great toe? Down. Which is the position of your great toe? What is the position now? So this is how you test for joint position sense. Both the sides, eyes closed after explaining to the patient. So this is the position sense. Next one. I can use you now. The next slide, please. All of you know stereognosis. Give a readily identifiable object to the person. Can you close your eyes? Tell me, hold this and tell me what is this? Now, what you can do is, this is one of the videos which I did last semester, give a series of very similar, a little different items. Let's give me these and one pencil. Okay. Now, with your eyes closed, I have got a few other objects here. With your other hand, pick these objects one by one and tell me which one matches the object in your right hand. I am testing the stereognosis by using the corpus callosoma. Tell us what color it is. That is synesthesia. That's a mechanical pencil. That's the one. This one. Good job. Good job. What we have done, I have gone one step beyond stereognosis. First, she identified this with her eyes closed. So that was stereognosis. And then I used her corpus callosoma to match this with that. So we extended the best of stereognosis. You have to give a familiar object. You should not give a strange object. So it's a coin or a key or a pencil or something which a person uses daily. And you should allow the person to move that object in his or her hand. They cannot just touch it. They should be allowed to move it in their hand. Because stereognosis is a complex system. It's a cortical sensation. It's a combination of touch, pressure and conscious proprioception. So all these things together will be integrated in the cortex. Remember primary sensory cortex and the superior parietal region and inferior parietal lobe. Or identification. Close your eyes please. If the person has got, let's say I'm going to do the next one again, then I'm going to do the next one. If the person has got, let's say she has got arthritis, rheumatoid arthritis, or she has got some injuries in her hand or she cannot move her fingers or something like that. Does that mean that you will not do stereognosis? We have other methods of doing it, right? What will we do? We will do the usual old-fashioned method. We will write this in the classroom. This is a familiar letter on the palm of the hand and ask the person to identify it. Again, don't forget to do it on the other side. Don't forget to tell the patient to close his eyes. I'll be watching for these things. So we did. So if you can do stereognosis you can do graphic thesis. You can write another one also. You can write something which you know the person is familiar with. So I know he's a highly educated and a highly intelligent man. He knows what is three and he does know what is eight. So he will definitely be able to identify it. So this is graphic thesis here and you know this is a cortical sensation. The next one. Two-point tactile discrimination. I don't have the object but you will be given a pin. You will be given a pin. So the two points of the pin you have to do it again with the eyes closed. You have to do it on the palm of the finger. So you can touch the two points. Do you or she can feel the two points separately or not? This is two-point tactile discrimination. Again do it on the same side opposite side corresponding areas. Normally the pulp of the finger is the most sensitive. They can identify two separate as even less than five millimeters. On the flexor aspect it becomes a little less sensitive but it is still sensitive. On the extensor aspect and on the back it is very sensitive. They cannot identify anything closer than three centimeters. Finger five millimeters. This is two-point discrimination. Next slide please. There are two related tests you will be doing them. One is called point localization and the other is called tactile extinction. We have told you all that, isn't it? What is point localization? You ask the person to close his eyes.  Where did I touch you? Show me please. You can open your eyes and show me. Similarly do it on the other side. Show me where I touched you. Now you can open your eyes and show me where I touched you. So this is point localization. And an extended version of that which is used for the trunk and for the lower lips. Can you sit down please? You have to keep saying it so that he knows that you are your sort of therapy. That's how you build a rapport. What I'm going to do, I'm going to touch you in certain parts of your body. I should have done it on purpose. It would have redeemed me. And you will have to show me where I... Please tell me where I touched you. Okay. So this is tactile extinction. Bilateral simultaneous stimulation to test for tactile extinction. And you have already learned that when the person has got superior parietal cortex lesion or when a person has got corpus callosum lesion anterior cortex or the corpus callosum which by the way, again, less than 50% of the person has got contralateral tactile extinction. So these are the tests for sensations. So again, these are the sensory systems. We do it for all upper limb and lower limb. The lower limb, we do precisely the same thing. I'm not doing it again. The only difference is in lower limb, you don't do stereoscis, you don't do graphysthesia because you can't feel a coin with your foot. Can you? Neither can you feel my writing on your foot. I don't think you'll be able to do it. So we don't do stereoscis and graphysthesia for the lower limb. Otherwise, the rest of the tests, we do the same. Okay. The next one, please. So we have finished with the motor system, sensory system, cerebellar, the last one remains, and that is the deep tendon reflexes. So here, can you sit down again? I'm going to use... So, all of you know the gender six maneuver.  Many of you are going to use the new hammer like I'm touching it. Of course it does happen. People use their shoulder, they use their all sorts of muscles. The new hammer is supposed to be with only your finger and your wrist. Finger and your wrist, watch. Finger and your wrist. Not your elbow muscles, not your shoulder muscles. No. Yes. So that's the first point. So look at the picture down there. You see how it is moving. That's when it's been designed. That's the first point. Again, there's a grading of reflexes. Zero, no. You have to know the grading. Generally speaking, two is normal. Three is brisk. Four is very brisk. Five is clonus. I'll tell you what is clonus. Less than two is hypo, and zero is absent. You have to know the grading of reflexes. Deep tendon reflexes. So that's about the knee hammer. How to fold the knee hammer. How to do the reflexes. Next slide, please. Upper limb. The three reflexes that we will be doing. I'm going to demonstrate the upper limb. I'm going to demonstrate the lower limb. The three reflexes that we'll be doing will be the biceps, the triceps, the brachiorgiasis. So let's start with the biceps. Before that, when do we use the pointed end? When do we use the broad end? There's some simple rules of thumb. If the tendon is narrow, use the broad end. The two examples where we use the broad end is brachiorgiasis and the tendocalcaneus. Tendocalcaneus because the tendons are narrow. If you use the narrow end, you're likely to miss it. That's why you use the broad end. Biceps is also a narrow tendon, but biceps is the only exception where you don't tap on the tendon directly. You keep your thumb on it, and we'll be watching that. Biceps, there are several ways of doing it. One is in the sitting position. The patient is sitting. What I would like you to do is keep your hand very relaxed on my hand. Absolutely. Ask the person to keep the full weight of the hand absolutely relaxed on your own hand. The patient should not be stiff or tense. Relaxed. Feel for the biceps tendon, and you will be able to feel it very easily. You will be able to feel it in the cubital fossa. It's very easy. Once you feel the biceps tendon, give a gentle pressure on the biceps tendon. In fact, if you're right about it, you will feel the positions of the brachiorgiasis right in the middle to that. So the biceps tendon, I'm giving an attraction. Now what I'm going to do is because the area is very limited here, I cannot use the broad portion. I have to use the narrow portion, but I have localized it with my thumb. I'm going to tap my thumb with the pointed end of the knee hammer. Are we clear? So this is how we will do it. Keep it relaxed absolutely. Did you watch the muscle contracting? You can stand up. So, there. It did contract. I felt it. It did contract. There. It is so sensitive that I can do it with my finger. I'm tapping it with my fingers. So I prove easily that it hurts. Similarly, do it on the other side. You can do it on the other side. Keep your hand relaxed Chanel. Again, feel the biceps tendon. Feel the biceps tendon. Tap on your thumb. Here. There. And you will be able to feel the contraction of the biceps. This is the biceps replace. If the patient is lying down, you can ask the patient, you can again put your hand like this and you can tap. The patient is like, you see, it's contracting already. See? Can you see? It's contracting. Yeah, you can see that. So that is with the patient. So if the lower two pictures, the lower two pictures, patient sitting, patient lying. Next, the triceps. There are three ways of doing it. The nice method is hang the limb out to dry. This is called hanging the limb out to dry. Like you're hanging clothes, you know. So I have made her hand hang as if I'm drying it on a clothes line. So keep it relaxed. Absolutely put the full weight of your hand on my hand. Yes, that is important. And you feel it just above the Holy Cranon process. And you tap this area. There. That is the triceps reflex. Do it again. There is another one. Can you do it again? Keep it relaxed. Keep your full weight. Ask the patient to be absolutely relaxed and keep the full weight of his or her hand on your hand. Usually, patients will be stiff. You will not get the reflex. Okay. In the exams, even if you don't get the reflex, we are not judging on that. I'm going to watch your procedure, how you're doing it, whether you're doing it the right way. Keep the full weight of your hand on me. I should be able to feel the weight relaxed. That is the crisis. That is one way. The other way is if the person is lying down, you can just ask the patient to flex and you can tap. There. So, that is another way to do it. So, patient lying, patient sitting. And the third one is the brachioradialis. Remember, I said brachioradialis, the tendon is very narrow. And it is inserted on the radial styloid process. The radial styloid process, you can feel it just above the anatomical snuff box. Remember the anatomical snuff box? Remember where you take your salt before taking your shirt? Okay. Sir, I can't bruise luck. You're getting bruised? It's all right. All in the name of science. Because I'm going to use him for the lower level of using you for the upper limb. So, feel the radial styloid process first. The brachioradialis is inserted on the radial styloid process. So, you have to go approximately one inch above that. We have to use the broad end because it's a very narrow. If I try to do it with, I may miss, you see. So, I'll use the broad end. So, hold the hand in a mid-prone position because this is the position in which the brachioradialis works best. And go slightly above that and tap. You can see the contraction of the brachioradialis there. That is how you test for brachioradialis. Again, do not forget to do it on the other side. Hold its support in the mid-prone position, feel the radial styloid process, and tap. That is the brachioradialis tendon reflex. So, we have done the three reflexes. Biceps, triceps, brachioradialis. Next one, please. I'm going to do the knee, ankle, and the plantar response. And I'm going to tell you what is clonus. So, the one way to do the knee is with the patient's sitting. Give a gentle upward, keep it absolutely relaxed. Give a little stretch of the tendon. And again, this is the place where you use the broad end. Why? Because the tendo-calcaneus is pretty narrow. There. Similarly, on the other side, don't forget. So, we'll watch whether you're using the right side, right end, and whether, again, elicitation is not the important thing. I want to see whether you're doing the procedure correctly or not. Similarly, you're grinding your... Okay. Again, no, keep it relaxed, absolutely. Patients will try to tense their limbs, I'm telling you. You have to repeatedly tell them, Mr. Bajat, keep it relaxed, absolutely. You give gentle dorsiflexion to make the tendon a little taut. And there. If you do it the right way, you will get it. 100%. When people are not giving the proper instruction to the patient, that's why you're not able to elicit it. Suppose a person is lying down. There's another way to do it.  Or there's no place for you? Or you can just lie down. Oh, my God. People bring their whole house here. That's all. If the person is lying down, there's another way to do it. Watch it. Can you cross your leg for the other? Keep it relaxed, absolutely. Cross one leg over the other. Keep it relaxed. Keep it relaxed. Again, give a little dorsiflexion to tauten this tendon. And tap. Keep it relaxed, absolutely. Keep it relaxed. There. You can see it contracting. So what do you look for here? This leg. Well, you're seeing contraction of the leg. Similarly, do the other side. Can you cross over? Keep it relaxed, absolutely. Give a little gentle dorsiflexion. You don't do it. I'll do it. Keep it gentle dorsiflexion. And tap. Note, I did not use my shoulder or my wrist. I just used my wrist. It should flow freely. There. Now I'll tell you what is clonus. Clonus is great five reflexes. Nowadays they call it clonus. Can you sit down? Exaggerated reflex. Suppose a person has got a very exaggerated reflex. You can hang your leg down. If the person has got a very exaggerated reflex. So exaggerated that even by touching the tendal alginus, it moves very briskly. I can elicit something called clonus. And I'll show it to you how to do it. That happens when the person has got a corticospinal, dense corticospinal tract lesion. Very high degree of deep tendon reflex. I just rapidly dorsiflex his foot. Like this. You keep it relaxed. I just rapidly, even now I elicit a little bit. I rapidly do it and it'll start flapping a few times. That is called clonus. That is, some books call it great five. So this was the tendo. Calcaneus. Now I'm going to demonstrate.  That's normal when it flaps. No, it should not. That's exaggerated. Average normal is two plus. Three plus is brisk. And five is clonus. Okay.  Again, the procedure. Watch very carefully. I think I'm going to use her for this. Because I'll show you. This is the place where you might have to do the gender six maneuver. What is the gender six maneuver? Remember? You have to ask the person to clench. You can see it in the previous slide. There. No, the ones before that. There. The top picture. Hook the fingers. Pull them apart. And ask the person to clench his teeth. That way you're increasing the gamma discharge. So we might ask you, okay. Let's say this person has got a very weak reflex. How will you exaggerate it? You will ask the person to. So we'll demonstrate both in this slide. Okay. Can you hook your fingers? Like this. Pull it apart hard. And clench your teeth.  Yes. This is the way we have increased the gender six maneuver. So, okay. I'm going to tell you when to do that. Now, can I ask you to cross your right leg over your left knee? Yes. First step. Again, tell the patient to relax. Many patients would try to keep it stiff. They are invariably stiff and the doctor is examining them. That's called the white coat syndrome. So, relax. Absolutely relax. The legs should be hanging freely. Now, you ask the person to do gender six maneuver. Let's assume that she's got a very weak reflex and I won't increase it. Can you do that, please? Feel the ligamentum patellae between these two bones. Which are the two bones? The patellae here and the tibial tuberosity here. The patellae here and the tibial tuberosity. Exactly midway between the two is the ligamentum patellae and that's exactly where we are going to hit. Keep it relaxed, absolutely. Again. Okay. Now, relax. Release this. So, now I've removed the gender six maneuver. I'm just demonstrating it to you. Relax. See the difference? It was there, but it was milder. When she did the gender six, it became exaggerated. Yes? Do the other one, please. Can you cross over the other leg, please? Keep it relaxed. You might have to spend a few seconds to tell the patient. Relax, relax. And when you tell them, invariably, they relax. I can feel her muscles relaxing. Patients always tend to tense up. Okay. Feel the ligamentum patellae between these two bony prominences. The patellae here, tibial tuberosity here. Can all of you see? Okay. You just have to do it once very gently. It will happen. Now, please do that. Gender six maneuver. Of course, patient does not know it's gender six. You'll have to explain to the patient what it is. Again, feel. Keep it relaxed. You see? Visibly how it differs. Gender six maneuver does this job. So this is the one. And now I'm going to do that. That's crazy. Later. I don't have a sharp object. So I'm going to use my key. I'm going to use my key. Stay. Can you go back? Exact procedure for doing the planter. I'm sorry. You have to start from the lateral aspect of the soul. The lateral aspect of the soul. And go from the heel. Go all the way up to the head of the meditarsals. And then turn medially. So this will be the procedure. Put a hand on the lower leg. Lateral aspect of the soul. And go deliberately. So this is the planter response. Normal. Normal planter response. All the toes with the planter flex. And the abnormal one you know. Do you see flexion is a great tool? Again, do it on the other side. Planter response. Can I do the last one on you? If you don't mind. Just lift up your... Can you lift up this? Are you feeling embarrassed? It's alright. The abdominal is shown there. Abdominal you have to open. He has a six-pack. It's alright. Anybody volunteering for the abdominal reflex? You go from the lateral to the medial. Along the rib cage. You go from lateral to medial. Search. Search. There is a six-pack. Come on. You have a six-pack. You just go from lateral to medial. Along the rib cage. Lateral to medial. Ah, there. He's the man. No, just lift it up. You have to lie down. Because the abdominal reflex is tested lying down. For obvious reasons, we are not going to do the cremastery reflex. And we are not going to do the anal to stick to the rib cage. Again, as a person to be relaxed. Keep your head down. Keep it relaxed. So this is the rib cage. This is the inguinal ligament. Go from lateral. Keep it relaxed. Absolutely relaxed. Go from the lateral. See, you saw the contraction. Again, go from lateral. There. So this is 789. This is 10. 1112. So that's the abdominal reflex.


So we are still in the middle of trying to prove nice properties for almost minimal sets, and I still don't have any boundary available because things are simpler there. And here I'm going to talk a little bit about rectifiability. So almost minimal sets are rectifiable, OK? And the proof, so it's amusing because with Steven we had a very complicated proof of rectifiability. Angren had the proof of rectifiability, but we didn't read. And we didn't understand why you could prove rectifiability without proving uniform rectifiability. And apparently, yes, you can, and it's not so hard. So let me try to talk a little bit about that. Also, since I was asked to do more pictures of a feather flaming projection, so I'll try to do at least one more picture of a feather flaming projection. So I'm in a cube, and let me talk about the basic step, which is I'm in a phase of dimension, let's say, d plus 1, and d will be 1 because it's simpler to draw pictures like this. I have a set of dimension 1 in there, and I want to project it in here. But the set, for a strange reason, let's imagine that the set is not rectifiable. So I was hesitating a little bit about, for me, all my sets are alphas regular from now on. And if you're alphas regular and you're not unrectifiable, I think it still means that you look like a counter set. At least you should not be connected because connected sets we find out are rectifiable. So it looks a little bit like this. So that's my set E. So of course, this set is not going to be a nice one of our almost minimal sets, but it's like this. And I still want to do some feather flaming projection on it. Now there is, so I'm going to use a variant of the basic of each feather projection theorem, which you might have seen coming. But I hesitated, but I will do just this picture. So imagine now that I'm projecting this set on a line, a random line. The basic of each feather projection theorem is that for almost every direction of a line that I look at this, when I project this totally unrectifiable part, let me say irregular, the projection of this set has zero measure. That's the basic of each feather projection theorem. Let me recall, so it was supposed to be before, and some people said, for me, rectifiable means that you are up to a set of zero measure covered by a countable number of, let's say, C1 graphs, something like this. Every set of finite measure has a decomposition into a rectifiable piece and the rest, OK? The rest does not meet, let's say, C1 curve too loud. It is too loud. OK, I'll try to be, I think, it's better here, right? OK, so any set has a decomposition into a rectifiable piece, which is rectifiable and a totally unrectifiable piece, which I also call irregular, which essentially never meets a set which is rectifiable, OK? And here I tried to draw the irregular part, all right. So let me return slowly. Projection theorem says that almost all projections vanish, OK? What we need is exactly the same thing, except that it's supposed to be almost all radial projections. And it turns out that by using Foubigny and writing down correctly, and this I owe to Vincent Favrier, but probably some people did this before. It's probable that Almgren knew how to do this before. But anyway, the same story happens with radial projections, OK? So I usually like to take one half of this one here. And what I'm saying is that if I pick a random psi here, almost every psi, and I project this set, this is likely annoying, right? Is there a way? Do you know if there is a way? No. OK, all right. OK, so if you take almost any center here, which I usually call psi, then the projection on the boundary will have zero measure. So it's going to be something like this, but really, really small, OK? Vanishing measure. OK, our sets are not always going to be purely unrectifiable. Usually they have a rectifiable piece and a totally unrectifiable piece. So in the next proof, there will be the irregular part that I have here, plus a tiny piece, rectifiable part. And this one will project somewhere here. But if the measure here is small, the measure will stay small when I project, OK? So that was one step. Of course, I'm supposed to iterate this, because maybe I'm not in the dimension one. When I iterate this, so here I will be able to get rid of the totally unrectifiable part inside the face. What is on the boundary stays on the boundary. So maybe there was an irregular part in the boundary too. But then next time I will project on faces of dimensions one less.  Right. So what I started doing here is preparing the proof of rectifiable piece. So let me now try to set myself correctly. I don't have a thing anymore, but I think essentially I'm trying to describe the story here, OK? So you want to prove that the set, your almost minimal set, is rectifiable. If it is not rectifiable, it has a totally unrectifiable piece, irregular. And by general density results, in fact, you can even select points where the density of what is not irregular. So in other words, the density of rectifiable piece is zero. Almost every point in the irregular set has density zero for the regular part, OK? So at this point, I will select an initial cube, and I'll draw it like this, OK? And in this cube is exactly what I was saying, which is there may be a large irregular piece. It doesn't look large, but irregular sets never look large when you look at them because of a basic of each projection theorem. And a rectifiable piece, which is small, as small as you want, because of a density story, OK? So you do the federal flaming projection, OK? And you will end up, when you do the projection, into a set of measures zero, which comes from the irregular part, plus a set of small measures, which comes from a rectifiable part, OK? And then again, we are exactly as in the same situation as for lower alpha's regularity. We have a projection which never contains a full face. So if it never contains a full face, you can do one more step of a projection, project on d minus 1 dimensional skeleton. And for all that matters, this set you make it disappear, OK? Right? And I decided that I wanted to save a little bit of time, so I will talk more and show slides less. So the same sort of proof that we had before works again, which is you have this set on a cube. So in principle, you do that. There is a more complicated picture because maybe you start it with a cube of dimension three. Then this is one of the inside cubes, and it was connected to another one here and so on and so forth. On the boundary, on a thin annulus, you have to do something slightly different, so you cannot kill the set completely. But if the annulus is thin enough, it doesn't count in the estimate so much. And at the end, you show that in this case here, if a set was almost entirely composed of unrectifiable pieces, you kill the set inside. Maybe you pay for it a little bit on the annulus, but you still get the contradiction because you were able to erase a big part of the set and not pay too much for it. One thing that I meant to say before I started and I forgot is now we know that the set is all false regular. So for instance, we know that the total measure of a set here inside is reasonably large. So if I can erase whatever is inside, I really erased a lot. I know this and this makes the estimate easier. The second thing that I should have said also is that now I know the set is all false regular. So in fact, it's not as dispersed as you would think. So for instance, in the middle here of my cube, I know that there will be a cube or a ball in the complement of a set because of a set, a false regular set cannot be sort of dense, which makes things easier because it means that the leap sheets mapping that I'm going to talk. So my psi, instead of taking it here, I will take it somewhere in the middle here. And then the mappings that I will get are even leap sheets with uniform estimates.  So that was rectifiability. OK. And again, I don't want to insist so much. So this was the estimates that I decided not to show you. Now, there is the last thing that I want to do about, there is the last thing that I want to do again about using federal flaming projections, which is the property of projections. And if it looks a lot like one of the slides of Antonio, sorry, but this is what happens. And it's exactly for the same sort of reasons that we have to do that anyway. OK. So the theorem is the following. You take an almost minimal set. And you suppose that there is a plane which is fairly close to the set or that the set is fairly close to a plane. I just draw the picture. The plane is here. The set is your almost minimal set here so maybe I like to draw a ball just to say I'm working in here. And again, this is my assumption. The main assumption is that the set is almost minimal and stays close to the plane. That's my assumption, which is in principle this one here. OK. Then there is the projection, the orthogonal projection on the plane. And I'm saying that the orthogonal projections of a set in the plane essentially contains all it could contain. OK. And this will be proved by contradiction. And again, it's going to be a picture that you've seen before.  I want to prove that the projection is essentially on two. And I proceed by contradiction. So I suppose not. OK. Supposing not meaning that there is, for instance, this point here where the orthogonal project complement. And if a set is one-dimensional, I mean R3 maybe is going to be just hyperplane. But don't worry too much about this. OK. Anyway, I will do the proof in co-dimension one because it's easier, or most of the proof. So I suppose again that this thing here does not meet the set. OK. And the set is contained in a very thin stripe here. And for some strange reasons, since I made a fuss of saying that I need a card shock, here is I'm drawing in advance a wall. So if I'm in dimension 3, the wall is just a thin thing around, but precisely, but then the set would be two-dimensional. OK. And how do I use this line? Let's stay in the plane, right? How do I lose this line that does not meet the set? It's easy because now I can project points exactly parallel to this direction, essentially irradially after you project or something like this. And you will get a new set. So the image of a set may be not the whole green thing here, but it will be contained in the little green walls. OK. Remember, we're trying to look for a contradiction. Very close to the contradiction. The set was at first regular, so there was a lot of mass here. I mean some amount of mass. Then you project it, and you project it on something like this here, which has a small length here, epsilon times r, an additional small length here, epsilon times r. OK. So you were able to manage to find a set which is a deformation of your initial set and which has much less mass contradiction. OK. Let me say two words. I also should revive this if I don't want to type my password all the time. OK. So suppose now we were in higher co-dimensions. If you are in higher co-dimensions, you do this projection, and you find yourself in the wall. But the wall has an infinite host of measure of dimension d. That's not good. It's not so bad either. Near the wall, you can do an extra feather flaming projection and, in fact, project on something which is essentially a grid around here. And the estimate, it works. So it's not infinitely harder in higher dimensions. It's just that you have one more step where you have to take a grid, you want to replace this wall by a grid of a right dimension. OK. That's the, OK. And the reason why I mentioned this, there are two reasons. The first one is that if you know that the set is uniformly overactive variable from this, you did use some extra property, like big pieces of elliptic graphs. But the main point is not this one. It's because it's useful for some other estimates that we'll show up later. OK. So that was this. We only do this in dimension n minus 1. So I'm sorry, this is the proof. But you will not even have time to read it. And I think that's the end of a list of regularity properties that I promised to you. And it doesn't go very far, because alphas regular is just pleasant, but it's not really a regularity property. Rectifiability is not very impressive. So we would expect better. OK. And this story about not having holes is not shocking either. I mean, it's good to know. OK. The last thing that I should have said also is that, of course, since the set is rectifiable, there are lots of situations where this happened. Because the set has, it's also alphas regular, so it has tangents almost everywhere. And near a tangent, you have a situation like this. So essentially it means that when you, I mean near a tangent, when you have a tangent plane and the ball is small enough, you have a situation like this with no holes in the projection. OK. Limits. So limits, again, you're not supposed to be very impressed by this theorem that's up there. You would be much more impressed if I told you it was not true, because then you would understand that we're in trouble some way. So here, this is the logical thing that is supposed to happen. You have a sequence of almost minimal sets. It converges to a limit. I will give you the definition in one second, but it's the normal one. OK. And you want to say two things. The first one is that host of measure along the sequence doesn't increase suddenly when you're taking the limit, lower semi-continuity. And the second one is that the limit is also an almost minimal set. And that's, I mean, it's the second one that really is interesting to you most of the time. And of course, the second one, there's no chance of proving that the limit is almost minimal, or let's say, think even minimal, if its mass is too large. So in the proof of part two, part one will be very important, of course. But unfortunately, as I'm speaking, and I hope it's going to get better, but OK, we'll see. Part one is easy to prove, and part two takes a lot of energy for some reasons that are technical. And maybe that will disappear within two months, depending on whether some person here that I don't see is working hard enough. OK. The tummy pretends not to be. OK. Right. So this is supposed to be the goal for a good part of this hour, except that again, I'll talk about part one and not part two. And I hope the thing is sort of correct. So I should say one or two things about it. The result is a little stronger than what I said here first, because it also works for quasi-minimal sets instead of just almost minimal, so a little bit more possibilities. And the second one is that I said for a limit of almost minimal sets, it also works for minimizing, I mean, let's say some minimizing sequences, which means that you can prove that limits of minimizing sequences are minimal sets. OK, so that's OK. That's one of the ways to try to find minimal sets. OK. And it sort of fits with what Antonio was saying. In this case, his proofs were easier than the one here. And again, I hope to revert that at some point of time, but that's not clear. OK. Right. So what are the ingredients? There is one ingredient which is important, and it is a little surprising. It is the rectifiability of any limit of those guys. OK. I think I forgot also one or two comments. No, OK. So I'll put the definition of limits here and discuss something else so that if you're in principle, you're not supposed to be surprised here. So one thing that I put in the slide and I should have said is the following. Again, my main estimate is lower semi-continuity for host of measure. Of course, if you take just any sequence of sets, this is not true. For instance, these sets, dotted lines, you can easily make them converge to a line or a line segment. And surprisingly, the line segment has something like 10 times more mass than the dotted lines. If you did the dotted lines, OK. So this is what you have to be afraid of or fight at least. It's not going to be so hard, but anyway. But at first, I mean, dotted lines we've seen in the previous case that they cannot be almost minimal, so there is no contradiction in math. It's just we have to be careful about that. The same way, I was about to say that the main ingredient was the rectifiability of limits. And you know very well that if you take a sequence of rectifiable sets, for instance, try to take your favorite description of a 1 fourth counter set using little squares. You'd get a sequence of little squares that are all rectifiable, bounded mass and so on and so forth, so there's nothing fishy there. The limit is totally unrectifiable, but the sets were rectifiable. So I mean, there is no way, in principle, you're not supposed to hope that if the sets are rectifiable, then the limit is rectifiable. Yet this is exactly what I'm saying here. And again, it's because it's special sets. So by now, you probably had time if you were worried to read what is the limit of sets. Anyway, OK, so I have my, it's good in any way. I have my normalized Hostert distance up there, which says when you want to see whether a set is close to another set in a ball, you're normalized by dividing by the radius of a set. And then you take the maximum distance from a point of the set to the other one and of a point of the other one to the set. And you get a Hostert distance slightly different from the usual one localized between two sets. And I'm saying that a sequence of set tends to a limit when the regular, when the normalized Hostert distances in any balls turn to zero, OK? Not surprisingly. We don't have so much choice in this definition because we want to be able to extract subsequences that converge. So in fact, this is the, I mean, this is essentially the only notion where we can do that. You could try to define more refined topologies. It would be good because then you would be able to prove better estimates, but it would be bad because again, I mean, given the sequence of set, I want to be able to extract a subsequence that converges. And then I have no choice. I have to take this definition, OK? Or an equivalent one because there is lots of ways to make them equivalent, OK? But you're not shocked. This is probably the idea you had of converging to limits. And it's better the limit is defined up to density or something like this. So we can always take it closed and that's what we'll do, OK? Rectify the limits, OK? So I made sure not to erase my picture here because now you imagine that in fact, this is not the set that I started with for a single guy. I write it as the limit set of a sequence of almost minimal set, OK? The thing that I call E infinity inverse light, OK? And again, I start the argument exactly as I did before. Suppose the limit is not rectifiable and I can find a place where the rectifiable piece is very small and the totally unrectifiable piece is most of it. Limit of alphos regular sets with uniform alphos regular constants. It's also alphos regular. The limit is alphos regular. Everything that I said here is fine. The set is alphos regular so I can suddenly find a bone away from my limiting set which is far from the limiting set, OK? In this picture, I can project the totally unrectifiable piece to a set of measures zero for the limit. The rectifiable piece is small so I can project it on a small piece. And the main point is that I can iterate the construction and find another mapping which is still lip sheets because I picked points far away from the thing which essentially takes my limiting set and sends it to a grid of dimension d minus one. OK? Right? So I have a limit set. I have a lip sheet mapping that sends the set onto a grid of dimension d minus one. And I'm essentially telling you now that, you know, I had a sequence of set that tends to this thing. The fact that it tends, it means that in this cube, the distance between my sets, so I would also have a set, let's say, e k which I, you know, I can try to draw. But the way I will draw it is by, oh, here we go, is by repeating the same story here. OK? It's close to the other one. My mapping is defined near the set here because this is the way it works. So I'm essentially saying I just can follow the construction that I had for the limiting set and project the other set up to a grid of dimension d minus one. So for k large enough, my set e k, I also can project it in on something small and make it disappear. And then I continue the proof as before. OK? So I get the same contradiction as before using the limit mapping that is corresponding to the limit set. OK? So this is one of the cases where rectifiability for the limit is just as simple as rectifiability of all the sets. Plus a little bit of being careful about having uniform estimates. But that's not so bad. OK. Lower semi-continuity of hd. And again, I will sort of move my hands around. But the proof is not more complicated than what I'm saying. OK? So with this lower semi-continuity of hd, it means you have this sequence of almost minimal sets. They converge to a set infinity. And you want to show that in any open set, the measure of infinity is less than the measure of the limits. OK? Let me try to at least draw a picture, so that I don't have to. OK. So here in the proof that I was talking about, there was an open set v. And the proof that I should have at last at least read the statement. And then I have this set e infinity, which is the limit of our sets e. And maybe there were sets e k. So I don't know if you have already here. But we're close by. And the thing that I want to say does not happen is something like this, right? That the measure of a limiting set is much larger than the measure of a set e k. OK? How do I prove this? Well, there is the usual way you start all these arguments by covering lemma. So we'll use the vitally covering lemma to essentially cover almost all of the limit set by little balls.  They will cover almost everything. And they will have some properties. And the properties will be properties that, for almost every point, small balls satisfy. OK? So this is just a little bit of techniques.   OK? And in this ball, I want two things. One of the main things is the set. At almost every point, there is a tangent plane. So I use this to say that for small balls, the set is very close to a plane. So this is the picture that I'm supposed to have here. And if needed, and I think it's needed, I also require the host of measure of the limiting set here, which is rectifiable. So in particular, it has all the properties of densities. So if I want, I think it should be here of the host of measure of the limiting set in the little balls that I cover is close to what it should be, which is omega d times the radius to the power d. OK?  And now what I have to do, so I have a covering. In principle, it's an infinite covering. But if I want to cover, let's say, 99.9% of a set, I just need a finite number of balls. They're still disjoint, so I take this final number of balls. And I will just prove that in each ball, there is enough, I can compare the mass of the limits to the mass of e k. All right? So I draw e k. k is large enough. And again, don't worry about the large enough because I have a finite number of balls to take care of. And I have to tell you why the measure of this set here is less than the measure of a red set there. And that's easy. The measure of this set here is not so large compared to the measure of its projection on the plane. And this set e k here, look at the way I can point to my pictures. OK, so this red set here, it satisfies exactly the assumptions of the previous lemma, which implies that the projection is essentially on 2. OK? So if the projection is on 2, the measure of a set e k is larger than 1 minus epsilon times the measure of the disk. And the measure of the disk is what I have up there. OK? Nothing more. OK? And I'm supposed to, yeah, it's even written here. I'm supposed to say that this proof is, so, it's amusing to me how simple this proof is. Because again, previously with Stephen, we had more complicated proofs using something which is called the Dalmazo, Morel, and Solimini concentration theorem. We've, I mean, it looked more complicated. And then what happened is that Fung had to prove the same thing for elliptic integrants. And then there was less choice. So this proof works for elliptic integrant. And the way we rediscovered or discovered that proof, in this case mostly him, was having to do with integrants. Right? And OK. So that's, again, that is supposed to be the main part of the limit.


Hi everyone, Joe for Jasper's case breaks calm coming at you a 2020 top stadium club baseball four box Random team break number one if you bought one spot like it's your two teams in this break. So like Sir mix a lot Let's double you up Or like double man gum All right, let's roll it. Let's randomize it six and a one seven times for each list one Two and a one seven the final time after seven we've got Courtney down to Adam All right six and a one seven times For the teams one and a one seven the final time after seven times. We got the Friars Down to the Cubs. What are we doing here? Oh? There it is all card ship Right there there you go So Courtney with the Padres and the Royals Adam with the A's Courtney with the Astros White Sox and Giant Zack with the Red Sox Richard with the Braves Brett with the Cardinals Adam with the Angels and Pirates Tang with the Tigers Adam with the Reds and Rockies Courtney with the Marlins and Blue Jays Adam with the Brewers drew with the Mariners Adam with The Diamondbacks Richard with the Rays Adam with the O's drew with the Indians Brett with the Mets Courtney with the Nats Anthony with the Rangers Adam with the Phillies Tang with the Twins Zaki of my Dodgers Anthony with the Yankees and Adam Harper with the Cubby Cubs Let's put all this on one screen right here and While you're considering trades the case is right above my head I'm gonna pop it open and we're gonna see which four boxes. We're gonna do four boxes All right do that right a stack of four right there and another stack of four right there All right, so on the dice roll we're gonna go one two three four So let's flip screens just for a quick second Let's use that Dodger blue die And if I roll if I roll a five or a six, I'll just roll again Like that that's two So it's one two, so we'll do these four boxes right here and the other The other ones we'll save for next time looks like no hint of a trade So let's TWC trade window closed. Let's print and rip Remember schedule is in the chat folks if you want to know what we've done and what's coming up and what we're doing now Four box Ram team number one 2020 top stadium club chrome baseball Thanks, everyone for getting in appreciate it. They're the same amount of cards in this I feel like packs are a little bit harder to open in this one. All right, here's box number one This Randy Arzirania Corey Kluber I don't know why some of these are flipped around and right side up just to drive us crazy probably loose Robert rookie going to Courtney in the White Sox and Is that our autograph? Wow two out of 15 lone-star signatures Cal Ripken, Jr. Adam Harper got randomized the Orioles in this one not too shabby It's a nice shot of Tony Gwynn right there There you go nice start box number one Box number two Now Jackson doesn't like the chrome you think things tops went overboard with all the chrome. Yeah All right, I like I like chrome black. I thought that was really nice. I like seeing the Ginter chrome There's only really a few extra chrome releases now Is it really that much more? Is there more chrome coming up? Is there more chrome coming up? I thought I thought it was just black stadium club and Ginter getting the chrome treatment in addition to the usual tops chrome and Bowman chrome. That's pretty standard though I don't know if that's overboard is it? Oh, they did have that Ben Baller, right? And I guess they do sapphire too. That's that's a kind of a chrome design as well Although those those resell pretty well, so I don't think a lot of people are Complaining about Well, you just don't like Ginter. That's what it is Jackson. Let's go. Let's get to the root of it I thought Ginter chrome was was pretty good Like I'm almost thinking the stadium club need a chrome I thought the Ginter chrome Which isn't that that sort of flat paper Kind of look nice seeing it spiced up with a little bit of chrome Go Gypsy Queen Chrome Maybe I'd like to see them do that though like if they don't let's say they If they like alternate years, I think that'd be pretty interesting like let's say it's Ginter this year And then it'll be Gypsy Queen Chrome next year that gets the chrome treatment. I think that could be pretty cool Love the photography in this and then we've got Brian a bray you Brian feel free to use the entire canvas here, buddy So on a graphing right on his leg That goes to the Stroze Courtney the Astros. All right two boxes to go So there's almost like a like in a stadium club update vibe To the did Ginter do the same thing Ginter chrome. There was more of like an updated checklist I'd like that Like have some of the regular sets Release earlier in the year And then later in the year release them in a chrome vibe, but give it an update feel Update it with any of like the sort of the hot rookies that may have just exploded or emerged out of the blue that kind of thing Like they I like that. They're kind of experimenting. You know what I mean? They might never they might never do this again You know or if it works out then maybe they will But I like that they're kind of saying hey what what kind of sort of tweaks can we make to existing product? Without redesigning an entire product are there some fan favorites that people would like to see give them the chrome treatment every once in a while It's an interesting idea Like the Ben Baller stuff.  I think There's a lot a lot of Conversation around it You know, I think it could be interesting to see if if maybe that Kind of pay sets the first foundation or paves the way for more collaborations with Even bigger bigger artists or designers in the future. I Think at the time we were joking around about like how cool would it be if they eventually got like I don't know Like like the creative director at like Louis Vuitton doing like or Gucci doing a Tops chrome cart.  I think that'd be pretty awesome You know, maybe maybe the little I like the designers hating club this here By the way, maybe maybe those little notches right there behind the team names could be like in Gucci colors or something like that Like a special trim around the edge. I could happen. I think that's a it's a good Good way to figure to kind of stretch audience is a little bit. There's Jake Fraley Also a little nervous about his autograph looks like It's a good autograph Jake It's just stretch that out a little bit that goes to the M's that'll go to Drew and I I Think I think I love those little those little color swatches That they've put there. I'm a big fan Of that design Remember all card ships, so I'm not super familiar with like whatever variations and stuff there may be I'm just kind of eyeing looking for autos, but but all card ships. So you'll you'll get everything kind of look for Louise Roberts and Kyle Lewis's but I feel like I only seen that Only seen that Louise Robert Early on cool shot of Belanger It's vocal Vogue feller Ty Cobb de Gordon All right, and the final box. Oh Did I miss both of those guys? Right in the first pack. I guess my brain wasn't in Wasn't ready yet. All right Good. I STL. Good. I good. I there's the Ars Aurelia for the Rays Richard And there's your AL rookie of the year Kyle Lewis For Drew and the Ems and Richard had the Rays All right final box in this Relatively quick four box braid. I've already forgotten what's coming up next, but the break schedule is in the chat I think a number block randomizer. Maybe or was it the opulence pack? One or the other? Pit and Northwestern college basketball in the background. All right. Good luck Mayhew Starling Marte Heroes of the zone Lucas Chialito Doc Peterson It's Mike trout Who won NL rookie of the year? Why am I blanking on who won NL rookie of the year? Kyle Lewis won AL rookie of the year Daven Williams Brewers, I guess he was just was not as memorable as Kyle Lewis or Louise Robert Now there are Zerania rookie for the Rays that'll be for Richard Oh, then there's the auto it's Tommy Edmund For the stl and that's gonna go to Brett and the st. Louis Cardinals All right, and there you go. That was four box random team break number one of the brand new 2020 top statement club chrome baseball Thanks for watching. I'm joe for jaspyscasebreaks.com. I'll see you next time for the next break. There's our autos Edmund Lewis Our Zerania Jake Fraley Brian abray you Louise Robert rookie and we started off with the out of 15 Cal Rook and jr. Not a bad break I'm joe. I'll see you next time for the next break. Bye. Bye