The start was incredibly hectic, a field full of racers who've hardly raced at all this year made for a very nervous peloton, and the first 20 miles were filled with crashes, surges, and bottlenecks. Going into the first pinch point, which was a narrow tunnel just a couple miles in, I found myself stuck behind a crash and spent more energy than I would have liked to catch back up to the front. Welcome back to another video. Today I'm going to be taking you through my race at this year's Belgian Waffle Ride Cedar City. I'm going to be getting into my ride data from the race, including my power numbers, my nutrition strategy, and I'm going to talk tactics. Okay, let's go ahead and get into it. For those of you who don't know, this race is part of a three-race series here in the US called the Triple Crown of Gravel. However, the other two races, which were slated to take place in San Diego and Asheville, were canceled this year, so Cedar City was the only BWR race on the calendar. BWR attracts some of the biggest names in US gravel racing, and this year was no exception. It also attracted fellow YouTuber Vegan Cyclist, and judging from the comments on his vlog from the day before the race, it seemed like people were ready for the ultimate showdown between Vegan Cyclist and Dillon Johnson. Yeah, well, he's already got you beat on the YouTube front because he doesn't sound like the human reincarnation of a calculator. Plus, Vegan Excuses is actually excuse number 39 on my list of excuses. Honestly, seems like the kind of dude I'd hang out with. The BWR Cedar City course was an interesting one. 125 miles, 75% of which was off-road. The race only had 6,000 feet of climbing, and the majority of that was on rolling hills that weren't too steep. However, at mile 107, you get a nasty 2.6 mile long climb with an 8% average grade, with some deep sand and steep pitches near the top. If you aren't paying attention, you could easily get off your line and have to walk here. After you descend off of this climb, you get a four-mile section of flowy yet somewhat rocky singletrack before hitting the bike path leading into the finish in downtown Cedar City. Cedar City is at an altitude of 5,800 feet with a high point on the course of over 6,500 feet, and while the altitude isn't anything too crazy, it was enough to affect my race strategy going in, especially as an east coaster coming from lower altitude without any time to acclimate. At this altitude, I was likely giving up around 3% of my aerobic power to competitors who were acclimated. Given this and the fact that the talent at this race was so deep, my plan going into the race was simple. Stay with the front group until that big final climb, and play it as conservatively as I could. No attacking off the front or going for a solo breakaway. Dude, you love to make these races as boring as your videos, don't you? Maybe you would have won if you had taken my advice. Attack during the neutral rollout at the start. If I was going to lose power due to the altitude, perhaps I could make it up by racing smart and staying patient. At least that's what I hoped. The sturt was incredibly hectic, a field full of racers who've hardly raced at all this year made for a very nervous peloton, and the first 20 miles were filled with crashes, surges, and bottlenecks. Going into the first pinch point, which was a narrow tunnel just a couple miles in, I found myself stuck behind a crash and spent more energy than I would have liked to catch back up to the front. It paid to be at the front, but I kept finding myself 20 or 30 riders back, which is not where I wanted to be. On the first major climb, which came about 20 miles into the race, I found myself about 25 riders back, and I could see the group start to splinter ahead of me, and I had to do a lot of work to pass riders and get back up to the front group. It didn't help that on the descent off of that climb, I crashed into a corner, and when I got back on my bike, I found my chain had come off. By the time I got it back on, I had work to do, but luckily I had other riders with me to help take up the chase for the front group. Within 15 minutes we had caught them, and shortly after that, the lead group of seven, which would spend the majority of the day together, was formed. This group included Keegan Swensen, Peter Stetna, Alexi Vermeulen, Griffin Easter, Ryan Standish, Eric Burner, and me. The selection to make the front group took about 38 minutes and required me to put out a normalized power of 320 watts. This is the point in most races where the front group starts to slow down. Everyone's made the selection, and it starts to sink in that they're still a long way to go. This was not the case here. At mile 40, we had another brutal push for 37 minutes, which required a normalized power of 302 watts. This was made more difficult by the fact that this section was extremely sandy and dusty, often with just two distinct lines, making it hard to draft. Sitting on the rider's wheel in front of us, we were constantly hitting rocks and holes at high speed, and there was no way to see them coming, because the dust kicked up by the rider in front was too thick. Fortunately, after this, we hit some road, and the pace did ease up a bit, and over the next hour and a half, I put out a normalized power of just 245 watts. We were still pulling through and working as a group to keep the speed high, but we took some time to lube our chains on the bike, which was absolutely essential on such a dusty course, and catch up on our nutrition. My nutrition strategy for this race was the same one that I used at the Sugarcane 200 and Shenandoah Mountain 100 with good success. It included one bottle per hour with two scoops of Flow Formula's drink mix, and one goo energy gel per hour. This was roughly 85 grams of carbohydrates per hour. This is the important part, though. Research shows that 60 grams per hour is the limit of how much fast carbs can be absorbed, even when large amounts of carbohydrates are ingested. However, combining different carbohydrate sources, such as glucose and fructose, have been shown to increase carbohydrate oxidation rates by 20 to 50 percent, because fructose can utilize a different transport pathway. So combining multidextrin and fructose in the right ratio could bump that absorption rate from 60 grams per hour to potentially 90 grams per hour. All the carbohydrates that I consumed during the race had that optimal 2 to 1 multidextrin to fructose ratio. Back to the race, though, even though we chilled out a little bit in the middle of the course, we still kept the speed pretty high. We worked well together as a group, and with 7 strong riders, we never slowed down too much. In fact, we did the first 100 miles of the race in just 4 and a half hours, which is an average speed of over 22 miles per hour. On gravel. Around mile 92, the pace started to pick up again with Griffin Easter, Eric Burner, and Peter Stetna all taking stabs at splintering the group. My legs were feeling pretty tosy at this point, and I just held on to the back of the group, hoping the pace would slow down soon. This hard stint late in the race lasted almost 10 minutes and required a normalized power of 308 watts to stay on. The only one to drop from the group after this big effort was Ryan Standish, and we found ourselves in a lead pack of 6, heading into the final big climb of the day. Immediately on the climb, Peter Stetna got to the front, and before too long, him, Keegan Swensen, and Alexi Vermeulen had a gap on me. At this point, really all I could do was ride my own pace up the climb, which at this point in the race was an average of 315 watts for a little over 16 minutes. I also hit my max heart rate for the race here, which was 183 beats per minute. Griffin Easter also pulled away from me on the climb, but I managed to keep him in sight, and he only had about 30 seconds on me going over the top. This meant that the battle for fourth place was not over. The downhill off this climb was a bit hairy with deep, sandy switchbacks and ruts, but I managed to get down it without too much trouble and with Griffin in sight. I put in a hard dig on the gravel section right after this descent, and managed to make contact with Griffin right before the single track. The single track was flowy, but also had a decent amount of rocks, making for a bumpy ride. If you were on a mountain bike, you probably wouldn't think much of it, but being on a gravel bike and having already raced 115 miles at this point, it took a lot of focus to ride it fast. I went into the single track ahead of Griffin and did my best to keep it fast and smooth. I wanted to ride the downhill sections as fast as I could, but I also didn't want a flat tire at this point in the race, so I kept my eyes peeled for sharp edge rocks. About halfway through the single track, I managed to get some distance between me and Griffin. Exiting the single track, I looked back and saw that I was completely clear, and all that there was to do now was to put my head down and crank as hard as I could on the bike path for five miles to the finish. I hit the finish line in six hours and 34 seconds, about five minutes back from Keegan and Peter in first and second, and about a minute and a half back from Alexi in third place. At the finish, we learned that Keegan had just won the race without a front brake, because it had gotten ripped off in a tangle at the start. Absolutely incredible ride from him, and if anyone was able to win this race without a front brake, it's definitely Keegan, because he's just that good technically. Alright, let's get into the numbers for the race. I had a normalized power of 266 watts for the whole race, a TSS or training stress score of 358, and an average speed of 20.6 miles per hour. Super happy with the top five finish here, especially given the strength of the field. Um, sorry dude, but who even remembers second, third, and so on places? Fourth place, last place, it might as well be the same thing. It's just like Ricky Bobby always said. Maybe next time try pedaling harder. This race has gotten me stoked to do the San Diego and Asheville race next year. If you're a gravel racer in the US, I definitely recommend checking out at least one of these events. It was super cool to meet vegan cyclists out there, and I also talked to a lot of people who watch my channel. It was great to meet all of you, and if you ever see me at a race, don't hesitate to come up and say hi. This is my last race of the year, and hopefully next year things can be back to normal so we can do this more often. Thanks for watching. If you want to stay up to date on my racing, the best way to do that is to follow me on Instagram. I also announced when I post new videos on there. If you enjoyed this video, be sure to give it a like, subscribe for weekly cycling videos just like this one, and share this video with your cycling friends. I'll see you in the next one.


What's up, everybody? JC here for jatsby's case breaks.com to the 1920 hip parade the rookie's graded basketball edition series one Just sold out. This is a five box half case break random teams number two So again, 30 total spots everybody gets a random team then be a college cards We'll first go by the checklist if there is a no checklist Then we'll go by our college rules Which is current team if they're active or if they're retired teams they played for the longest to get one great It rookie per box either BGS or PSA featuring LeBron Durant and Curry Luca Zion Trey Jotate and Kauai and every box is one card per box hundred hand numbered boxes produced and Pretty nice cards guys. So let's check it out. See what we get here So let's roll the dice and we got ourselves a six and a five for eleven times. So good luck one two three Four five six seven eight nine ten So men and a so men eleven times One two three four five six seven eight nine ten And eleven Hawks down to the Warriors So many of the Hawks Roger with the Raptors Ron with the Rockets Chris You have the Kings so men with the Jazz Chris with the nuggets John C with the Blazers down with the Magic Ron with the Bulls Celtics and Mavericks Robert Runkle You have the heat Chris with the Suns Lou with the 76ers Roger you have the Kings John C with the Hornets Oliver with the Clippers Oliver Smith that is Ron with the Pacers John C with the Lakers James Connell. You have the Spurs so men with the Grizzlies King with the T-Woods Shea with the Thunder Matt with the Pelicans round with the Nets James with the Cows Brian last Balmogel Bucks Oliver Sororio with the pistons John C with the Wizards and so men with the Warriors So if anybody wants to trade The trade window is open give you guys a few minutes Cornets are up for trade. Don't mind me folks. I'm just gonna put these R&B teams in really quick All right guys, I think I'm gonna close it John C. Unfortunately doesn't look like nobody wants to trade Not a TWC. Let's print and rip now. All right, so looks like Sean did the first half last night Here's the second half Each box is hand numbered so this is box six of a hundred So good luck. Let's see what we got here Here's everybody else in the break. So we got a PSA slab and it is a nine PSA nine minutes and Wow, it's a zebra Gary Trent Jr. 2018 Panini select For the Blazers. There you go PSA nine Blazer that's going to John C. There you go Very nice Next one Box 39 out of a hundred looks like we have a graded to graded nine And it is John wall that is a dyke up from 2010 11 playoff contenders patch our tenders patches Rookies of the year contenders dyke up gold That's a bgs nine and out of 99 was the Zero number there Wizards also going to John C. Wow. They go back to back maximum is a PSA slab It is a 10 Looks like a Donner's optic 2017 rated rookie shock Lonzo ball for the Lakers He still sells pretty well actually There you go Lakers Wow three for three. Oh my god.  I didn't actually you think think you had the Lakers, but man Have yourself a break. I'll get a scratcher a lottery ticket. Yeah, I sometimes box 89 out of a hundred I've got a bgs To graded nine Jason Tatum very nice rated rookie Everything was a nine five, but the surface got a eight five which I guess kind of messed this grade up but There you go Maybe maybe a PSA 10 or be or nine over there as well There you go Ron with the Celtics 65 at 100 last box You have a bg. I'm sorry PSA nine and Wow, we got a sell sheet hit Yannis onto decompo That is a rookie from prestige 2013 and that's right on the sell sheet I believe So there you go Very nice, and that is gonna go to last spot mojo Brian T with the Milwaukee Bucks Very nice And there you go guys Yannis PSA nine rookie Jason Tatum bgs nine a PSA 10 Lonzo ball the graded nine John Wall and a Gary Tran Junior rookie Zebra PSA nine So there you go guys if we have a fresh case up on the website now number three jazby's case breaks calm. Appreciate it


The seven student recipients have attained athletic scholarships to study in Jamaica and are being rewarded for their fine achievements with the presentation of a laptop each, an item that remains essential for studies in this modern era and in this present COVID-19 environment. This week, the Department of Education, Innovation and Vocational Training held a small ceremony to present the students with the electronic devices, ticking off the item on their to-buy list to pursue their studies. Parliamentary Secretary in the Department of Education, Innovation and Vocational Training, Senator Honorable Dr Pauline Antoine Prosper says the seven students are being rewarded for their tremendous efforts at the secondary level, which has translated into their successful acceptance at a Jamaican tertiary institution. We are indeed very proud of them. When students work hard, they get their just reward. So before they leave, I know some of them have left island, but we still have some of them here with us, to receive laptops from the Ministry of Education, to allow them to better able to cope with their program of work when they get to Jamaica. We know they have been in the comfort of their parents. When they get over there, they have to get a new level of independence. They have to become responsible. So I want to wish them all the best. Dr Antoine Prosper is certain the students will make St Lucia proud, especially with the notable achievements of St Lucia at the just concluded Commonwealth Championships. They will be trained to become international athletes and I know all of us have been proud of Julianne Alfred and we have many more students who will make us proud in the future. So let me wish them all the best as we give them an additional tool to help them with the task ahead. The students accompanied by their parents were each presented with devices that have been fully activated with the necessary software to aid in the pursuit of their studies. Former student of the Choselle Comprehensive Secondary School, Jada Emmanuel, is one of the successful recipients of a laptop. She thanked the department on behalf of the rest of her fellow recipients pledging to make full use of the devices. We the athletes would like to thank the Ministry of Education for providing us with these laptops as we start our journey in Jamaica. We assure you that they will be well utilized. Thank you. The other laptop recipients include Vanny Henry, Heathan Monero, Geneva John, Deshaun Fannes, Jaheem Ferdinand and Leicester Emmanuel. From the Communications Unit of the Ministry of Education, Sustainable Development, Innovation, Science, Technology and Vocational Training, I am Chris Satney reporting.


Today, I have the pleasure of speaking with Kim Oishi from Datable Technology. How are you? Great. Tracy, thanks for having us on. And of course, Kim, I've known you for years. I've known you as an investment banker. I see you're lending your name to a public company. What kind of company and what technology do you have at Datable Technology that you would basically join the team? Yes. I've been involved now for a few years and I'm very happy to be involved and put my name on this company. Really, we're at the beginning of, I think, a very big growth phase for the company. It's partly because we've built a great solution that some of the biggest brands in the world are using, but it's also because there's a trend now in our sector towards first-party opt-in data from consumers. There's a lot of pushback right now from regulators and from consumers on some of the big giants out there, Facebook, Twitter, Google, well, the way they use data and the way that they are contributing some of the privacy laws. And there's been some big fines and now there's going to be a big move in legislation to prevent some of the non-permission use of data. And our company gets permission from all the consumers and really rewards consumers for sharing their data with these big brands, with our big consumer brands.  They have the right name. If I understand you properly, you're like a cloud-based loyalty and data program service solution for corporations. Is that correct? That is correct. Yes, we provide a software as a service platform that consumer companies can license and they use that to really engage with the consumers, collect a whole bunch of data about who they are and then really retarget them with meaningful offers, all with the consumer's permission. Of course, we had you on investor talk earlier today.  Can you tell us a little bit more about this? Yeah, I've learned over the years of investing in this company and then getting a bit more involved in the operations. That is a real big challenge for a small company to sell software to a big company. And so you have to pass all their, you have to provide them return investment. That's the bottom line.  And because we're actually getting some of the world's biggest brands to license our software, store consumer data on it, and use that platform to re-engage with consumers. It's taken us a few years now to prove that, but now we're well on our way with some of the world's biggest brands to ramping up their engagement with us to the point where we're becoming a big part of their program. Of course, you've been very public about having clients like Universal. Is that correct? Yes, they're a client. And of course, I've noticed the doubtable technology. When I first met your CEO, he was very focused on the business side. You've been handling more the public company side. And your news release flow has started to pick up. You just announced a partnership with Dabble. Can you tell us about that? Yeah, that's a really important partnership for us. Really, what Dabble does is they have their own database of consumers. And our big customers have been asking us, we know the kind of data you collect for us. If you guys had your own database, we'd give you budget for that. And so we looked at building your own database. We realized that was going to take too long and cost too much. And so we decided to partner with companies that already have consumer databases, use our software to link them with our big consumer brands. And we partnered up with Dabble. And so far, we've done two deals after just the last month, one with Universal, our biggest client, and one with Coca-Cola, which is a new client. Well, thank you so much for joining us today, Kim. We'd like to see you every single month. Promise me you'll start doing more regular interviews because we had to work hard to track you down. Absolutely. I'm on board to get our story out there. And thank you for the opportunity to do that today.


Okay, we would like to, I would like to make some more comments about the solution to the random walk problem, the linear random walk on a linear lattice with a bias. There are certain points about this solution which are general in nature and I would like to start with that and then go on to some more properties of general birth and death processes, okay, together with hopefully some physical examples of what is happening. Now if you recall our random walk problem, so this was random walk on a linear lattice, if you recall we had these sites on the lattice, this was site J and this was J plus 1, J minus 1 and so on, all the way only the side over this full set of integers and the rule of the game was that from every site J you jumped to the site J plus 1 with a mean rate which was lambda times alpha and you jumped from J to J minus 1 with a mean rate which was lambda times beta such that alpha plus beta is 1 and then we discovered that if you start at some arbitrary origin say 0, the probability P of J, T starting from the origin, this had an explicit solution and the generating function for this was z to the J summation J equal to minus infinity to infinity was a quantity we could evaluate explicitly and this was e to the power minus well e to the power lambda T times alpha z plus beta over z minus 1 and that was it. We interpreted this in two different ways, one of them was to write a birth and death equation for it and solve it using a generating function or to say that this process, this random process J is the difference of two Poisson processes with rates lambda alpha and lambda beta and that immediately gave us this as a generating function, okay. Now from this the mean values could be written down, the solution itself could be written down etc and just to recall to your mind what happened, this was e to the minus lambda T and then we could write the rest as e to the 2 lambda T over 2 square root of alpha over beta times z plus square root of beta over alpha 1 over z and that helped us immediately identify P of J, T as a certain Bessel function, right. So this immediately gave us the solution P of J, T starting from the origin to be equal to e to the minus lambda T and then the Bessel function ij of 2 lambda T times square root of alpha beta and then there was this factor alpha over beta square root to the power J or this to the power J over 2. So that was the explicit solution, okay, right to this probability for this probability. Now from this we can read off all the moments etc, etc and interpret them in some sense. For instance the mean value J of T, this was equal to if I call this thing the generating function f of z comma T equal to this, this was the generating function, the mean value here is just delta f over delta z at z equal to 1 and that follows directly from here you differentiate this you pull down a lambda T and then an alpha minus beta if you put z equal to 1 this goes away the exponent goes away and you have this is equal to lambda T times alpha minus beta. So you see what is happening is that this bias alpha minus beta this differential preference to the right or the left depending on alpha being bigger or smaller than beta acts like a velocity. So this is like the mean position of displacement after time t is proportional to the time and of course it must be multiplied by a velocity in this drift velocity is essentially lambda times alpha minus beta. So lambda times alpha minus beta is like a drift velocity. You can now compute the mean, the mean square and so on and we know that the variance actually proportional to lambda T. So one should do this a little more elegantly and so going on differentiating this function here let us just find the cumulant generating function that will solve the problem in one shot. Now the cumulant generating function if you recall is the log of the moment generating function and the moment generating function so k of u is the cumulant generating function equal to the log of the moment generating function m of u but that was the same as f of e to the power u and that is equal to all we got to do is to take logs out here. So this is equal to lambda T times alpha e to the u plus beta e to the minus u minus 1 that is it.  So this becomes equal to lambda T times alpha plus minus 1 to the power r the first moment first cumulant is of course the mean value itself. So it is clear that this k 1 equal to j of t and that is of course alpha minus beta which you already derived right but what is interesting is that the variance is independent of this bias. So the drift is cancelled out by the fact that you subtract the square of the mean when you compute the variance from this mean square and therefore k 2 equal to the variance of j this is equal to lambda T this is a crucial result it is typical of diffusive behavior we know that the root mean square displacement must go like the square root of the time and that is exactly what is happening here when you compute the variance you subtract out the systematic drift and then you end up with precisely diffusive behavior. We can of course examine and ask whether p of j comma t itself has a limiting distribution or not remember we are in an infinite lattice now what would you physically expect I would expect if I start with probability 1 of being at the origin at t equal to 0 as time goes along you are spreading you have an infinite amount of space to spread out on both sides. So although the particle is somewhere on this line the probability of being at each particular point vanishing should be vanishingly small so you would expect it should go to 0 and there should be no stationary distribution in this problem. So in a birth and death process when you have an infinite lattice when this variable is not is unbounded from both sides then the probability stationary distribution will not exist unless you put in some external condition like you would put in a current of particles from one side and let them jump out from the other side or something like that but that is an external condition without that in general it will turn out that this probability should vanish as t tends to infinity but that is that happens here we can check that out because it turns out that ij of whatever is inside ij of let us call it whatever variable you want to call it xi whatever it is this tends as mod xi tends to infinity this fellow tends to e to the power xi over square root of 2 pi xi that is the leading behavior of the modified Bessel function and it is independent of j the order j provided the order itself does not become infinite. So if you apply that here it is immediately clear that P of j, t on 0 tends for long times which means lambda t much much greater than 1 tending to infinity in fact because the time scale in the problem is set by lambda inverse that is important remember this tends to e to the minus lambda t times 1 minus twice square root alpha beta and then alpha beta to the j over 2 divided by square root of whatever square root of 2 pi so that is 4 pi lambda t root of alpha and this quantity vanishes exponentially rapidly in t as long as this is bigger than that and remember that this quantity is 1 minus 2 root alpha beta equal to 1 minus 2 root alpha times 1 minus alpha where 0 is less than alpha is less than 1 and when does this quantity become large the largest at alpha equal to half because otherwise on both sides it is a parabola it comes down on both sides at alpha equal to half it is maximum and then of course the 1 cancels out. So it this quantity dies down exponentially as long as the coin is biased as long as the random walk is biased either way we do not care but this will exponentially vanish on the other hand when alpha so P of j t 0 tends in the case alpha equal to beta equal to half it goes like a power law so now this factor cancels out and it goes like 1 over square root of 4 pi at 2 2 pi lambda t goes like 1 over t to the half that is typical of diffusion in one dimension linear problem instantly now that we have written this down we can actually write down the solution to the random walk problem on an arbitrary dimensional lattice square lattice or a hyper cubic lattice or a hyper cubic lattice there is no problem at all in writing this down because one can do this by inspection because all the jumps are independent of each other and then you can see what is going to happen so let us generalize this right away when we come back to this so suppose I have a d dimensional cubic lattice or hyper cubic and let us suppose that the coordinates of any point are labeled by j 1 j 2 j d now let us call this the vector j so the components are all integers and they label the lattice point I start with some arbitrary origin it is an infinite dimensional lattice and then suppose I put biases on both sides which you can always do so to move to the right there is a probability to move to the left there is a different probability to move up or down or move in or out and so on right so you can associate probabilities alpha alpha r beta r where r runs from 1 to D and the sum of all these alphas and betas equal to 1 they are all positive numbers then we can write down what the solution is for this quantity p of j t given that you started at the origin what would this be what would this be because the total rate of jumps out of a site is lambda and that is now split earlier it was split between lambda alpha and lambda beta on this site now it split between lambda alpha 1 beta 1 alpha 2 beta 2 and so on the whole thing adds up to 1 so what do you think will happen what do you think will be the generalization of this now it is not the difference of two Poisson processes there are several processes going on at the same time right and they are all independent of each other so one can actually write this down by inspection what do you think it will be well yes you certainly would let us write it down here this j you certainly have this factor as before this comes remember it came from the generating function because there was a mind you subtracted in the master equation you subtracted minus p of j, t with alpha plus beta added to 1 so that produces this e to the minus lambda t and then the rest of it is sitting here so what you would have is simply the same thing as this except this would be alpha r over beta r j sub r over 2 and this would be j subscript r alpha r beta r here e to the minus lambda t a product from r equal to 1 to j to d and that is the solution it immediately follows that this is the solution in a d dimensional hyper cubic lattice so once again one can ask what happens if t tends to infinity lambda t tends to much much greater than one so this tends lambda t much much greater than one they call this the diffusion limit very long time limit what would this go to all you have to do is to use this fact up there and then whenever there is a bias there is going to be an exponentially damped factor what happens if there is no bias at all what would you expect if there is no bias unbiased random walk what would this correspond to for each alpha and beta on a hyper cubic lattice yeah so you have for example from this point you have up you can go down you can go this way you can go this way you can go into the board you can come out of the board and so on so there is six nearest neighbors in three dimensions in d dimensions there are 2d nearest neighbors right so for an unbiased random walk alpha r equal to beta r equal to 1 over 2d so when you sum over all these 2d numbers you get unity then what would this become these factors disappear all these factors disappear this factor in the exponential there cancels out exactly and you are left with the product of these fellows and alpha or beta r or 1 over 2d so there is a 1 over 2d multiplying this gives you some constant etc but the crucial point is unbiased the crucial thing is the t dependence and what does the t dependence do there is this factor for each of the Bessel functions right and there are d such Bessel functions so this immediately becomes proportional to 1 over t to the d over so it is a power law dk but it is proportional to 1 over t to the half d over 2 where d is the dimensionality of the space when we solve the diffusion equation in continuous time and space then again you will discover this is Gaussian solution has a dk which is exponential which in general is 1 over t to the for an unbiased diffusive process it is 1 over t to the dimension over 2 this fashion so for 1 dimension it is 1 over square root of t which is what we found this now okay so you can begin you can see that there is going to be close connection between this and the diffusion process and we will explore that when we go to the continuous space case but already from the random walk on a lattice one can deduce these facts now of course this depends you would say on a in higher dimensions it would depend on the lattice the nature of the lattice and what are the nearest neighbor jumps etc etc but actually this this feature is very general although this solution is very specific to that kind of lattice this is very very general and it actually follows from much more general considerations so we want to get into that right now except to say that I can go to a much more general kind of random walk I can say that I am not on a lattice I take steps in different directions of different lengths they could be distributed they could themselves be drawn from some distribution as long as the step length has a fine is a distributed in such a way that it has a finite variance finite first two moments this this kind of feature will always persist these these general features will persist so it is independent of dimensionality it is independent of the nature of the walk etc as long as the walk is Markovian this independent steps the steps are not correlated with each other if on the other hand you have a real material in which you have some correlation then this whole thing goes out of the window if for example you jump from left to right and then there is a predilection to jump back to the vacant site back again then of course you have correlation between different steps all these things have to be modified or if you have a situation in which you remember what happened earlier and you never is visit the sites you already visited once and those have a lot of memory and they go completely outside the purview of these Markovian random box okay so Markov assumption is very crucial here yeah now let us try to generalize this a little bit and put it in a slightly more general framework and that is the framework of what I called birth and death processes they have other names as well in the semiconductor industry business they are called generation recombination processes and so on and so forth there are different names in different areas will stick to this birth and death business now what was the fundamental assumption the assumption here was that on a linear lattice you jumped either one step to the right or one step to the left or in state space if J labels the states of the system their integer value and then J changes by plus 1 or minus 1 this is all if you generalize this a little bit then once again not with any reference to a lattice or anything like that but if I just write down the states of the system some random variable which takes integer values and you are at some point here let us call it N not let us call the let us call these sites by J once again so here is site J and if the process is such that you change this the transitions occur the W matrix I am going to write down will only connect neighboring states then I want to model for this quantity W K J which if you recall was W K J the transition rate to go from an initial state J to an initial to a final state K if this thing only connects neighboring states then there is got to be something which is proportional to a Kronecker delta such that K can only be J minus 1 or J plus 1 so there is a transition probability this way and one that way from J and all the other transition probabilities are 0 then what is the most general thing you can have you could have this to go such that the final state is out here with some rate and in the random walk problem we said that is a constant rate lambda times beta or the time apart from that lambda factor let me just call it beta but this could be dependent on where you are so as you move down the states the rate at which it makes transitions you still assume it goes to neighboring states on either side but that could depend the rate could depend on where you are in which case this would be some beta J times this plus the final state could be J plus 1 you could jump out there and in difference to the random walk problem that we used alpha and beta for the bias factors let us continue to call it alpha but it could depend on J now there are three possibilities for the state space either the state space which is takes on integer values runs from 0 to n or 1 to n some finite set or it is infinite on one side goes 0 1 2 3 all the way to infinity or it runs over the full set of integers these three are three different classes of problems altogether because when we write equations down with finite boundaries then I have to change the rate equation at the boundaries to make sure that the space is confined to that range just as when we did the Poisson process I said you have the probability rate at which the probability of 0 decays in a time t changes that decreases with time and then 1 2 3 etc etc they are all functions of time this is a Poisson distribution but the rate equation for DP 1 over dt was different from that for DP 0 over dt we will write the rate equation down once again right. So you have to be careful about the boundaries and then you can put all sorts of boundary conditions on it but for the moment let us take J to be a general number integer then what does the W matrix look like once you have this suppose J runs from 0 1 2 3 in that case you would have a finite matrix this kind if it is bounded from the other side to otherwise it is infinite that way and what does it typically look like let us look at W 1 2 for instance so J so in this case K is 1 and J is 2 so this is 1 sorry this is beta 2 and then when K is 1 it fires so you certainly have something here and then you have beta 2 in this case and this term contributes 0 okay all the others are 0 0 0 etc and what happens to 2 1 so if you look at W 2 1 this term does not contribute but this contributes K is 2 and if J is 1 it contributes a beta and what an alpha and what does it contribute it contributes alpha 1 and everything else is 0 down here and when it comes here you have a beta 3 contribution because that could have jumped to the left on this side and when you come here this could have an alpha 2 contribution on this side and what would the diagonal element be it would of course be we know this is equal to alpha 2 plus beta 2 this alone because I started with 1 2 3 4 labeling things with 1 2 3 4 there is no state 0 here in this problem this alone would be minus alpha 1 that would ensure that this is a stochastic matrix the sum of each row each column must be equal to 0 but the general structure of this matrix is a triangular matrix with something on the diagonal elements negative elements and then the super diagonal has all these beta factors and the sub diagonal has all the alpha factors so typically at some point in the middle on the jth column jth column everything is 0 till you hit a beta j and then a minus alpha j plus beta j and then you hit an alpha j and on the right hand side you have a beta j plus 1 this diagonal keeps going this diagonal keeps going and on the left hand side you have an alpha j minus 1 that is the general structure of this matrix okay and if there are end points to this matrix then you got to be careful at those ends etc and what would the rate equation correspond to in this case what is the rate thing now let us get over get rid of this j because that had this connotation of a lattice point but the examples we looked at earlier like the Poisson process etc we looked at a random variable n some number n so what would the rate equation be so let us write that because we are going to look at cases where n is running from 0 to capital N or 0 to infinity or minus infinity to infinity and what does that look like corresponding to this W the rate equation dp over dt dp n over dt as a function of t what is that going to be equal to well it is W times this p you write this p down in this fashion and what is the first term that is going to appear again you can see what is going to happen the growth of any particular knowledge call this n the growth of the probability here depends on fellows jumping from in from here and people jumping in from here right and whatever is jumping in from here has got to be beta but dependent on the site n plus 1 and what is jumping in from here is alpha dependent on the site n minus 1 right so it is clearly alpha n minus 1 p n minus 1 of t plus beta n plus 1 p n plus 1 of t minus alpha n plus beta n those would be these 2 processes which go out so this is alpha n beta n here this fellow was an alpha n minus 1 and this was a beta n plus 1 jumping in and these 2 other ones that jump out and that is multiplied by p n that is the general equation which you have for a one step birth and death process in which the elementary transition probabilities only connect you from the state n to the state n plus minus 1 and these are in general functions these rates are general functions apart from the fact that they are positive or non-negative you cannot say very much more so this is the general equation general master equation or rate equation and we looked at special cases of course we looked at special cases of it so random walk bias random walk alpha n equal to alpha beta n equal to beta alpha plus beta equal to 1 right what about the Poisson process what happened to the Poisson process and incidentally n was the element of the set of integers what about Poisson what did that correspond to we had a certain rate lambda but n now ran from 0 upwards and the Poisson process equation was for n equal to 0 1 2 etc to infinity and in this case alpha equal to beta equal to lambda but the process was dp n over dt equal to lambda times p n minus 1 so you had finished n minus 1 jumps in time t and then in the time that interval delta t after that you did one more with probability lambda delta t but you might have already reached n and you are now jumping to n plus 1 dk so therefore it is a lost right so this equation was this minus p n and that was true for n greater than equal to 1 and for n equal to 0 you had dp 0 over dt was minus lambda p 0 it is clear this is a special case of this very general thing with suitable choices of alphas and betas right this is a pure birth process because the number n kept increasing with time it did not ever decrease beyond a certain value so the left words probabilities were all 0 and you only had increase on one side incidentally this was a stationary Poisson process stationary in the sense that the statistical properties of the system do not change with time which means this rate lambda does not change with time what would have happened by the way we know the solution to that right we know that we know completely for the Poisson process Poisson process we know that p n of t is e to the minus lambda t lambda t to the n over n factorial n equal to 0 1 2 we know we can write down the generating function for this and compute what the coefficient of z to the n is and that is the end of it we did that explicitly by the way what would happen if this Poisson process was non-stationary suppose it turns out that for some reason lambda equal to lambda of t and you have a non-stationary but Poisson what would have happened to the solution this equation is still true because all you are saying all you are saying in these in this entire birth and death businesses you are saying that in a time interval delta t sufficiently small time interval delta t either there is a transition to the left or to the right or no transition at all it does not say that cannot be transitions to further points further states it just says those are of order delta t whole squared and so on and so forth whereas a transition to the nearest neighbors is proportional to delta t itself and then we got that differential equation so now the question is what happens if it is non-stationary you have a nice function lambda of t but it systematically changes with time in some deterministic fashion what would happen to the solution I would get exactly the same rate equations as before except this that this becomes lambda of t on this side and the initial condition is once again at t equal to 0 n is 0 okay what would have happened to that solution well the way we got that solution was we multiply this by z to the power n and summed over n to write the generating function down right and we got an equation with said essentially delta f of z, t over delta t was equal to lambda times z minus 1 f of z, t we got a z because there is an n minus 1 here so when you multiply by z to the n you got remove a z and write it as z to the n minus 1 and sum okay so that is how the z came out now what is going to happen is this once again the boundary condition is the initial condition is the same as before we know that only p 0 has a value at t equal to 0 that is 1 so f of z, 0 equal to 1 this is the initial condition what is the solution to this equation with that initial condition this is not a constant so how do you solve what is the solution yeah it is e to the power z minus 1 integral from 0 to t dt prime lambda that is it okay you have to integrate both sides its separation of variables immediately gives you this solution that is the general solution in the case when lambda is constant that exponent becomes lambda t as you can see okay and it satisfies the boundary conditions we got a unique solution so if you define this quantity you define this to be some lambda of t call it that when we are ready to write down what the probability density it is a probability itself is once again it is just the coefficient of z to the power n so you would get exactly the same solution except that you now have e to the minus lambda of t lambda of t to the power n over n so this particular making it non stationary is quite trivial it is quite a way with the solution immediately okay this occurs in the problem of what is called time dependent short noise okay but it is a trivial extension of the original Poisson process what is much harder to do is solving the general equation this equation here this is not at all a trivial matter even though it is a one step process in which you only go from n to n minus 1 or n plus 1 even then if these coefficients these coefficients are sufficiently independent in a complicated way then writing down an explicit solution is out of the question for the set of couple differential equations okay constant no problem that was a biostrandom or problem when alphas and betas are independent well the next thing you would guess after that which is solvable would be to say suppose these are dependent on n linearly that would be the next natural thing to do linearly for instance as a physical problem in which you have a quantum mechanical harmonic oscillator say levels are all quantized and let us suppose it is put bed in radiation of the right frequency so that the oscillator can absorb a photon go to one excite a state higher than it or it can emit a photon of the same frequency and go to a state lower right and then you ask what is the population probability of population of the state n of this oscillator that problem would be exactly this kind of rate equation in which the alphas and betas are linearly dependent on n. In fact that is how Einstein actually derived that is how Planck originally got the Planck law in that case what happened was for the radiation problem turns out that alpha n plus 1 equal to some constant times n and beta n equal to some of the constant b times n alpha n minus 1 was proportional to n and beta n was proportional to n once again with some constants a and b okay. I am going to leave it as an exercise for you to solve this set of differential equations given this not altogether trivial but at least find the stationary distribution in this problem n runs 0 1 2 3 up to infinity they label the levels of the harmonic oscillator right. So n is and find P n stationary I will give the answer to it is a geometric distribution which depends on the ratio a over b okay. So try to derive that what you have to do is to put this in and then equate this put P stationary here everywhere no T dependence and then equate it to 0 okay and then you try to find out what the stationary distribution is in this case but actually when you have a linear process you can go a little further and that is interesting because this rate equation can give you some physical information and here is how it happens let us suppose for ease of algebra let us suppose for a moment that n runs over all the integers so that I do not have to worry about these boundary points otherwise I have to be very careful about the boundary conditions and put in appropriate conditions each time I might for example if run n runs from 0 to infinity I will have to define alpha minus beta minus 1 as identically 0 put in a formal beta and define it to be 0 and so on but let us just say that n runs over all integers suppose n element of I look at this and I ask what is the average value of this random variable n at any time T. So what I need to do is to compute n of T this is equal to summation over n n times P n of T over all the integers since I am summing over all integers whether the summation index is n or n plus 1 or n minus 1 does not matter it is over the same set I am going to freely shift things okay then what does what happens to this what is D over DT of n of T equal to I multiply both sides by n and sum over n over all the integers then the first term gives me an n but I make it an n minus 1 and remember to add that one later on so it is going to be a summation n minus 1 alpha n minus 1 P n minus 1 plus summation now in this fellow here I multiply by n so I make it n plus 1 and subtract the n later on. So summation n plus 1 beta n plus 1 P n plus 1 minus summation n alpha n P n minus summation n beta n P n and then let us be careful I multiplied by n I wrote it as n minus 1 so I got to add so there is a plus I add 1 so this is summation alpha n minus 1 P n minus 1 and then I have to subtract this fellow here no no no I had an n I wrote it as n minus 1 plus 1 I had an n I wrote it as n plus 1 so I subtract 1 so minus summation beta n plus 1 P n plus 1 that is overall n but I can shift the summation index to n minus 1 and it is over the same range and this term cancels this and this term cancels this. So we have an interesting result which says I do not care what these coefficients are but if they are linear whatever they be I do not care there is an equation which says d over dt the average value of n of t is equal to this quantity and that quantity but what is this equal to again I translate the summation index to n but I am got the weighted average of alpha sub n whatever function of n that be so this is equal to alpha sub n so I have an equation actually pardon me a minus minus that equation could be non-linear in n in general it could be complicated etc so it is not trivial to solve it but you have an explicit equation for the average value in terms of possibly higher moments in general but you have an equation similarly if I multiply by n squared and compute what is n squared of t here again this thing is equal to n squared P n and the trick is exactly the same as before write it as n minus 1 squared and n plus 1 squared shift it and that will cancel against these fellows here but there was a 2n plus 1 which you added you must subtract those fellows out add or subtract those guys out but remember each time whenever these fellows n minus 1 you better match that here so in the linear terms you got to be careful once again subtract etc and you get a closed equation once again an equation in terms of average values so in this case you do not remember what it is but one can work this out on the right hand side you are going to get things like average value of n times alpha n plus beta n and then there is possibly an alpha n minus beta n etc plus something times there is maybe there is a 2 here because there was a 2 remember each time etc so these factors can be worked out but this is the sort of equation that you would get okay now tell me if the process is linear in n what is the special feature that emerges at once suppose the alphas and betas are at best linear in n each of them is some constant times n plus some other constant what would what happens then to these 2 equations sorry this is d over dt what happens then what is the special feature that emerges well this fellow is also linear in n so at best it is going to involve this guy so you get a closed equation for it right away which you can in principle solve okay and then what happens here again the worst you get is a quadratic in n the average value so this set of equations is closed completely and you can solve it even if you are not able to solve the full time dependent problem for p of n comma t you can still solve the equation explicitly for the average value as a function of t and the variance completely provided the process is linear provided the coefficients are linear so when I say the whole differential equation these are linear equations in the piece no doubt about that but when I say linear nonlinear etc I mean these coefficients if they are linear in n or nonlinear in n you have a big difference if they are linear then not only do you get a close set of equations for the a for the mean and the variance but you can also solve these equations explicitly but if it is nonlinear then it depends changes from problem to problem okay we will I will give some physical examples of this next time but you have already seen that the simplest of cases like the random work problem and everything that is mapped on to the random work problem these coefficients are constant and then when it is linear you have the radiation is an example of this chemical reactions would have similar kinds of rate equations etc a very interesting question is is the existence of a stationary distribution and the rule was and we saw already explicitly that in the random work problem there is no stationary distribution because j ran from minus infinity to infinity but when you have finite boundaries you physically expect there would be a stationary distribution unless these boundaries are absorbing boundaries because the system to disappear and we will give examples of that so let me stop here today and take it up tomorrow.


For soldiers in support MOS's performing combat drills and clearing houses aren't their top priorities But they still need to be competent and capable to take the fight to the enemy if the situation demands That's where Staff Sergeant Jacob brooch comes in He's training headquarters company soldiers of the 508th military police battalion in a variety of tasks from calling in unexploded ordnance reports Commission unknown reacting to indirect fire It's not the kind of training that they do every day that doesn't make it any less important like the army always says you're a soldier first You never know when you could be deployed overseas and and be engaged in combat You've got to know how to handle yourself and take care of your battle buddies to your left and right For Staff Sergeant roach sharing his knowledge isn't just something he enjoys it can prove vital to helping soldiers face future challenges It kind of gives me an emphasis on what I really like about being an NCO is doing the fact of Teaching and having somebody pick up the information I have some of this information that these soldiers are known in a day Is going to save their life at some point in time and if they can pick up that information and teach their soldiers and we can all come Home, that's what I want as long as there are soldiers in the army There will be training as long as there are NCOs like Staff Sergeant roach There will be trained and capable soldiers for the fifth mobile public affairs detachment. I'm army sergeant Brian's Bradley


The next question is from Blower18. How can you know how good your muscle building genes are? Wrist, ankle, and neck measurements? And what would be good measurements as opposed to bad? Okay, there's so many. I've heard of this now, like how accurate. Okay, so there's, okay, so they did some, and I can't remember the site, but they did some calculations of what they believed to be some of the best natural bodybuilders of all time and what their top measurements were, and then they correlated them to their wrist, ankle, I think wrist and ankle measurement, or wrist, ankle, and wrist, or something like that. And then they said, okay, this is the, based off of these people, this would be your upper genetic limit to how much muscle you could build. Now, here's why that's super general. There's so many factors that go into your ability to build muscle. For example, I'll give you one example, right? So one might say your testosterone level might play a role in how much muscle you can build. Well, they just- Might play a role? Well, they just did a study, that's why I said that. It does play a role, but here's why it's not that easy, okay? They just did a study that showed that testosterone levels didn't play that big of a role in how much muscle two groups of men built. What played a bigger role was androgen receptor density. The androgen receptors are what testosterone attached to. So in other words, if you have 600, if your testosterone measures at 600, but you have incredible androgen density. You've got nowhere to park on. Well, no, you have great androgen density, and someone else has 900 testosterone, but their androgen density is terrible. The 600 might actually be more impactful on muscle building. So there's hormone levels, there's androgen density, there's muscle fiber breakdown and density. There's myostatin, myostatin's a thing that we learned about over the last 10 years that controls muscle, and you turn that switch off and the body just builds tons of muscle. Muscle, belly length, and there's so many factors. It's very, I mean, could I look at someone just without working out and say that they probably can build with it? Yeah, somewhat, but sometimes I can't. I've known people who you'd look at and you'd think, oh, that's an ectomorph. I've known this in gyms. And then they work out and they just build muscle so easily. You're like, whoa, I wouldn't believe that. I just feel like this is always the case with the fitness industry is trying to catalog all of this and try and simplify everything. So you could basically, you could have a general standard. So where do I fit? And then that way you can get marketed to and like kind of shuttled into products or different type of training methods or nutrition. And they've done this with somatotypes and they've done kind of generalizations that people sort of identify and relate with. And so it's like, you know, something that kind of seems like it's logical. But again, these are so generalized that there's no way you can be like that accurate when you're predicting these. Well, there's so many variables, right? There's so many variables with that.  And the same is true on the other end, right? So my clients that had really small wrists, really small ankles, tend to have a harder time building muscle, but had an easier time burning fat.  There's many other variables that trump that, like your testosterone talk, your discipline, how about your behaviors and discipline too? How about somebody who doesn't have as much potential to build muscle, so they had to build more work ethic and discipline around nutrition. And because of that, they have a better lifestyle and habits and now see more results.  Yeah, and then you also have the question about measurements, what are good measurements?  Like a really lean 16 inch arm on a guy and natural, right? Is impressive to most people. Most people, if you saw a man with a lean muscular 16 inch arm, that would look more impressive than a guy with an 18 inch arm whose body fat is 18% body fat, right? It just doesn't look as good. So that's one of those things as well. Now I can answer and say, what would be considered like really muscular lean for most, and this is just from my experience of reading, for years and years about lifters and this and that. For men, if you're natural and you get your arms up to 17 or 18 inches, that's a lean, relatively lean.  That's a very big arm, natural. The 20 inchers that usually comes from super genetics and anabolic steroids. But again, I mean, it's so different from person to person and getting lean, I've done this. I've lost 15 pounds, worked out and everybody comes up to me and says, oh my gosh, how did you gain so much muscle?  Well, exactly. Each pose, the pros and cons, right? So each side has, like if you're, if you have a bigger bone, you may, your arms may naturally look bigger or put on muscle easier. But like, so I mean, my wrist and ankles are like a 13 year old girl. So I have like these tiny little petite fricking wrists and their dainty ankles, right? Now the benefit of that though, is like all the years of building muscle and working towards that. And then when I get on physique, when I was competing, man, it looked way more pronounced. I have this tiny little waist because that's my bone structure. I have a very small waist, I have tiny wrist. So the muscle that I did put on, it looks more pronounced. It's exaggerated. Yeah, it's more exaggerated than the guy that had the boxier square waist and the thicker wrist and the thick, he may even have more muscle, but when you look at it and we present it on stage, I look better for those reasons. So, you know, they all have, they all have their pros and cons. I think getting hung up on, you know, is it easier for me or harder for me or is it better to have this or that? Yeah, you know. You know, the old, there was an old body, but this is like from back in the day, I'd say in the 19, this is probably the 1930s, there was a standard for balance that they used. And they used to say that your arm, and they actually used to do this to see if their body was balanced.   You have a balanced physique, kind of interesting. Yeah.


Something tells me that Elon Musk's new Twitter blue program isn't going to win back the advertisers that fled the platform. So for those of you who don't know, anyone can now become verified in the event they pay $8 to Twitter. And I don't think that this is going to bode well for brands whose number one priority is brand safety. Let me show you what I mean by that. A verified Nintendo of America account tweeted this image of Mario giving the middle finger, and this image remained up for hours before it was taken down. Oh, no. Now, Elon Musk already knows, based on conversations that advertisers have claimed that they had with him, that brand safety is the number one priority of advertisers. So now if anyone can become a parody account of a major brand and gains lots of lots of traction, it's going to be kind of a disaster for advertisers. They're not going to want their brand associated with that hellscape. And I've got to say, the parodies have run wild on Twitter, and it is absolutely hilarious. TMZ reports Twitter paid verified check causes frenzy after fake LeBron trade tweet. And the tweet in question is a verified LeBron James account saying, I am officially requesting a trade. Thank you, Lakers Nation, for all the support through the years on to bigger and better things. Now, TMZ is probably overstating the frenzy that this caused because they cited no examples. But I've got to say, you know, even with that being said, if Elon Musk's true goal was to cleanse the site of bots, the opposite has happened with the rollout of the new Twitter Blue program. Because if you open up the door to anyone paying $8 for a verification, there's going to be some that think the laughs are worth the $8 alone. So here's some examples of very high profile verified accounts gaining lots of traction. So a verified Ben Shapiro account tweeted, Matt Walsh won't stop calling me and talking about genitalia.   George W. Bush tweeted, I miss killing Iraqis and a verified Tony Blair responded saying, same to be honest. Now, if you look at the header of this George Bush account, it reads, So what if I did 9 11? Beautiful. You love to see it. Also, Jesus Christ is now on the platform. So why pray when you can just tweet directly at our Holy Lord and the Savior? So that's convenient. You've got a verified Dave Chappelle tweeting out support for trans rights, a verified OJ Simpson confessing to murder. And you've got different versions of Pope Francis conversing with dead historical figures tweeting about popping champagne and whatnot. It's just hilarious. But it gets even more absurd. So a verified Ben Shapiro tweeted, I have always wondered what a woman's body feels like and looks like in real life without clothes. That would be so cool. Now a verified Ted Cruz responded to the verified Ben Shapiro saying, The first time I entered my human wife, I said groaning into her ear. This is exactly how mother said it would feel. Now Ben Shapiro responded to that saying, OMG, you got me kind of horny right now, Mr. Cruz, to which Ted responds saying, Have you ever tasted the entrails of a man Ben? There is no carnal pleasure as delectable. Ben responds by saying, Ted stop, they aren't supposed to know about us and then share this cursed image of a human with I guess a dear body. I don't really know what I'm looking at, but it's it's terrifying. So this Elon Musk is what happens when you open up verification to anyone who's willing to pay $8 mass chaos ensues, and the bots increase in their numbers. Now I want to share a one minute 40 second ish audio clip of Elon Musk during a Q&A Twitter space events. And he is asked about the insanity that ensued following the rollout of Twitter blue.  It's almost funny. So let's listen at checkmark used to stand for something. Now, anyone that pays $8 a month can get the checkmark. What's the what's the process by which accounts are verified in in this new world? Well, it is a I mean, someone has to have a phone and a credit card and $8 a month. So it that that's the bar. However, we will actively suspend accounts engaged in deception or trickery of any kind. So it is a leveling of the playing field here. The it will be less special, obviously to have a checkmark. But I think this is a good thing. So if somebody if it likes it, if there's impersonation, trickery, deception, we will actively be suspending accounts. So I think it's gonna be a good world.  I think we do. You know. So I actually just don't I don't like the loads and peasants situation where some people have blue checkmarks and and some don't and this is, you know, at least in the United States, we fought a war to get get rid of that stuff. So anyway, this is just thought post-opically how I feel and maybe this is a dumb decision, but we'll see.  Because you know, one person one vote, how can anyone still claim that this man is a genius?   And I love how he referred to what Twitter used to be as a lords and peasant system. And so now by making the peasants pay $8 per month for something that notable people get for free. Apparently that's evening out the playing field. That doesn't make sense because look, I was verified on Twitter before Twitter blue rolled out and he hinted that he'll be taking away the verification of people who were previously verified. So that's fine. I'm not paying. But I'm getting Twitter verification for free and other people have to pay $8. That's just inherently unfair.  But the way that you even the playing field by making $8 mandatory for verification is supposedly more democratic. He just the ways that he thinks aloud about these ideas.  And he's also a really terrible boss. So in his first company wide email, he paints a very grim picture for the platform saying the economic picture ahead is dire and adding without significant subscription revenue, there was a good chance Twitter will not survive the upcoming economic downturn. We need roughly half of our revenue to be subscription. Yeah, good luck with that. Now he goes on to announce an end to remote work saying starting tomorrow, Thursday, everyone is required to be in the office for a minimum of 40 hours per week. So it seems like Elon Musk is a very great boss. I'm being sarcastic, of course, he is emailing them with terrible news saying the company might not survive. And he's saying, Oh, also, if you're working remotely, you've got to come in now. That's done. I don't understand why bosses impose this on their employees if they're just as productive working remotely. But I mean, it's Elon Musk. So you can't begin to fathom what's going on in his mind is probably just emptiness and tumbleweeds.  And I think that these past couple of weeks should confirm this for anyone who was still in doubt. Now I do want to share this company wide email circulated by Twitter legal, because I think that the first two paragraphs are particularly damning for Elon Musk. This was shared by verge editor, Alex Heath. They write over the last two weeks, Elon has shown that he cares only about recouping the losses he's incurring as a result of failing to get out of his binding obligation to buy Twitter. He chose to enter into that agreement. Elon has shown that his only priority with Twitter users is how to monetize them. I do not believe he cares about the human rights activists, the dissidents, our users in unmonetizable regions, and all the other users who have made Twitter the global town square that you all have spent so long building and we all love. And I think that that's absolutely correct. Now there were also resignations from Twitter from pretty prominent individuals. And it just it's there's so many reports about the sheer chaos. I've seen one person I can't remember who described it as the Trump White House where it's chaos, insanity. There's high stress. People are leaving and changes are being made and then reversed. And it's just really an unstable environment, especially if you work there. But in terms of him trying to get 50% of users to convert to paid $8 per month Twitter blue users, that's just delusional. That's not going to happen. So if he doesn't find a business model to make Twitter profitable, then he's in danger. And as he continues to scramble, it's going to get worse and more chaotic. And I just feel really bad for the people that work at Twitter. But I've got to say I am enjoying at least the effect that he's having on Twitter because you have everyone dunking on him all in unison. And you have this influx of parody accounts that have taken over Twitter. And the platform has just become more enjoyable. So even if it's become more enjoyable and it may not be long for this world, I'm going to enjoy it while it lasts because I honestly haven't had this much fun on Twitter in a while. He even considered or at least floated it openly, making it mandatory that you pay $8 per month to use Twitter. And I guarantee you the website will not survive if it does that. Even if YouTube did something like that with billions of active users per month, they will not survive. So you can't just make something that was previously free, a pay for service. You can't put it behind a pay wall and expect people to still stay, but he's willing to try anything if it makes him a profit. Because again, as Twitter legal points it out, he's mad that he was forced to buy Twitter when he got himself into this mess and now it's profit or the whole ship is going to go down. It's sad but also funny in a variety of ways. But it's sad for the employees. I really feel bad for what they're going through behind the scenes.


Welcome to NTN Nightly. I am Jassi Léonce. This edition's top story is St Lucia records two new cases of COVID-19. The public is urged to adhere to infection prevention measures. Prime Minister Hon. Alan Chassney lobbies the World Bank for better access to finance for small states. And the Ministry of Equity and Social Justice joins forces for the comfort of an elderly denry resident. St Lucia has recorded two new cases of COVID-19 in as many days. Wednesday, October 21, 2020, Case 38 was confirmed. The individual is a 53-year-old female from Grosé-les. On Tuesday evening, 20th October, Case 37 was confirmed. The individual is a 43-year-old male from Grosé-les. During the contact tracing process, he was identified as linked to cases 33 and 34 and was placed in quarantine. He is now isolated for care at the Respiratory Hospital. The latest case, the 53-year-old female of Grosé-les, was also identified during the contact tracing process as linked to cases 33, 34 and 37. She has been in quarantine and is now isolated for care at the Respiratory Hospital. Dr. Sharon Belmar George is the Chief Medical Officer. The new cases for this week have all been identified for the contact tracing process, and that tracing process continues this week. All efforts are being made by the public health team to rapidly respond to contain further spread of cases. We anticipate new cases as we continue the process to identify, test and isolate further contacts. As we proceed with the necessary public health interventions, a serious appeal is made to the public to cooperate with our health officers and to practice daily the behaviors which can protect your health and safety. We remind every individual that 80% of persons who have the virus experience mild symptoms. As such, it is important that we all remain vigilant and respond promptly to any symptoms of concern to avoid further spread of the virus. The Ministry of Health, we take the opportunity to remind the public to adhere to the infection prevention control measures and show that a mask is used always when going out in public. Maintain a safe physical distance from others when out as well. Wash and sanitize your hands often throughout the day. If experiencing flu-like symptoms, seek medical care immediately at the closest respiratory clinic. We also want to remind the business places to ensure that all of the protocols that are in place to keep your patrons healthy are sustained. That was Dr. Sharon Belmar George. Now on the regional front, the Caribbean Public Health Agency, CARFA, is preparing to officially launch two important initiatives to protect the region's tourism sector and safeguard the health and safety of residents and visitors during the pandemic. Dr. Joyce and John, CARFA's Executive Director, explained that the new tools which will debut on November 5, 2020 are part and parcel of CARFA's Travelers Health Program, which provides an early monitoring and response system to public health issues that impact the tourism sector. The Caribbean Travelers Health Assurance Stamp for Healthier Safer Tourism is a measurable and verifiable recognition award for tourism entities and destinations that are implementing the recommended proactive COVID-19 health monitoring and safety measures. The Caribbean Travelers Health Mobile app is a unique multi-faceted health information repository designed for travelers and health and tourism stakeholders. It provides travel health information by each Caribbean destination. Prime Minister and Minister for Finance, Economic Growth, Job Creation, External Affairs and the Public Service Honourable Alan Chastney is currently taking part in the annual meetings of the International Monetary Fund IMF and the Board of Governors of the World Bank Group. The annual meetings held in October bring together central bankers, ministers of finance and development, private sector executives, representatives from civil society organizations and academics to discuss issues of global concern, including the world economic outlook, poverty eradication, economic development and aid effectiveness. Joining Prime Minister Chastney at the meetings is the Acting Permanent Secretary in the Department of Finance Esther Rigaburt, officials of the Department of Finance and the Department of Economic Development. This year's meetings will be held in a virtual format and feature seminars, regional briefings, press conferences and other events focused on the impact of COVID-19 on the global outlook, the pathway to recovery and the developments in the international financial system. And meanwhile, the Governors meeting with the managing directors of both the IMF and the World Bank will be held. Prime Minister Chastney will participate in the virtual round table. The discussion is on CID's access to finance under the theme of identifying solutions for resilient COVID-19 recovery. It is a critical meeting for small states as they face dire economic fallout from the pandemic. Lisa Joseph has a comprehensive look at the contending issues. Prime Minister Hon. Alan Chastney has long been an advocate for better lending policies to be applied to small island developing states by international financial institutions. As the COVID-19 pandemic takes hold of economies worldwide, small states like St. Usha are finding it increasingly difficult to avoid economic collapse. Prime Minister Chastney describes it as war on two fronts, health and economics. According to the World Bank's semi-annual report titled The Costs of Staying Healthy, the economies of the region are suffering from lower foreign demand, increased economic uncertainty, a collapse of tourism and the consequences of months under lockdown to try to contain the spread of the disease. With the pandemic expected to continue for an extended period, healthcare systems should consider reforms to improve effectiveness and reduce the cost born by governments and individuals. In addition, governments will need to find paths back to fiscal consolidation after this necessary period of high spending on economic stimulus and emergency social transfers. Despite this recognition, Caribbean countries who may have been looking toward debt forgiveness as a means of economic relief have been dealt a devastating blow. World Bank chief economist for Latin America and the Caribbean, Martin Rama, says countries in the Caribbean should not count on getting any debt relief and should therefore look seriously at other alternatives of effectively managing and growing their economies. Barbados' prime minister, Hon. Mia Motley, has been lobbying for debt forgiveness for Caribbean countries that are on the brink due to the pandemic. Barbados' debt-to-GDP ratio had been reduced in June this year to 124.7% from 175%, making the country the fourth most indebted nation behind Japan, Greece and Sudan. But Rama contends that many of the Caribbean countries are among the richest in the region. They tended not to fall within the low-income bracket and tended not to have very high debt as other economies do, so it would be more difficult to make a case for debt forgiveness or debt reduction. Prime Minister Shasne disagrees that to use per capita GDP to use debt per GDP is unreasonable because in average it's fine, but in absolute terms, meaning if you multiply that ratio by the population, it's an insignificant amount of money. And we've been arguing to use what we call a vulnerability index, and sadly that vulnerability index was established in 1989 by the Commonwealth Secretariat. So this was really just, I mean, we're certainly not going to take this lying down, but it just tells you in the midst of all of these problems that a statement like that can come out and take anything for granted. And you would think that the evidence speaks for itself, but to change that global architecture, economic architecture is difficult. At the same time, Caribbean countries have been told by the World Bank to contain cost from COVID-19 while awaiting a vaccine. The advice is for countries to spend in the first instance on health programs, on social programs, a critical step for countries is to reopen schools. Looking longer term, the World Bank says infrastructure is a very important part of a country's growth. You know, the managing director, Kristalina, came out early and said government should spend as much as they possibly can and keep the receipts. Then we're told that invest in capital investment projects because getting roads going and construction going helps now augment the social stabilization program. So instead of just literally handing persons income support, it's actually putting them back to work. And so at the end of the day, there's actually some physical investment into the country as well. So it's a win-win situation.  So we're all, most of the small island where the struggle remains building confidence in global travel. St. Lucia's prime minister has been relentless in his lobby for pre-testing as a safe route to rebuild in the travel sector. IATA, American, United, all over the world, people are now embracing that idea and I'm very proud that idea came from St. Lucia, has been embraced by our colleagues in the Caribbean and we've been out there agitating to make that happen. We've been yielding further results with the UK government last week announcing the establishment of a task force to look at the introduction of testing at Heathrow Airport. From the Government Information Service, Lisa Joseph reporting. Youth workers attached to the ministry of youth development and sports have presented their quarterly reports. Ryan O'Brien has the details. Youth workers attached to the ministry of youth development and sports delivered their latest reports to the ministry on Thursday, October 15, 2020 covering the previous quarter of their activities. Director of Youth Mary Wilfred commanded the youth workers for their efforts in the field to date and urged them to continue striving for excellence. At every quarter we do a reporting session so that youth workers can come in to account for the work that they're doing and for us to shape best practices for us to encourage one another for us to learn lessons that we don't have to replicate and so this is a usual meeting for us in the youth department. Also present was permanent secretary in the ministry of youth development and sports Caroline Eugene. I am so much looking forward to hearing from you all the good stuff I know that you are doing because constantly I speak with Miss Mary and she always tells me of all the good work that is being done with every one of you around the island. This morning I join you to listen to what you've done and I'm sure more or less you might highlight some of the challenges that you encounter listening to the challenges might put me and the rest of the team in a better position to see how we can alleviate some of the problems that you encounter as you're in the field. The ministry of youth development and sports made a fundamental shift to provide more in-depth focus on youth work in January 2017 youth work forces the ability to critically evaluate one's own individual situation in relation to others and society by applying a variety of plan practical measures aimed at ensuring the emotional, social, ethical intellectual and physical development of young people in a caring and secure environment. So far 20 youth workers are enrolled in the program from the Ministry of Youth Development and Sports. I'm Ryan O'Brien. The Ministry of Equity, Social Justice, Local Government and Empowerment through the Department of Human Services has assisted with the construction of a house for an elderly Dennery resident Gilton Joseph contractor Collins Lynch volunteered to build the structure. His company Triple L provided the materials and labour. Projects like that we people need to get involved with because just going around the community have so many people who need that help and I understand what is happening and I'm going to do my best once I can I will. In the past I probably do maybe 15 or 20 of these projects in the last 10 years around the valley Dennery already. I'm hoping I can get the strength and help from God to continue to do this. On behalf of the Ministry of Equity, particularly the Department of Human Services elder care unit we would like to say thank you for doing this beautiful project for Mr Gilton we're very grateful we happy he's comfortable and we're actually saving one older person to be comfortable for the rest of the years. So we appreciate you we appreciate your guys your company and we thank you very much. I would like to say thank you to Mr Lynch for the great work he did because Mr Joseph has been in a deplorable condition and he came on board he assisted us and we are thankful for what he did. Culture Minister Senator Fortuna Belrose says the scaled down Creole Heritage Month celebration this year is in keeping with the true spirit of the tradition as she appealed for adherence to the protocols during the observance the minister says keeping Juniquial celebrations within the family unit is consistent with the heritage promotion details in this report. The pandemic has impacted the way cultures all over the world observe customs that draw mass crowds disconcerting yet necessary postponements and cancellations of traditional events are being made to mitigate COVID-19 transmission risks. Fortunately organizers of Creole Heritage Month here in St. Lucia have found a way to observe the 2020 celebrations in adherence to national protocols by targeting the cornerstone of society the family unit. Juniquial Lacainu is this year's event theme encouraging residents in St. Lucia to celebrate with their relatives. Minister in the Ministry of Culture and Creative Industries Senator Fortuna Belrose says this approach is not only COVID conscious but is fundamental to Creole Heritage promotion. If you know the history of Juniquial when it was initially designed and thought of by the Fokrisud Centre, what they planned was always to reach the point where families embrace this and the true spirit of community came through and I think what we're seeing this year with the advent of COVID and the build-up over the years is a design to make that happen. So this year hopefully we will see lots of families gathering and participating but keeping it within families. Officials are not opposed to a family from multiple households celebrating together once they observe the protocols. Since the island registered an increase in local cases of COVID-19, the protocols have been reviewed. Mass crowd events have been reduced from 500 to 100 persons. I expect families to invite each other to come to their homes but I think we must be mindful of the protocols with respect to the COVID. We encourage people to ensure that they have below 100 persons in their activities. That is the rule. Our police will also be very vigilant on that day. We've been told in terms of ensuring that there are no mass gatherings beyond 100 people. But the focus, like we say, we want you to encourage and to push is that we celebrate within our community, within our families. So it is not unusual for a family to move from souffle to viewfort to dennery to want to celebrate with their family but we want them to keep it within the family and maintain the numbers. Complimenting the family size, the Juniquial celebrations, Creole Heritage Month organizers are now also rolling out a slate of virtual events and activities to promote Creole Heritage in St. Lucia. Up next we have Primus Hutchinson with the NTN Nouvelle Quial. If you are in receipt of an abnormally high bill it is highly possible that you have a leak. That leak may not always be visible. Before you contact Wasco conduct a do-it-yourself test. 1. Record your meter reading. 2. Do not use water for 30 minutes to 1 hour. 3. Take another meter reading. If the reading changes you have a leak. Contact a plumber to identify and fix the leak at the earliest. A message brought to you by the Water and Sewage Company Incorporated, Wasco. Welcome back. Time now for the NTN Nouvelle Quial with Primus Hutchinson. Thank you so much Jesse. Thank you Madam Department of University of St. Lucia. For information on the government of St. Lucia G.I.S. and the National Television of the NTN as well as the Nouvelle Quial as well as the Prime Minister Hutchinson. For the Ministry of Finance of St. Lucia we have Alain Chastney. We have participated in a discussion on the national finance agency which is taking place every year. The GoaGueck Bank also has a description. A description which affects as it says every year in October to bring the GoaBank Ministry of Finance Development, Executive Secretary of the Executive Board of the Civil Organization with the academic to discuss various issues that affect the land. Among them is the economic situation to facilitate economic development in order to assist those in need. The Prime Minister has participated in the discussion and the discussion with the IMF to discuss the different solutions of the resilience of Corona. Among the GoaGueck Ministry of Finance Secretary of Finance of St. Braffit, Finance and Economic Development the GoaGueck discussion which is made by visible communication on the internet. The GoaGueck also has a discussion with the IMF to discuss how to address the Corona situation in order to help the development of the international financial system. On October 20th, this year, COVID-19 was confirmed. Individuals from the Secretary of the GoaGueck have found an exercise in order to help the development of the Corona situation in order to help the development of the Corona situation. Both the GoaGueck and the GoaGueck have a discussion with the Ministry of Finance and Finance and Finance The work that is supposed to be done is to keep it in contact with the Corona Resort, so that we can keep it in contact with the TRT-4. Because it also has to be tested for quarantine. The Ministry of Health has opened a response to the sale. We have to continue to do so. It's not possible to get sick because of the disease. We have to say thank you to all the people who have come to buy and to select people who have come to buy and to continue to buy the sale. The Ministry of Health has also taken the opportunity to make the public change, to obey all these protocols, to prevent and control the disease. We have to always serve ourselves and the public, follow these rules that are in place of business, to keep distance from people who buy and sell in place of business. Always wash your hands, sanitize your hands, so that you don't have to go to the doctor immediately. You have to go to the hospital, to take a shower, take a nap, and live. That's the way it is. And then, your company has made a construction. The owner of the house, Mr. Gilton Joseph, who is working in the village, is in a condition that is very important to you. But the Chief of the Triple L Construction Limited, Collins Lynch, and the representative, Edmund Estefan, and the family of the organization called SSDF, and the Department of Human Services, collaborated to make this project a success. According to Mr. Lynch, your activities, which you have always done, have already built up to 15 or 20 projects like this. That's how it is. It's a pleasure to have you here. Mr. Declarecki, it's a pleasure to be able to complete a project like this, and to make an appeal to other people who are capable of this, to follow the same direction as you. Mr. Lynch, it's a pleasure to have you here, who has a very comfortable life, and who has a lot of knowledge, and a lot of knowledge, and a lot of necessities, which is very important to you. And then, Mr. Gilton Joseph, Mrs. Catherine James, who is also working in the village, is very happy to have you here. By the way, this morning, I gave this to the village. I am very happy to be here. I am very happy to be here with my employees. Mr. Lynch, I am very happy to have you here. I am very happy to have you here. By the way, I gave you a lot of help. I really do have lots of work here. I have a lot of friends here. Everything here is very well paid. If there was any help, I would tell them Well that brings us to the end of NTN Nightly. Join us next time at 7pm with a repeat at 7am. You can also catch up with us anytime on the St. Lucia Government Facebook page or our YouTube channel. I'm Jesse Leon signing off for now, but do stay tuned for more NTN programming. Goodbye.


OK, so let's try this one. It says, supply the missing components and show the reaction mechanism of these steps of the reaction. So what kind of reaction is happening in the first reaction do you guys think? You want to say, are you a substitution reaction? What kind of substitution reaction, like what number? Is it an SM2 or SM1? It could be an SM1 reaction. What would be the, if it was an SM1 reaction, what would the, what would be over the ReA genera? Might be easier for you guys if you thought about it as an SM2 reaction. What would it be if it was an SM2 reaction? What would be right there? How do we do the last one? Yeah, so what? Well, sodium and then what? Na, what would the rest be? S-H. And then, will we have to put something down here? What would we put? DMF. DMF, why would we put that? Solve it. What kind of solver? Polar. Protein. Polar A-protein solvent, OK? Those are the types of solvents we need for SN2 reaction. So, what about this step? What's happening? It's being deprotonated. Being deprotonated. So what do we need to have here? A hyodorant base. A base, yeah. So a good base would be what? Sodium hydroxide. Sodium hydroxide. Would that deprotonate like that? Yeah. OK, so should we go over the mechanism of this now? OK, so this step, right, what are we going to get when we put this into DMF? I get it? The sodium is going to be a spectator ion. And then the Cl, the chlorine would be a leaving group. Very good. And then we have the same thing, replacing substance. So this is your nucleophile, electrophile. We're going to have the SN2 reaction occur, like that. So when we do that, we get this plus what? The leaving, right? And then when we react NaOH with this acid here, what happens? It would deprotonate it. Remember the same thing, any spectator ion deprotonation like that? H2O. So notice, in these reaction sequences, oftentimes they only show the organic product, OK? So don't think that, just because they don't show the inorganic, that it's not showing you everything. Any questions about this one?