Yep, all right. Welcome back to operating systems. Yeah, the exam content is exactly the same for 353 so Here is the first session for final exam review So I told Satow to start grading lab 6 to so if you have finished it already Then you can get your grade for it and you don't have to worry about it So you can know your grade ahead of time. So he is periodically marking it. So pay attention to announcements so Any questions? We're here for review anything in particular. You want me to go over otherwise. We'll just randomly go over exams and you can stop me Yeah all right So let's randomly start at Let's see So here is the last semester three five three exam three five three exactly the same course As your one it just lasted for a week longer. So Here is the final exam. So let's breeze through it and see what we want to do So looking at the topics here. Is there any topic we're particularly interested in? Locking we all like locking the hardest part. All right votes for locking all right So locking consider the following code snippet So we can see that so we have three threads Thread one that grabs mutex Mutex one and then mutex two and then thread two that grabs mutex two the mutex three and then lab or Not lab thread three that grabs mutex three then mutex one So the question says assume we only have three threads. We create three independent mutexes. So all mutex One mutex two mutex three are all initialized for us and each thread executes its own different function above So thread one executes thread one thread two executes thread two thread three executes thread three So any questions with what's given there? So Let's see what the first question is Identify and explain the deadlock condition that can occur in this program So I was nice and told you that it there is a deadlock So can anyone explain what a deadlock condition is here? So each thread just grabs The first mutex and then we get context switched. So in that case Let's see if I can write better thread one would lock M1 Thread two would lock M2 and then thread three would lock M3 whoops not M2 and three Now in this case if every thread just grabbed it the first lock Well can thread one make any progress right now? No, because thread one it's going to try to acquire Mutex two which is currently held by thread two. So it can't make any progress Thread two is going to acquire mutex three Which is currently held by thread three so it can't make any progress and then thread three is going to acquire Mutex or try to acquire mutex one which it can't because it's held by thread one So no threads can make progress in this scenario. Therefore. We have a deadlock Questions comments concerns about that seems like a deadlock to me. All right, so Four points to explain that so that is the correct explanation Six points Propose a solution to avoid deadlock in this code modify the code or describe your proposed solution and Briefly explain how it addresses the identified deadlock condition. So how would we fix this deadlock? Yep in the second statement for all of them So just try What else do we need to do in the try Yeah, try in a while and in the while loop. We would have to do that unlock yield lock thing, right? Yeah, so in this case if we try to get M2 then we would if we fail we would unlock M1 Yield or something? Whoops, I don't know I Can write C not English So lock and one and then we could have that a while loop and We could have that in every thread so we get rid of anyone remember what that condition for deadlocking is called Holden weight. Yes, so that eliminates hold and weight because While I'm holding a mutex if I don't get it I give up the one I was holding So I do not have that deadlock condition. So that is one Is there another solution to this that only requires me to swap two lines around? Yeah Yeah, just swap these two like that All right, if I swap those two lines so instead of locking Three and then locking one. What if instead I locked M1 and then locked M3 Do I have a deadlock in that case? No, why do I not have a deadlock in that case? Sorry Yeah thread now thread one got the M1 lock then thread three wouldn't be able to acquire Lock three without also holding lock one So remember what that's called? That we've broken this case Sorry, so Thread one whoops, let's see if we can come up with the name for this. So thread one in the deadlock condition was waiting on thread Two then thread two was waiting on thread three and then thread three was waiting on thread one Can we come up with a clever name for that not a race condition? circular weight Circular weight was another condition for deadlocking where I don't acquire the threads in the same order if I acquire the threads in the same order in All of my threads then I have a set order and I do not have a deadlock because I will not have a circular weight So that is also a valid answer is just to always acquire them in the same order So you could get six points real quick if you just swap two lines and you explained it All right, see locking is not that bad. That was like what? Okay, it looks like 18 minutes. Okay, maybe it's not that bad All right. Yep. Yep full marks for the tri ones. Just a lot more writing, but it's fine still valid solution Okay, oh, do we want to do center for us? Okay, so let's see if I can make this Okay, I'll use you to cover up some answers Okay, that didn't work. All right, that's scuffed All right, so Says consider that looks okay, whatever so it says consider the following code we have Define that says total threads is eight We have a center for that we can initialize and then a run We have this initialize everything function and the comment says we want only thread zero to execute this and That green line was not there originally But you would have to have an if condition there. So I'll just give it to you and then here it says we want all cores to Execute this initialized thread function only after initialize everything finishes So a question says assume we have n threads all set up to start executing run and each thread Receives a unique thread ID in addition that initialized center for Function executes before any threads get created. So it's safe to initialize the center for Then the question asks using that single center for Sam Enforce the synchronization constraint constraint specified in the comments You may add code directly above and see or pseudo code be sure to give the center for an initial value Try to make a solution that supports any number of threads assume that thread zero already always exists and for a maximum of seven points you can use that total threads in your solution and Assume it's the number of threads executing the run function So using a center for how would I enforce those conditions? So I will give you a few minutes to think about that Okay, where should I start? Yeah, you could start with the initial value so What do you want the initial value to be? guess one So sometimes thinking about the initial value is Usually the second step first step. It's usually easier to figure out where to put the weight So in this case what should be waiting? Yeah, the other threads that are not zero. So if I have this is if condition and then let's say I have an Else so I could put the same weight in the else and Now I should probably think about then initial value. So if I want to prevent Any thread that is not thread zero from executing then what should the initial value be? Zero. Yeah, zero. So No Sorry So the initial value is zero actually can I just erase it? Nope, okay So the initial value is zero. So now in this case if I am not thread Zero then I wait in this case. What's going to happen? So thread zero will execute initialize everything and then Break out of its if and then do initialize thread and then all the other threads are going to be waiting So next I should probably place my post. Where should I place a post? Yeah Yeah, after I initialize everything right here. I can do a SEM Post right. Is that all I need to do? Yeah post also here Two threads can wait on a SEM4 So SEM4s are remember SEM4s are atomic. So it'll decrement only if it can So should be okay, right? So here first we can argue What happens if we don't have this post? So if I have eight threads say well all let's say all Thread one thread two all the way up to thread seven We'll be sitting here at the weight and the only thread that could execute is thread One or thread zero It would execute initialize everything and then post so my center for value would change from a zero to a one and then One of those threads will be able to successfully pass the weight because it can decrement it now from a One to a zero and then if I just left it as it is right now Only thread zero and then one random thread can go ahead and execute this initialized thread the other Six threads will be stuck So that's why I had to add a SEM post here So if I add a SEM post here then what will happen is as soon as one thread of Thread one all the way to seven makes it past the weight it will post to increment it back from a zero to a one and then Another thread will wake up and make it past the weight and then it will post then another one can execute And then it will post another one then another one. It's like that DJ Khaled song. Is that the one? Another one. Yeah, all right, so if I Didn't want to put a post there if that was confusing What is something else I could have done that would have made? You know the seven threads make it through the weight So what about if I just did like Had this post But instead it was like for one to numb threads So thread zero after it's done just post seven times That would have also worked But that solution well that was this one that was for a maximum of seven points So you got minus two if you wanted to use that so that essentially Doesn't work with any number of threads. You have to essentially Anytime you update the number of threads you have to recompile everything The first solution with just a post after it doesn't matter how many threads will wake them all up All right any questions about that one All right Part two. All right So consider the following solution without center fours So we have a run Then we have if thread ID is zero Initialize everything otherwise instead of the center for anything. We just have a good old-fashioned yield So now the question says assume that we have cooperative user threads aka like lab for for you is This a valid solution that Actually adheres to those conditions Explain why or why not? Yeah Yeah, we want to initialize everything first before an initialized thread comes in So yeah, the only condition is here is that initialize everything should execute before any thread runs initialized thread So assuming this is like your lab four if you yield what happens goes to the next one Yeah, it goes to the next one. There's like a FIFO queue you had right so it just goes to the back so Assuming you had a FIFO queue with this work so initially all threads are somewhere in the queue in any order and then You get a turn and then if you get to turn you just yield so you go the back of the line So eventually as long as you go to the back of the line Eventually thread zero will come up before any other thread Wakes up again and in that case thread zero would call initialize everything and then the others would call Initialized thread after they wake up Or after they get recued again. Yep. So whenever they get recued, they'll resume back from the yield, right? So the contacts which back and they'll resume from the yield and then they'll just Fault oops, and then they'll just fall through and then execute initialized thread. So It seems like a valid solution, right? If you had lab four so assuming like this question says assuming you have a FIFO queue and It's essentially your lab four So for you it's lab four. It was lab three before So Everyone would give up their turn No other thread would get recued ahead of thread zero and then initialize everything would run first Next part says assume we have cooperative Kernel threads now running on multiple cores. Does the solution work now? So let's yeah, so if it their kernel threads they could run in parallel and It could even be the situation where Thread yield doesn't even do anything. So say you had let's just start off with core zero core one and core two Say this was executing thread zero. This was executing thread one. This was executing thread two Say you we were down to the atom time scale or something like that and core two executed and thread two executed so it would go to this yield and While since the kernel decides scheduling decisions Thread two could yield and it could be like oh well that core is not doing anything else anyways So just continue executing it Don't worry about it and then thread two would go ahead and then just call initialize thread and It would be broken and while they're running in parallel So you don't know what's going to happen and because their kernel threads they can be scheduled independently You don't know what the scheduling algorithm is So even if it couldn't run in parallel that this would still not be a solution because a real kernel can just ignore your yield It's just a suggestion. So it ultimately decides the scheduling so Question says no, this doesn't work since the kernel threads. They might also run in parallel So you can't ensure any kind of order All right any questions about that All right, what we want to do next So what are our choices? so Choices are one of those topics or one of those topics and we look at a different exam file systems All right, that is a good choice So file systems For the following questions assume your file system has a block size of 4096 Each pointer to a block is four bytes and i-nodes are a hundred and twenty-eight bytes each So first question says what is the minimum amount of space in bytes? You need in a file system like ext2 aka your lab six to store a hundred files Or sorry a thousand files assume that each file is 96 bytes in size Include the size of the i-nodes in your calculation You may skip the final calculation if you don't have a calculator. So each file needs an i-node. So each file Needs a hundred and twenty-eight bytes for an i-node and then even though a file only consumes 96 bytes it still gets an entire block, right? So since it gets an entire Tire block and only one block then it would need this many bytes per file So we need 128 plus 4096 which is what? 4224 Times a thousand files so Our final answer is that number that I'm not going to try and say So questions about the first part All right second part says for the previous question How many bytes are lost due to internal? Fragmentation you may say zero if that's the case You know 4096 minus 96 so that's per file and then times a thousand so that should be 4,000 times a thousand which would be four million Do-do-do-do-do All right, so questions about that one. Yep. Yep Yeah, full marks if you write down the right thing So for this next question Why might copying a directory containing a single Large file be faster than copying a directory with many small files Even if the total size of the small files is less than the size of the large file My inspiration behind this was well I was copying files on my computer and then I got to a bunch of small files And then you know the windows progress it just went and then oh wait The class should be able to explain this now. So I wrote a question So why would that be the case? It would still need them. Yeah, you still need to make a copy of the data like actual copying files But you're on the right track. So for a single large file. It's one. I knowed right and then All of its data would be in a bunch of IO blocks that are full essentially, right? They would all be full except for the last one So like if you have a single large file, it would probably look like, you know, I knowed And then that one I knowed if we just had its blocks and Didn't look at the structure. It would be pointing to like block zero all the way up to I don't know block What's large? Block one million. I don't know. Maybe that's too large. Let's say ten thousand block nine hundred ninety Block nine thousand nine hundred ninety nine So that's what a single large file would look like, right? so Block zero to block nine thousand nine hundred ninety eight would all be full and this one You know might have a little bit of internal fragmentation at the end, but It's total internal fragmentation is going to be negligible If there were a bunch of small files well for each small file It would be an I knowed To a block and this block Could only have I don't know like a few bytes in it. So like ten bytes hundred bytes whatever but The file system still has to read the entire block. It can't just read part of a block in so if we had a bunch of small files Say we had a lot of smart files. So say we had Wow, that's not a good brace So say we had ten thousand of these So if we had ten thousand of them, we have to read the same number of blocks as that large file but the contents of it this could only be a few bytes so This could be like ten bytes and I'd have to read the same number of blocks for way less data. I'm only copying ten bytes of block That's actually useful and for each of those. I also have to copy an I node so most of my copying is going to be copying I nodes and just accessing empty blocks all the time and usually when Windows shows you File copying process it only cares about the contents and the size of the I node outweighs the contents even And that doesn't even count. Yeah Yeah, so the I know it has a size on that knows what's valid, but whatever you're reading From a disk you can only read blocks at a time. It doesn't matter, right with the SSD Stuff you can only read blocks or pages at a time So even though that it only has a few bytes valid Given by the size you still have to read the whole thing in you wouldn't have to copy all of it They still have to read it in from disk So that is also why once you hit small files Performance goes down because it only keeps track of copying the contents Hey, the I nodes could be bigger than the contents and they're not even counted Yep So so the question is if it's a regular file it's super super small Can we have the same? Optimization as we had with the sim link where we store the contents like on the I node Yeah, so in that case the reason that optimization does not exist for regular files is because well remember they're also Mapped to virtual memory pages So they have to correspond to something if the contents were stored on the I node itself And you did like that n-map magic thing then suddenly If you tried to map its contents of the page that page would also contain like the whole I node and All the neighboring I nodes so then a process could just change I nodes which would not be good So even for regular files It does that so that it's on a page and it can map it to a page in memory and then Carry on from there Yes said optimization is only for sim links because you can't really access its contents like just the kernel reads it anyways, so it doesn't matter and Also sim links generally don't change and all sim links are generally smaller than 60 bytes anyways So that's why they do that optimization all right Oh, let's see so Next question assuming an I node has 12 direct blocks. Whoops and one indirect block What is the maximum file size that can be supported? You may skip the final calculation if you don't have a calculator so I will write the important things so The block size Was equal to 4096 Which is 2 to the 12? and then the pointer size Was equal to 4 bytes Or 2 to the 2 So if my I node has 12 direct blocks and one indirect blocks What is the maximum file size in kilobytes that could be supported? So how many blocks could I point to with an I node that just has 12 direct pointers and one indirect so Let's start off with first if I only had 12 direct pointers. How big could the file be? Yeah, 12 times the block size. So in this case, it would be 12 times They would be pointing to a block So 12 times the block size, which if we want to just keep it in kilobytes it would just be 12 times 4 or 48 kilobytes Okay, webbo if I just had a single indirect block, how big could the file be? So the first idea behind this is like with page tables. So it's like How many pointers Could I fit on an indirect block? 2 to the 12 or Sorry Yeah, so 2 to the 12 So it's block size divided by pointer sizes. How many pointers I could fit on a single block Which would be 2 to the 10, right the number of pointers per block So if I only have a single indirect block then I can point up to 2 or 2 to the 10 things so I could point to 12 plus that 2 to the 10 Which is equal to this is 1024 so in total I could point to 1036 blocks and if each of them is four kilobytes then That is the maximum size of the file In that case, it would be what is that and times four So that would be 4,144 Kilobytes All right, any questions about that one Yeah Each block is four kilobytes. So this is aka four kilobytes But if you just wrote it in bytes Probably fine Yeah, probably I think It was in bold. So I think it was like a minor deduction if it wasn't in kilobytes I forget Yeah, if you just did something like as long as it you knew what you were doing it So if you did like Even wrote 12 plus 2 to the 10 times 2 to the 12 All divided by 2 to the 10. That's fine So the multi-level page table this says just one indirect block so That it kind of implies single indirect Maybe I should have said single indirect But the ones you're talking about it would be explicitly like double indirect and then triple indirect I guess this should have probably stated Single, but if you just made up double or something for that I guess I would have to give you full marks because I didn't You could argue that one Okay, what do is there more? Oh, yeah, okay, so Let's get rid of No Okay So how many directories need to be accessed when attempting to read a file located at Home user uToronto ec blah blah blah labs grade dot txt assume grade dot txt is a regular file So how many directories do I need to access to actually get to that file? And what are their names? Yeah, yes Yeah, so Root And then this this this This right So that's five so Yeah, five So This question is mostly so you knew that the root directory was a natural directory. The other answer I mostly got was like four so Next question You think you should create a copy on write file system But someone who hasn't taken this class Says you don't need to because you can already do the same thing with hard links Explain the differences between file one and file two being hard links to the same inode And the concept of copy on write can copy on write be achieved using hard links. Yeah, so basically That probably would have been full mark So if you just said that if you have two hard links to the same inode Well, if you change the file through one or the other it changes them for both They're not independent at that point. So you wouldn't get the same effect as copy on write what you would want Because they share the same data what you would want is to oh Jesus What you would want What are you Stop it So what you would want is for Two inodes to share the same blocks if they are the same and then if one tries to modify it Then you create an independent copy of it and you could do that if you want for the file system So you could make like that copy command Essentially do copy on write instead of copying the contents and there are our file systems that do that But they would have different inodes and then internally the file system would have to keep track of the pages Exactly like in memory Yep, yep Yep, okay. I think that was it for file systems. All right anything we want to do real quick in the last six minutes Okay, that's a blank page. Let's see Threads we want to do threads as quick as we can Sure, okay So here's our program So we declare a bunch of threads we get a bunch of id's Then in the main thread We create What in this case we create eight threads So we create each threads each with their own id and then we join them and we print a global sum Global sum is this variable And then there is another global variable called array And then in each thread Well, it seems to Start us off at a unique Index that doesn't overlap with any other threads. So like thread zero would get I don't know Let's say Index is zero to Zero to ten Not including ten and then the next thread would get like ten to twenty And then the next thread would get 20 to 30 So on and so forth So real quick Is it necessary to protect access with the array variable? So is there a data race with this array variable here? So anyone off the top of their heads remember Definition of a data race. Yeah possible for two concurrent actions With at the same location or with the same variable with at least one of them being a right so Even if they overlapped In what parts of the array they are accessing If we have the array on the right hand there, is that a read or a write? It's just a read So local sum is being written to in red, but array is just being read So do we have a data race with array? No, because it's just being read. All right Next question is do we have a data race with local sum? Yes No Yeah, no, right. So local sum Is a local variable in each thread so each thread has its own independent stack So therefore There's no concurrent accesses to the same location because each thread gets its own unique location So no data race with local sum Is there a data race with global sum? Yes, why? Yeah, so here This is a right and they all are concurrently writing and well, guess what they're also reading and writing So all of them have access to the same location. It's the same variable. So all of them will be reading and writing There's no protection. They could all be running concurrently and therefore we have a data race with global sum So what is an easy way to fix this? Lock and unlock so create a mutex And then where would I lock? Just before the global sum because I would want to make My critical section as small as possible and then I need an unlock Right after right Boom fixed I think that was all the questions Oh, then last one really really quick if we change all the threads to detach threads Is that a problem? So now I detach them And if they're detached then I can no longer join them. So I don't have this So is that a problem? So it's not a problem Yeah, so in this case it would be a problem because I probably care about the global sum What could happen if I just detached everything is Before all the other threads run the main thread just prints the global sum Global sum is zero so it would print zero and then Return from main which is the same as exit and now the process is done So could do that before anything runs or it could you know have a thread one thread updated and not all of them Recipe for disaster here Because we want each thread to be done before we print the global sum So we need joinable threads in this case or center fours or something like that All right, so with that remember fooling for you


Welcome everyone, we will continue with our topic of optimization. If you remember, we were previously studying what is called real analysis. Real analysis is a careful study of real numbers and real numbers and their associated properties. So we studied the following topic so far. We have defined what the sequence is. We defined what it meant for a sequence to be bounded. So we defined a bounded sequence. We defined what it means for a sequence to converge. So all concepts related to convergence, what it means for a sequence to converge, what it means for a sequence to not converge and what the limit of a sequence is. And from that we also defined what is called a sub sequence. These were the four topics we covered so far in real analysis. Now let me take off from here. So it is very easy to see that if a sequence converges, then every sub sequence of that sequence converges. And it converges to the same limit. It does so to the same limit as the original sequence. Now can you tell me if the converse of this statement is true? So if a sequence, if every sub sequence of a sequence converges, then does the original sequence itself converge? Yes, no? Yes. Someone saying yes, why yes? That is the correct answer. So the sequence itself is a trivial subsequence of the original sequence. So the converse is actually trivially true. This statement is the non-trivial one. Now let us, we were so far looking at sequences that were in living in Rn. So these were vector value, the sequence of vectors. Now let us come down to sequences that are in on the real line only. In that we have a famous theorem which is called the Bolzano-Weistras theorem. Bolzano-Weistras theorem simply says the following. This does not necessarily have to be in, this is not necessarily true for real numbers. So I will let me, this is true for vectors also. So I will tell you a more general version of the same statement. So the statement is simply this that every bounded sequence in Rn has a convergent subsequence. If you consider sequences in Rn and make, look at those sequence, if you and consider a bounded sequence in Rn and look at all its possible subsequences. Amongst all its possible subsequences you will find at least one which is convergent, convergent to some limit. It cannot happen that all the, all these subsequences do not converge and yet the sequence remains bounded. It is not possible. Now the, this is actually a very deep fact. Essentially what it is saying is that if you constrain the sequence to be in a box, so if you suppose here are my axis and my sequence is living in this bounded box. Eventually it will, the very fact that you are constraining it to live in a bounded box would mean that you can extract some subsequence out of this such that the, that subsequence eventually starts accumulating around some point. The sequence cannot dance around in such a wild manner that even its subsequences are always dancing around and never will you find a single subsequence which is convergent. So this is actually a very useful fact because it, convergence of algorithms are make extensive use of this particular proof, convergence proofs of algorithms. I will just give you a general sense about this. See when we are computing something in optimization what we are effectively generating is a sequence of one, sequence of iterate. Sequence you have iterate at one then another you go through another loop straight to the next iterate then you get to the next iterate then you get to the next iterate etc. So what you get are these, is this iteration x of 1, x of 2, x of 3, etc, etc, etc. And what we want is eventually that this sequence, if you look at the limit of this sequence x of n, this limit should converge to the solution of your problem, solution of the problem under consideration. So for example if you are looking at this, if you want to, if you are talking of optimization problem, you want this to converge to the solution of your optimization problem. Now to show one of the big challenges that occurs in analysis of algorithm is making sure that this actually happens. And we may often the steps towards arguing that go through, you need first a way of arguing that the sequence converges at all to begin with. And that comes from Bolzano-Weistra theorem. You argue that there is at least a subsequence that converges and from there you build your argument. It is a common way of arguing. So this is Bolzano-Weistra theorem. Now let me come to sequences or sets in the reals. So now let us look at just the real line and look at suppose some set of points on the real line. So for instance, look at the set which is, I will just write this in words, set of positive rational numbers for instance. So this is a set of all numbers m by n, n not equal to 0, m and n, m comma n both positive and they are natural. So if you look at this set, this is a set of all positive rational numbers. Now we say that a number l is said to be a lower bound, l is said to be a lower bound if it is less than equal to all elements of s. So now if you take s to be the set of positive rational numbers, what can you give me an example of a lower bound minus 1, 0, these are all lower bound. Likewise number u in r and upper bound on s the opposite is true. x is less than equal to u for all x in s. Now again for the same example set of all positive rational numbers, can you give me an example of an upper bound, there is no upper bound. Now what we will, if a set is bounded, if a set which is a subset of r is bounded, then does it have an upper bound and a lower bound by definition. So it does have an upper and lower bound. What did we say, what did we mean by a set is bounded? We said we look at the norm of the elements in that set and all elements should have a norm less than equal to a prescribed number. So what it means, in this case we are talking of a set of real numbers. So the norm is just the absolute value of the number. So the absolute value of every real number, every number in that set is between minus m to plus n where m is some positive number. So if the absolute value is between minus m to plus m, then what does this mean? So mod x is less than equal to m, this means that x is less than equal to m and greater than equal to minus m. What does this mean for all x in s? What this means is that m is an upper bound and minus m is a lower bound. So a set if it is bounded will have an upper bound as well as a lower bound. Now upper and lower bounds are not unique. If m is an upper bound, then m plus 1 is also an upper bound. Likewise if l is a lower bound, then l minus 1 is also a lower bound. You can keep making lower bound smaller and smaller, they will continue to be lower bound. If you make upper bound larger and larger, they become continue to be upper bound. So here is the another concept which is called least upper bound. Least upper bound is the smallest such upper bound amongst all upper bound. What does this mean? That if I take a number, if I take a number even slightly smaller than this least upper bound, then it cannot be an upper bound. Let me write this in English first. The least of all upper bounds, what does this mean? If I for all epsilon greater than 0, there exists an x in S such that x is greater than, sorry, sorry, let us write this better, m is set least upper bound in A set S of R. If for all epsilon greater than 0, there exists an x in S such that x is greater than, x is greater than n minus epsilon. So m is said to be the least upper bound on a set in S which is a subset of real numbers. If for every epsilon greater than 0, you can find an x such that x is greater than m minus epsilon. You cannot make m even slightly smaller and still have it as a lower as an upper bound. So there will be at least one element whose value will be greater than m minus epsilon for every epsilon. Likewise, l is said to be the greatest if for all epsilon greater than 0, there exists an x in the set such that if I increase l even slightly, then I can find an element that violates my, is this fine? Now, there is a chicken and egg problem that arises in trying to define what this, trying to show that such a thing exists. The very fact that to show if you want to show that the asset must have a least upper bound, then what you want to what you need is that the set of upper bound must have a lower bound. Likewise, if you want to show that the asset must have a greatest lower bound, then it means that the set of lower bounds must have an upper bound, a smallest such upper bound. So, this is worked out using what is called the completeness axiom. Completeness axiom simply says that the bounded set of real numbers upper bound. So, if your set is bounded, then it does have a least upper bound and a greatest lower bound. If your set is just bounded on one side, means it is bounded above, then it has a greatest, it has a least upper bound, but may not have a, but does not have a greatest lower bound. If it is bounded below, then it has a greatest lower bound, but does not have a least upper bound. But if it is bounded, it has both least upper bound and greatest lower bound. So, this leads us to the definition. So, once you have with the axiom, you know that such a thing exists. So, the greatest lower bound has a name, instead of calling it the greatest lower bound on S, we simply say the supremum of S and it is written as this, sorry minus vector. We simply say the infimum of S and least upper bound called the supremum.


at Fibregate because it's fun, you get to meet a lot of people and you just have a great time. Learn new skills and meet new friends and have fun with my brigade. I just do this for fun as an after-school activity, I get to be around with friends. I love how at the end of the year after we've finished all our demos we can come together and it can join space and compete for the finals. I like doing Fibregate because it's fun and I get to hang out with friends. You make lots of new friends.


What's up guys and welcome to Rotorite! My name is Cricket and this is your boy Vortex! We're going to tell you why pinching is better than thumbing. No, thumbing is definitely better than pinching.  So thumbing is like the traditional Xbox All-Ball Bear.  What do you do your thumb for? Nothing. What do you use your thumb for? Other than that.  But you have no precision with your thumbs. You play Call of Duty, you pinching? I would. Your thumb? Get some new audience. It's dumb. The thumb is dumb. The thumb is dumb. But when you add the pinch, now you have some precision with your movements.  But I actually hold it with a little like in the middle of my index finger. So I guess that would be considered a hybrid because I do use my thumb as my dominant finger to make any maneuvers. For me, personally, just the way my hands are, I feel like I can't move them. It definitely has a lot to do with the way your radio is set up as well. If you see- So with this stick being longer like that, that means there's going to be more available travel. Tip of that stick there to there is a longer radius than mine. It's a longer throw. Although I feel like my gimbals overall are more throw than yours. Well, so I actually shortened mine and my radio. That's interesting. So you see where this one stops at? Yeah. So you can change that. That's interesting. On the IS-12, if you pop this little cover off, you have an adjustment here. And I'm going to move that completely over. But at the top, it goes higher now. With the factory settings on this, I can't pinch it all because you lose a whole area of movement. I don't know. I just feel like it depends on your hands and how your body works. I don't think you can definitively say one is better for everything. I can now. I can now. Here's why I can because I thumbed for a while. And I even tried to pinch and then didn't pinch and then took a whole day and just this is what I'm going to do and it made me a better pilot. No, I already knew why people say it's better. I just don't agree that it's better for every single person. Okay, I can go with that. I think that we should you pinch and I thumb. I can just tell how unnatural it feels to me that I'm not going to like it. Well, why are you going way out there? Because to do a roll, you got to go all the way. Okay. See, so that also has a lot to do with it as well. Your rates and everything are set up different than mine where for me to do a whole roll, I only have to move like that. Well, I don't have to do full stick. I don't agree with that because when you use the full stick, that's a known distance. So that's how you get consistency. I never go full stick. Like I don't have to go full stick deflection to roll. So what's the most you ever move? Do it like that. Oh yeah, right here. Right there to there. That's as much you ever move it. You're just wasting all that resolution. Yeah. What am I wasting that for though? I mean, that means that anybody can do this. If that's the case, if everybody just bumps. Staying horrible.  I think watch. I think they watch how I fly then. I think most people do. I don't need it all. Unless I do.  You feel like it. Boys and girls. I think we fly me. I think we need to see this. Talking about these pinching and these thumbs for just. Well, we already know. What have you guys learned today? The thumbs are dumb. Pinching is better. Don't ever touch the end of your stick travel. Why, who would do that? I'm going to do both of them.  Try to fly in a way that shows off why you think pinch is better. Show me some smooth flying. No crashes. That was pretty precise. And remember that full stick deflection you were talking about? Yeah, you still are not doing that. Never. Never. See, my thumb stops it from hitting full stick deflection. I heard a pump there. No, you didn't. See some snapper rolls? Yeah, you're going home. Okay, there I did. Okay, I felt it that time. All right, all right. See if I can go to thumbs here. Oh, this is weird. Oh, so you're on thumbs. I'm on thumbs now. Looks like you can still fly. Yeah, but it's full stick deflection every time on those. I just don't feel like I have so much more control as what I usually do. Oh, snazzy. That's a tree there. It looks fine to me. Maybe I prefer thumbs. Maybe I've converted you. Isn't it more relaxed? Don't you like that? No, I don't know about more relax. Okay, all right. See, it makes me get more sporadic. I feel like I'm not as precise with my maneuvers. I don't know about that. It's looking good to me. Oh, no, where am I? Oh, it's a turn. I don't know. I'm conflicted here now. Because it doesn't feel bad, but it also... You used to fly with thumbs? Oh, my gosh. Yes, I did. See, that would have never happened if I didn't have, if I was flying. For me, it'll be...  I didn't have a neck strap. There's a difference. Let's go back to pinching here. Oh, jeez. Scared me. I don't know. I still prefer pinching. I feel so much more controllable, I feel like. Oh, that was nice. It was really nice. So, I do see where thumbing can... I like it somewhat, but I feel like if I need to have for precise flying, I still prefer pinching. I'm really curious to see you pinch. Yeah, pinching for me is actually going to be different. You've already done that before, but I've never... You've never pinched. I mean, maybe a little bit in the sim. I've never tried to actually fly my ball. It does give you more easier to be juicy, should say. Because you have like that, like... Woo! Thumbs where for me, the thumbs. I feel like thumbs... You can get more juicy. Okay. Juicier. Where we're pinching. Right. But pinching...  What channel are you on there? I'm on a race band of one. Okay, I got you. So, what is this right now you're doing? Thumbing. See, I don't know if I could do... I guess I can. I was going to say fast maneuvers like that, but... Yeah. See that snaz right there? That's that... I feel like I'm not doing that. That's that thumb snaz. If I'm pinching, I'm not going to be able to do that. Woo! That's that juice I was telling you guys about. Let's see some pinching. All right. Let's see some pinching here. Getting all snazzy. This is pinching. It feels horrible. It feels horrible. I can't do it.  I don't know how to hold the radio, is it? You got it. No. You have to be able to do it. But just put more concentration on your thumbs and let your index fingers just kind of guide you. Not really put a lot of motion on those. No, I'm going to do that. There you go. All right. Horrible. Let me see what you're doing here. See, I feel like you're using your index finger too much. I can't help but to do that. Control it more with your thumbs. Well, then I'm just thumbing. So what is the point of pinching? It's a guide. It's just a guide. A guide? I don't need guidance. I know where I'm trying to go and what I want to do. You guys here next. I feel less precise about doing this. Oh, are you kidding me?  What are you flying right now? I don't feel like this is... Are you pinching? Doing anything for me. Are you pinching? Okay. All right, all right, all right. Look at that. I've noticed a big difference already. Killing it. I think I could do the thumbs too. Try to do it with thumbs. What you doing right now? Okay, here we go. Here's thumbs. See all those extra adjustments that you're making now? Oh, what? The thumbs are dumb, guys. I'm proving my point. Let's try it again. I just feel like I'm just going faster now. So maybe that could have a lot to do with it as well. I feel... See, I guess I would say you're right. I'm not going as like perfectly straight. It does. If I maybe I'm also not focusing as much. But yeah, they're not as precise. See? Yeah. You see this? Yeah. There is some truth in that. Look at that. I suppose. Yeah, beautiful. It is a little more precise. You just have to rip it. Like maybe I just have to switch grip. Like now I'm thumbs. Yeah, now I can rip. You know, do all that. Well, hold on. I got to slow down a pinch and switch back to pinching. Like I need to be really precise around this. But I suppose... So now if you implicated that all the time though and learn how to or what you needed to switch your hands to do. Still feels alien to me. I just want to thumb it up. Let's do some technical flying with the thumbs. Oh, that was hot. Yeah, but I guess if I was really, really just trying to like be super precise, I guess that does kind of help. Because it allows you to not be able to so easily move the stick. And that's what that's funny to me because you fly Bandos. You used to fly Bandos all the time and you always thumb.  Do you think that if you were to implicate that a little bit? I just can't get over the insult. It would, I guess. I would have to say so because I was more precise. But I still don't like it. I'm still not going to do it. And that's exactly how I felt when I first switched from thumbs. And then when I went to switch to pinching, it was horrible for me. I felt the same way. Like this is not the way it's supposed to feel. Take a whole day, try it out. Every time you get back like, oh, I wanted this thumb. Now just pinch. Just try to pinch. Do you have a tree? Mr. Vortex here, the Bandos Slayer just proved my point. Am I right? I'm maybe. Well, you were on video saying that your thumbs were better. No, I didn't say better. I said I feel like I can get more juicy in like an open pinch. So it opened up something for you? Yeah, there was a moment.  Each of you. I don't know how you got me thinking, you said. Yeah, each of you were like, oh wait, maybe there is something to the other side. Which is good because it should be an open thing that's per pilot. Like how would you feel if you think the thumb's better? Thumb should be better for you. You know, as a real weirdo, Vannover. You right now, he's doing one hand his thumb and one hand his pinch. I call the ultra pinch. I don't think anyone does. It's like the hybrid pinch. Quick backstory. I used to thumb, then I tried pinching because I saw a bunch of professional helicopter pilots doing it. And then I'm like, OK, this feels weird. So I did what we call hybrid, which is basically where your fingers rest like this.   So I can't bend it in all the way. So now I do hybrid pinch on the left and just thumb on the right. So I used a thumb and the reason that I went truthfully from thumbs to pinch or hybrid because I was trying to do professional helicopter flying as well as 3D airplane flying. And every single person I would aspire to be like was always a pincher. Every single one. I never saw one top pilot who thumbed. I got better resolution and dexterity on the controls. Versus when you just have your thumb on the controls, it's almost as if you can lose the grip. Now what I've found when I've had to now switch back to thumbs on one side and pinch on the other is that I feel like I can actually move the stick a little bit quicker. But I still kind of miss that extra dexterity and that extra like resolution. It's almost harder to fly smooth in my opinion. Me and Jeff had our big debate about stick thumbs. It was a good test because we all came down to I think that thumbing can actually be beneficial in some areas. And Jeff in turn also felt that pinching could help his flying in certain technical situations. So now we're going to pick Jamie and we're going to make her into a pincher. Well, I already do both. I already fly both. Little Seller Fox. I've been flying for almost two years now. I primarily thumb, but lately I have been doing a lot of pinching. I don't really pay attention to the way that everybody else does their grips. Like I've just started paying attention to that. Like who does what? Because it's like, it's really interesting to see how it translates into their flying style. I definitely can see how the racers almost primarily all do thumbs because it's faster. And then a lot of the freestyle pilots and a lot of females pinch, which I found was kind of interesting. I actually did a poll. Only like one other girl does thumbs, like all the females that answered the poll. So I think whatever's better for you to do is whatever you feel comfortable doing. But I don't know. He had somewhat of a good point because I was able to do precise flying a little better pinching, but it just, I hated it the whole time. We both agree that the best way in a perfect world, if you could pinch when you want to and thumb when you want to, would be switch if you could just switch it. That's like super difficult. I can switch while I'm flying. I can start in one and go to the other. Let's see what you get. This is pension? Yes. So what do you think about it? Just off quickly, what do you think? Well, since I've been flying both of them, I do really like pinching. I really like the control. I love how smooth it is. So you get up in these trees right here behind us, some technical, closer areas. All fast. Whoa, see that, Jeff? That's that precision flying, bro. Yeah, that's how I'm gonna pinch. And don't you feel like you can get in those holes a lot nicer? Yeah, because there's just more control. Now switch the thumbs. It's definitely not going hard. I just, I have way more experience with thumbs. Yeah, it's definitely... ...way more comfortable. Thumbs make you fly faster. Nice and good. Pinching, pinching, pinching. But my battery's about to be so we'll bring him in. I will say the hardest part about going back and forth is that pinching, taking off is a lot different than thumbing and taking off. Like, that was the hardest part. When I first tried it, it took me a minute to get the feel for where to go forward. It travels. Yeah, just because it wasn't there. But yeah. Looked like you did just fine both ways. I don't think you're really mad. I really, I really think it depends on the place. I still prefer thumbs solely because I fly it a lot. Sorry. I'm just more comfortable. Like when I'm in an uncomfortable situation or a new place, I'm gonna revert back to thumbs, but it's solely because I don't have the time with pinching to feel comfortable in a new place like that. And then after that, when I feel a little bit better and warmed up, I like to switch back and forth for the last couple of weeks so that I can get a feel for what's best for the spot. To switch back and forth from thumbs pinch, thumbs pinch all the time, probably not good. You should probably figure out which one you like and just always do that. But I completely agree with that too. I think anything that you're gonna fly, that you start to get comfortable with, if you're gonna try something different, try it, but pick one or the other. If you switch back and forth, you never have a consistent flight. You don't think that it adds adaptability and being able to do lots of different things though? Because you have the pros of both. It could possibly and for some people it might work, but for me personally, I like to keep everything the exact same way I've been doing it for forever and then it'll always be consistent when I grab hold of it. Do you think you'll settle on one eventually? Yeah, honestly, I'll probably end up settling back onto thumbs because it's what I'm most comfortable with. But I'm gonna give it some more time before I make that total decision. I like going back and forth. But let's just get a poll of all the pilots out there and who does. It'll be like over one of these areas. How many of you guys pinch? How many of you guys thumb it? We'll do a little poll and see how many it adds up to. I'm gonna say my personal opinion and what I think more people thumb than pinch. I think so. I would say that that's probably just... It comes from video games, man. Yeah, a lot of people do. I will give it that. It took me a while. I don't want to say like I just jumped in the pinching guys. Like I thumbed for a good bit of time and then it just, I just switched. I hope you guys enjoyed this episode today. Pinching, thumbing, we are friends so the disagreement doesn't leave anywhere, but here you guys are the only people I know about. I'm pretty upset. I'm pretty upset about it too. I'm not very happy. It's pinching. It's not upset. But please, if you like this video, hit that like button. If you want to see more of the glorious things that we do here at Rotoride, please, please hit that bell. And if you, if you fly thumbs, could you thumbs up the video? You can't pinch it. Joshua Bardwell, pinch your thumb.


Okay, so thank you so much for agreeing to do this interview. If you want to start by just introducing yourself, telling us a little about your work, that would be great. Sure. So my name is Katherine Munson. I am a Tufts alumnus. I work at a company called KSAT, Kongsburg Satellite Services. So I run our US office for KSAT. KSAT is a company that provides ground stations as a service. So for those not in the space industry, essentially what that means is that all of the satellites that are in orbit and then also the rockets that are getting satellites to orbit need to have a way to communicate back to Earth. So they need to share telemetry data, which is essentially the state of health of the rocket or the spacecraft, as well as whatever information that they're capturing. So satellites that are taking pictures of the Earth that you may have seen on your Google Chromecast or, you know, any time that there is any satellite imagery that's in a newspaper, all of that data when it's collected by the satellite needs to find a way back to Earth. So we provide that communications link from space to Earth through a series of radio waves currently, but actually the future is also including optical communications. So using lasers to communicate. So that's one of the kind of major things that we do at KSAT, but we also provide analytics based on satellite information. So we're looking at that satellite data, that satellite imagery, and we're helping folks extract information from it. So some of those use cases are oil spill detection. So being able to see is there an oil spill A and then B being able to prosecute and hold someone accountable or, you know, making an oil spill. Illegal fishing is another application. So we're looking at being able to control fisheries that would be outside of a terrestrial awareness. So once you're 50 miles off coast, you are kind of under the curvature of the Earth. So there's no way of getting a radio signal back. So it's very hard to monitor coastline that isn't directly on that coast. So illegal fisheries is one application. And then we also are doing a lot of work right now with Arctic monitoring. So some of that is helping ships figure out what is the right way to go across the northern pole and have a way that is not going to get them stuck in ice, but then also from the climate science perspective to be able to monitor how quickly is ice melting, where is it melting more quickly, and being able to provide some of those inputs for climate scientists. So that's kind of what we do at KSAT, but it's essentially we're working with satellite-based data. So this is obviously like a really interesting and important field of work, but I don't think a lot of people like understand what it looks like. So could you maybe explain what the day-to-day looks like at your at your role? Absolutely. So I think when I was a student at Tufts, I was majoring in international relations and I really was interested in defense policy. So I had a security concentration for the IR major and at that point in time I think I had the world view that the only way that you can do policy is if you work for the U.S. federal government and I quickly learned that that's actually not the case, but there's a huge amount of policy work that is driven by industry. So KSAT being a private company, we're a member of industry. So my day-to-day work, you know, spent a lot of time on the phone in coronavirus times. Before that I did a lot of international travel. So I probably was traveling between 50% of my time up to 75% of my time. So the space industry is very global. We work across the world. We have ground station locations, so big antennas, that we run at 23 different sites on every single continent. That includes a site up at Svalbard, which is it is the northernmost inhabited land mass in the world. So it's up at 70 degrees north, all the way down to Antarctica. So we're the only private company to operate in Antarctica. So we're working truly in a global environment, which means that in any given day I could be talking to customers who are located in any country in the world, as well as some of our host partners who operate those ground stations. And each of those people is also potentially impacted by policy. So each country with their own space, with their own jurisdiction can set their own space policy. So I have done quite a lot of work in the United States working with the Federal Communications Commission, the FCC, as well as NOAA, which is the National Oceanic Atmospheric Administration. I believe that's right. Maybe it's agency. We'll have to double check that one. But so FCC and NOAA set a lot of space policy right now. So working with those folks as well to create policies that are going to protect people's use of radio frequency spectrum. So quite a lot of policy work happens from industry, and I guess that would be my big take home for students at Tufts, is you don't have to work for the State Department and the Defense Department to be involved in policy. So this is obviously a field that's always developing. So can you tell us a little bit about what sort of developments you've been most excited to see in the field thus far? Absolutely. So, you know, the field is not very old at all. So it's about 50 to 60 years old, depending on how you want to start measuring. So in a very short amount of time, right, there are people alive today who remember the very first satellite, which is Sputnik. So the entire field has developed in a very short amount of time. I would say that the most exciting thing in the last five years is really how commercially viable space has become. So before it was not a way, space was a very tough place to have a business unless you had big government contracts. So unless you were, you know, Boeing that was building the International Space Station for a big United States government customer, it was tough to make a business work, because it's so incredibly expensive to build something that is often either very small and very technically complex, and then launch it, which costs millions of dollars to buy a rocket, and then to keep it, you know, keep in communications as a hard engineering task. So it has been in the past very hard so that only governments were really space players. But what we've seen in the last five years is that the same technology that, you know, allows my cell phone to be this size and not, you know, a car phone that's an entire box has happened in the space community as well, where we're seeing folks are able to do a lot more with a lot smaller platform. And because that smaller platform is then rockets cost, they scale pretty exponentially with regard to mass. So if you have a smaller thing, you can launch it much less expensively, which means that universities can now launch CubeSats. High school is our launching satellites. And all that means is that people are getting more experience in space platforms and pushing the boundary of what we think was possible. So I think that's what's really exciting in the last five years is that there's a huge amount of growth, because people are experimenting because that experiment is now affordable in a way that it wasn't 10 years ago. So on the topic of the commercial space industry, obviously COVID-19 has had a large impact on all industries. So could you tell us a little bit about how it's affected the commercial space industry? It's a very good question. I think one of the things that was very humbling for me to remember is there is an entire segment of the space industry that is really focused on helping people communicate who don't otherwise have that type of infrastructure. So one example is a customer of ours called Iridium. And Iridium is a large constellation that's in a low Earth orbit. And what that means is that there are these satellites, they talk to the other satellites, so that if you are anywhere in the world, then you have an Iridium phone, you're able to use the Iridium constellation to communicate. So that type of infrastructure is increasingly important when folks are looking at providing healthcare to regions that have been greatly impacted by coronavirus, but would not have the same infrastructure to be able to support, you know, health services. So all of the telehealth type applications that we're seeing, all of that only works if you have a telephone. And those are the types of things that we, you know, that I living here in Boulder County, Colorado or living in, you know, the Boston metro, we take for granted, but there's so many parts of the world still that aren't connected. So space communications platforms allow those folks to be connected. So I think that's definitely one positive application. One of the other interesting things that we've been following very closely is there, some of our partners, a cart lab, or based down in New Mexico, they have been doing a lot of very interesting analysis and that showed up on the front cover of the New York Times by looking at, you know, when people stayed home, how, how did the atmosphere respond? How did, you know, looking at the climate science of folks not driving, you know, buildings not running their air conditioning. So that's also been a very interesting application from the COVID-19 times is really finally having an interesting beta test of, you know, here's what normal human activity looks like. If it scales way back, how does the earth respond and how quickly? So that's been a really fascinating data center that the folks that they part lab have been looking at.  It's a good question in that I think. So a mentor of mine, actually a Sherman who used to run the IGL once said, respect everyone and be in awe of no one. And I have really taken that to heart over my career in that everyone is a person. So, you know, you may not like someone, you may have personality differences, but they're a human being regardless of how impressive they may seem on paper or what role or title they may have. I think in some ways, you know, I when I was at Tufts, I was studying security. There are certainly I have very good female friends who are also in that security concentration. I went on to do a fellowship at the Pentagon where my boss was a woman and her boss was a woman, which was actually quite rare as I look back on it. But in all of those circumstances, it is safe to say that it was male dominated, right? And if you say, it really don't actually quite like that framing. So there are more than 50% of the people in that group were identifying as male. And I guess I don't, I've never really thought about the number so much because I've always been able to find a sense of community regardless of whether it's 50% or it's 40%. So that's maybe a piece of the advice is you see what you choose to see in some ways. So I choose to see that I've had amazing female mentors, you know, Heather at the IGL is a fantastic female mentor, for example. And there are, I would say in the space community in particular, there is a very strong support network for women. So I have now been part of two different, you know, groups in my career. One when I lived in San Francisco was the Bay Area Women in Space Organization. There's another very strong organization here in Colorado run by a former colleague of mine, Carolyn Bell. And both of those groups provide fantastic friendship opportunities, fantastic career opportunities in terms of networking, in terms of support. So in many ways, I think actually having that type of group is an advantage.  There just is the space industry. So I think in many ways it's, if you look for the silver lining, it's usually there. And in particular, I think in aerospace, there are incredible women who are running companies. I mean, Gwen Shotwell is a good example of running SpaceX. There are quite a few others that I could name as well. But I really don't see that we have so much of a gender diversity issue in the space industry. What I would say we absolutely have, and there are good people working on ways of helping change this issue, is there is a demographic diversity issue in the fact that most of the space industry is white. So there are not very many people of color represented in the space industry period. And there are especially not very many people of color represented in space leadership. So that I do think is a big problem that the space industry needs to grapple with. Because the things that we're trying to do are hard. And if you don't have the best of everyone, you're not going to be successful. So there are some scholarships that folks are working on to help provide support for folks looking to join the industry. Because I do think that's a real problem. You know, I can look to Gwen Shotwell and see an example of a woman who runs a company that is incredibly successful. If I were a person of color, it would be a lot harder to find that example. It's really interesting. And then over the course of your career, how have you seen international policy change in relation to space? That's a good question as well. There's a good example I suppose I can draw from. So before I was at KSAT, I was at a company called Spire Global, which launches cube satellites that are about the size of a wine bottle. And they are looking for weather data. When Spire was started, it was founded in San Francisco. And at that point in time, the policy was that U.S. companies were not allowed to export U.S. satellites, which prevented them from launching with rockets such as the PSLV, which is the Indian it's a big workhorse for the Indian Space Research Organization. And so at that point in time, at Spire, we made the decision to move the manufacturing of the satellites from the United States to Scotland. And once they were UK, you know, UK satellites, they could be exported to India, which allowed us to launch on the Indian rocket, which was a fraction of the cost of the options that were currently available in the U.S. So this was before Falcon 9 was really kind of in a good cadence. That one decision essentially caused the United States. And we did a lot of advocacy work as well to say, hey, look, we're an American company. We want to launch in the United States, but there isn't a competitive market. There are not enough launch opportunities yet for us to be able to only launch in the United States. And that type of advocacy then caused the rules to be rewritten. So I do think that space industry is lucky in that there are some very, very dedicated, intelligent people in the industry who are willing to work with regulators. And I give the regulators a huge amount of credit in the United States because likewise, they're willing to listen to industry and try to understand the problem set. So we've seen a lot of change in terms of, you know, U.S. companies can now launch with just about anyone's rocket. You can launch on the Soyuz and the Russian rockets. You can launch with the Indians. And that's a change in just the last six years. There's also been quite a lot of change with regard as to how the security of satellites is managed. So before the security barriers were incredibly high because the expectation was that if you were launching a satellite that you were probably a government and that you were getting government quality data. But now when you have high school students building CubeSats, that's not the goal, right? They're not looking to try to spy on North Korea. They're looking to try to understand how do you build, you know, how do you do the engineering? How do you do the mechanical, the electrical engineering to make this all the subsystems work? And they still need to be able to launch as well and have a set of rules that applies to them. So there's been also a lot of good policy work that's been done to create an entire track of licensing for experimental satellites or tech demos, which has allowed a lot of people to try a lot of different things and not have to meet, you know, an incredibly expensive and also a pretty tough regulatory bar in terms of, you know, having a network operation center that set up industry best practice. And that's not even to get into all the moon policy, which is a whole nother conversation that we could talk about that is happening right now. So along with that, what do you see as the next development in the global space race that's ongoing? Yeah, it's a good question. I think there are kind of two pieces that are happening in parallel. One is the increasing commercialization of space. So people who are running businesses. Some of those, again, are pretty straightforward. So telecommunications, earth imaging, you know, any type of science application that you can sell that data potentially to a finance sector, mining sector. But then we're also now starting to see some of these businesses that were maybe a bit too early five years ago, start to look more viable. So folks who are doing in orbit servicing, which essentially means you have one satellite, you have another satellite that comes up that robotically docks onto the other satellite. Keep in mind that these satellites are moving in incredibly quick speed and is able to do maintenance or is able to give it more fuel to be able to adjust its orbit. So that's an entire set of businesses that wasn't viable five years ago that is now starting to be viable. All the way out to folks who are still talking about mining asteroids to be able to do mineral extraction. So there's quite a lot of interesting work on the policy perspective to be done with regards to how does ownership work in space and who's jurisdiction is it to show ownership. A lot of that also applies to the moon. So NASA has now publicly said last week that there is water on the moon. Hey, that's fantastic. That means a lot of things might be a lot easier than folks maybe had worried that they would be. But if you start building things on the moon and you take things away from the moon, do you own it? Just the United States own it? Who owns it? So there's quite a lot of interesting research and policy I think to be done with regards to ownership rights in space. And all of that is going to impact whether or not there's a business case to be closed that allows people to invest the millions hundreds of millions of dollars that it will take in order to make some of these projects become real. And then on that topic of commercialization, what do you believe will be the next influential space technology, like for example, GPS that's going to impact the lives of like the average person? Oh, that's a good question. I do think that there and maybe the average person is not who's going to be impacted, but they're the telecommunications constellation. So Star Link being an example, one web being another example, the ability to connect people who do not live on the grid is going to be very important for those people, right? So it may not affect me living in Boulder County. But if I lived even, you know, 10 miles up the canyon, I wouldn't be able to get internet. And then I wouldn't be able to do my job. So I think it will very much help create an infrastructure that is a lot more dynamic. That's particularly helpful in places where there are infrastructure damage. So that could happen in any type of hurricane and storm situation. It could happen from civil unrest in places where governments control the terrestrial fiber. This now provides an, it provides a more independent network for people to be able to communicate. So I do think these telecommunications network is going to, networks are going to have huge impact for the people that need them. So for those of us who are comfortably using terrestrial fiber, we probably don't notice as much. But there's a huge percentage of the world's population that doesn't have access to that infrastructure. And then finally, this is a pretty broad question. But what do you think is the future of international relations in space? For those who are interested in getting involved in the field, like what can they expect in the future? Ooh, I wish I knew the answer to that question. There is so much that has not been decided yet because it hasn't yet been possible. And that is a very exciting position to be in. I have found my home in the space industry because there are so many people here who are incredibly dedicated, who are incredibly passionate, who are incredibly intelligent. The challenges are very tough from a technical perspective. They're also tough from a commercial financial perspective because it's expensive to do all of these things. I think there is a huge amount of opportunity because everything that is done right now essentially creates precedent. That is not true in so many different domains. So you can spend an entire career looking up, you know, various policies for things that have happened on earth and you would have to deal with those precedents and you would have to change those precedents in order to make change. In the space industry, you just have to show up because every single day people are doing different things and trying to figure out how to make it all work. And it's going to take all of the various sectors to make it work. It takes government, it takes, you know, the regulators, it takes industry. And so there's a huge atmosphere of collaboration because it's never been done before. So I would say for folks who are excited about having an impact, the space industry is really just getting started in many ways. And so just by nature of being here and being part of the discussion, you're having an impact because we're all doing it for the first time. Great. Thank you so much for having this discussion with me. This was really informative and interesting. And we really appreciate your input and expertise. Well, thank you. I am super excited to see more Tufts alumni in the space industry. Pretty much every space company that I know of is hiring right now. So for those folks who are seniors or juniors and looking for career opportunities, definitely check out any of the websites of any of the major space companies. It is an incredible time of growth and Tufts students I think are uniquely prepared to be able to look at the world and look at problems. And instead of seeing those borders or barriers, the opportunity. That is really great to know for all of those future graduates. So thank you again for your time. We really appreciate it.


Hello and welcome back to the craft box. My name is springton today when episode 87 There was a 101 death walk-through last episode if you haven't checked it out. We made it into Stormriven and We did some things and stuff and today We're starting by talking to Keralak night spinner It cannot be you have returned that which could not be found You have returned the pieces of my medallion, but it is still broken Can you place it upon that nearby pedestal that will restore its energy flow and enable it to be of use to us? Okay Really don't trust the sky, but that's fine You have restored my shadow seeker medallion and with it my power is restored You think you seek the missing portal pieces, but you are wrong if you came to this sunken place It must be in search of your doom Did you really think I would put aside centuries of hate to help you? Okay, we're going to Do this Yeah, oh he does have a minion. Okay, and it's an annoying one. I was really hoping he wouldn't but that's fine That's a nice one. That's not cool That's not cool, man That's not cool Okay Good not our shield. Mm-hmm. That would be bad Tower shield in the first round Yikes, let's do that and I hope he doesn't touch up the boss because that would be that that would be bad And what are you gonna do you're gonna hit Why was that even a question? What are you gonna do hit? Yep blizzard. Nope. Okay trap. Okay. That's cool Do Boop, boop. Okay, this is gonna do a bit. Uh-oh Yep, that did a bit That's slightly unfortunate I mean, I'm not too worried This is also gonna do a bit. Let's get kill me Oh yikes, this could be bad one one three six. Let's see Don't do too much Thank you. Okay Oh, we need to wait for a Nice wee scarecrow, which should hopefully be coming soon Coming to a spell deck near you Okay, thank you. Thanks for that, man Yep, much appreciated Um Should have hit should have hit should have hit should have hit should have hit oh well I want to kill him in one go Mmm. Yikes Okay, blizzard's not gonna do too much. That's fine Okay, good Not really good, but good This ain't gonna do too much may not even kill the minion, which is unfortunate, but we need health. We're at 222, so we need health Boop boop boop this Quite a lot on the boss, which is good. We're nearly full. We might be full health Also ps there, which is good. That was my phone. That's awkward Hmm Okay, basically just one more one more scarecrow to be honest. We'll do it. Yeah One more scarecrow should be enough, but let's just blade Do-do-do-do-do This is gonna do a bit. Okay. Yep, that did a bit And what's this wyvern? Nope storms or fire isola. Sorry Get your skulls right branches No Okay, that basically took me down to nearly dead. Thanks game Um Yeah, we need another blade.  They've got two pips three pips between them So yeah, not too worried Fortunately that sign fell gone, but They didn't shield so that's fine as long as we don't fizzle which now I've said that we will It'll be fine Ready for the fizzle. Oh, we didn't fizzle. What a surprise Okay, one down Two down. Yay. Perfect. We did it. The irony is thick You have given me what I sought most my own destruction When carolac night spinner falls, he drops a piece of the celeste in portal Okay, let's go back to liland. I'll be back in just a sec when I'm at lilam because I did not leave a mark Okay, um back You've got it that can't have been easy to find You've got all but the last fragment of the portal stone. Don't be discouraged It's more than any of us got as you know Much of what we do is dig around in search of broken bits and fragments of things Usually far less important. You've earned a rapport with the morgan team soldiers trapped in this place It's quite remarkable how you did that. I've spoken with one of them a fellow named vassic shadow spite Don't let the name fool you.  He might be of help finding that last portal piece Okay, um, we're just gonna mark here just because we can And we're gonna head on over to vassic um, in fact, I'll be back when I'm at vassic because It is all the way at the end where we just were Okay, we are diving into storm riven hall It's quite cool So that's basically what's in that big trench storm riven Hall, okay vassic You don't look marley bonion and you're no celestian The one named liland hawkins sent you very well, then I will aid you in recovering the remaining portal piece Long ago when the portal was broken up the final piece was taken and given to a being called Tempest storm fist storm fist is a servant of the powerful storm titan that sunk celestia beneath the waves And he is dangerous beyond measure Storm riven hall had three gems called the storm shards when together they called the storm titan's avatar After celestia sunk the storm shards were taken by water lurkers and morgan tine soldiers One of them was lost in rubble if you can recover the three lost storm shards bring them back and place them within the carved kraken statue Okay, we are going to get the um The what's it called the lounging lizard Which should be back here. Hello Amazing, um, and I'll be back once I've got the artifact Okay, just got all three of the artifacts. Let us go and use them on the pedestals Which is just over here Joom Oh Hello, okay, and they're sick. They're sick. Let's go and talk to you again And see what you want us to do now Very impressive, it's good. We never fought one another You must first use the moon dial to charge the storm shards then place them upon the altar After that tempest storm fish should appear and you must defeat him He will likely have with him the final piece of the portal He needs it to manifest completely in this world when you've defeated him Go and tell liland hoggins that I was of aid to you okay Let us go and use the moon dial then Which is just down here You charge the storm shards by placing them on the moon dial. They soon glow with power That's quite cool and storm altar And storm lord's temple, which is up here Have to defeat him so we're gonna put a couple of those And we're going to And three of you and two of you is fine and enough blades. This looks exactly like some of this stuff and What's it called? thinking mobile who dickie was it the gate has defenders You must deal with them before you access the storm altar Oh have to defeat these people Well, I'll be back in a sec once I've defeated these people.  He's probably gonna wild-bolt us a lot And we're probably gonna die, but you know what?  Okay blade for him. That's fine Okay, that's good No worth quake is always great No perps. Okay. How much health do you have? 3,000. Okay, interesting Do Oh, okay, half health right away that's fear.  Oh, what a surprise. Oh good did man. She's good Um Still fine on that front. We're probably not gonna use too many of you Are we still waiting for another blade? So They're like no pips. We are going to do this also hopefully to get um Some extra power pips because we desperately need power pips at this point Um, okay. Okay, this could hurt. We need to redo fortify Wild-bolt. Okay Blade for days. Okay. We're going. Don't care We're just doing this. We don't have enough blades, but that's fine Need health gonna die There we go for health. It's good and you're dead as well. Perfect. I forget myth boosts We boost on myth which is oh, he's not dead. Not quite. Okay. That's unfortunate Um, okay, that's fine. Let's just storm them hurt because that could have been bad I mean I have more myth damage than storm damage. So that's fine I mean resists not damage. What am I thinking about? What am I talking about? Who knows? Um Now we get what we need. Okay, that's cool Um, okay, that was Okay No more myth person Yay, there we go. Perfect. Just storm Which is fine draw so means we can Rife instead of vampire not vampire scarecrow because that's going to do more damage But we're going to fortify now And then next round we will probably pull a blade Fizzler, thank you. I'm actually really nervous For this 1,400 before we die It's unfortunate. Thank you for fizzling. Okay. As long as we don't fizzle It should be gg We didn't fizzle so that's hopefully gg Which is good Boop boop Yum Yep, there we go. Perfect. That is battle over You are gone Yay, we did it.  Is this where does this port go? Hopefully back to liland Was I smart enough to do that? Please I was actually that's fantastic of me. You've recovered it, but oh something doesn't look right Not always lost. I'm sure we can get that portal piece fixed up in no time Head to the astral archive the archivist should be able to help you. What else is it for if not that? Um, okay. I'll be back in just a second once I am at the archivist Okay, I am at the archivist. I am the archivist a construct to aid research in the astral archive I sense the presence of a damaged section of the lunarium portal stone If you wish to restore it to full function, please follow these steps First place it on the preceptor of contemplation to study its current condition Second consult the preceptor of contrivance to determine the method of repair Third place it in the preceptor of confirmation to restore it to its original condition Finally repeat the following incantation to align it with the remaining pieces of the lunarium portal stone The archivist teaches you an incantation in the ancient celestian language Okay, let us go and do this A preceptor of contemplation Back to these preceptors gotta love them Gotta love a man Like don't like like like excuse me Hello, okay Luckily this time it doesn't tell us what we Tell us a whole lot of our dialogue Which is fantastic, but we have to use them still No Okay Scrap iron yas. Good job.  Okay the archivist I sense that the lunarium portal stone has been restored to full integrity I recommend you restore the lunarium portal stone to its correct alignment within the portal to do So exit the astral archive and proceed in an orderly fashion to the area currently designated Celestia Base Camp Okay, we are going to Get a couple of these Probably like that many Waste all our money. That's fine Celestia Base Camp Okay Where are we going over here? Restore the pieces of the Lunarium portal and soon it shines Let's welcome sight to see Now that the portal is active, it's your chance to enter the Lunarium and see what's inside! If you find the moon celestial, bring it back! We can finally unlock the keys to the Astral School of Star Magic! I'm filled for you, but be careful in there! No telling what's inside! Exactly where I put some of the video! And remember, craft! Outside the box!


Gold, gold contract down $9.80 traded $180.03 an ounce, you get Silver down $0.50, $20.24 an ounce, LightSuite crewed up $2.40, $94.32 a barrel, notes and bonds. Ten-year note, down $21.00, tick trade in $119.03, the 30-year almost off two points at $140.01 and $KingDollar. $KingDollar down $83.00, tick trade in $105.00, the Euro is out here at a price point, where are you Euro, come on baby, at $103.00, the yen is trading at $132.00 and the British pound is trading at $121.00 to $1.00 US. We get open and take a look at the S&P folks, the market couldn't hold price, that's how it's set up and what I suspect we're going to have here, this is going to be pretty cool how this sets up now. So what do you do? Today we got to the, one of the benchmarks out there is $429.00, you got to $424.00, gave it up, that's saying, you know, bottom line when I'm looking at this thing that this thing can pull back somewhere, you know, $406.00, right now you're at $420.00 and the Q's in the NBX, it's going to be interesting to see what happens because I think what you're going to see here is that this will get everyone real nervous too, man. Bottom line, you couldn't hold price, the Q's ahead of the spies, no doubt about that. And where the Q's took their last leg up is at the $298.00 to $300.00 level that we can get down there, man. That's the real bottom line. I haven't done confluence on this yet, but I suspect just looking at this, that's going to be confluence between the very low because I suspect what we're going to have here, this is going to be the retracement off the low. That's what I'm looking at right now. If we just took, let's just do this quickly, let me just do this one and see what a .382 is. Yeah, it's coming in the same way. See, the .382, man, I love this when you, when you practice these folks, sometimes just after you've done them a long period of time, gauge it, look at it, speculate yourself, then put it up, the .382 is right there, man. And that's, see that, that's the last time we launched the volume. And on the Q's, that's $308.00. That's top of it, $298.00 at the bottom of it. And now here's the kicker, man. This is crazy. The dollar, this market is, is really, you know, dollar sensitive. I went ahead with the dollar. Dollar's down to 104 today, comes up to 105.092, and that's where you saw this market basically giving it up. And I suspect what we're going to have, and this is a classic Bud Rolves. This is going to be a test of the break. And, you know, when you get a slice of break and a test of that break, that, that dollar can go right back top side, testing that down break. Stay right there, folks. Come right back.


Through two years, we've worked hard and we've persevered and through it all, we've found ways to thrive. We've adapted and innovated with groundbreaking discoveries and inventions, bringing exciting possibilities. Every aspect of healthcare has been disrupted. We're finding different ways to deliver care and to serve patients beyond their traditional office visit. New software, devices, and ways to connect are changing how healthcare providers and even back office staff work. Clinical teams are collaborating and communicating as never before. Patients are working with providers, taking more of an active role in their own care. And now, it's time, it's time to reemerge, to start creating the next normal and to start rebuilding healthcare in a way that's more equitable and that works for everyone. To do that, we need to gather from around the globe, the visionaries, the big thinkers, the always curious, the thought leaders, and the bright, motivated, forward-thinking change-makers. We need you. We're ready to reconnect. And ready to share ideas. And ready to reimagine health. Together. Welcome to Hymns22 Digital.


so that is like amazing that is an amazing salary as a new graduate what's up you guys it's adana i am back with another video for you guys so a lot of you guys have been asking about this and so i said let me do a little bit of research because i want to know too so what is the median salary that a p8 makes like what's the average salary right and with the profession just on the rise it has only gotten better you guys forbes has this thing out um just talking about the salaries that the pa made i will leave that link um to the actual article in the description box below for you guys so you guys can check it out yourselves but it just gives a little bit of a comparison with the new authority the prospective authority that we have through otp what the salary is and how it has raised um just recently so average on average a pa makes about 102 thousand dollars a year i know that in the state that i'm in and in the city that i'm in at some of the hospitals here a new grad can make upwards to 130 000 if you're working in the er so that is like amazing that is an amazing salary as a new graduate 25 26 27 you know 33 42 however old you are coming out that you can make that much money just coming out straight out of school that's honestly like that's beyond that's you know that's actually like an anomaly that's not what all new grads made coming out of school but that is what can happen here in the state and city that i'm in however the average salary is about 102 000 um 102 000 dollars generally it can run a little bit lower like 98 000 a little bit higher um 111 000 130 000 um that's all with incentives and sign-on bonuses and such but that's generally speaking the average um i know that forb stated that with the new prospective authority that's actually going on in the pa profession that um 43 states have uh actually like adopted this in any of the states that have adopted the full you know kind of prospective authority um which is otp the average salary has gone from 103 879 to 106 594 so that is a that's a nice little pretty jump you know that's three thousand dollars extra um a year that they are now getting and i think that it's only going to rise um as more people get gain access to health care as the baby boomers start to retire and need you know a little bit more health care the profession is only going to rise and the demand is only going to rise and therefore the salary is only going to rise so currently it's about 106 000 but it's only um going to go up from here uh there are 43 states plus the district of columbia that have actually adopted the full prospective authority which is otp meaning that you're able to collaborate with the physician you no longer need them to sign off you're not like dependent as you were before everything is determined at the actual practice level as opposed to like state and national level so that's actually like a benefit with respect to salary and what is expected coming out of school and you know what you can look forward to when you are negotiating those contracts there are some states that still need to come on board obviously but 43 is not bad like that's a good number to start off with so kudos to you 43 states and the district of columbia and um this article came out actually maybe four days ago so who knows maybe something happened within these last four days where some other states came on but we don't know quite sure yet so we'll continue to look out for that one um so specifically a pa um actually says that pa's will tend to make an an additional like two to four thousand dollars more annually so the actual salary is only going to rise about two to four thousand dollars more annually but i honestly see that happening um i think that's a really modest rise i think it's going to be a little bit more than that especially as pa schools become more competitive um as the pa profession becomes more widely known um and as you know pa's go out there and do some amazing things i think it's only going to be um a lot more money uh that they're gaining annually each year so for the states who have adopted um actually like no longer needing any type of co-signature or um you're just actually determining things at the practice level i believe there's 29 states per Forbes um the actual salary is a hundred and seven thousand dollars as opposed to a hundred and four thousand dollars so again as the more autonomy comes that salary is going to only rise and um the the best way of making things like that happen is just by going out there and being great practitioners really serving your community serving those people that you're trying to help and and doing an amazing job job and showing that pa's can do it um we can do that and you know it's kind of just heartening like you all like you almost feel like you know like a little child like yes we are the babies in the profession or like man like we can do this like hey big brother i can do this i can do that too um so you kind of feel like you're just striving and fighting for um the opportunities that you feel like you should already have that you know that you can do um but at this point in time that's something that we have to do everyone has gone through their growing pains um and p's had to do it and now pa's are doing it and we'll get there you guys so don't worry about that all right we will definitely get there all right so just to give you guys a little bit more of insight on the trends that have actually happened um Merritt Hawkins uh stated that the starting salary for pa's in 2017 jumped to 120 thousand dollars and again that is with incentives and bonuses sign-on bonuses and such but that is in comparison to 114 thousand dollars last year and 107 thousand dollars in 2015 so as you can see it's like you know seven thousand dollars is being tacked on for sign-on bonuses and it's only going to rise so this is a great profession to be in it's a great time to join the profession it's a great time to apply to pa schools and get into pa schools and become a pa because the profession is on the rise you can find areas where you're able to get really nice um signing on bonuses and really great starting salaries and ultimately you're still able to help your family but also serve the community which is what it's all about so again the average salary or so is about a hundred um in two thousand dollars like just starting off but you have your higher ends and your lower ends and as otp continues to take um root in these different states it's only going to rise um so hopefully you guys are excited as i am about the future um and what it holds for the pa profession i cannot wait to see where we are in 10 years and um even 10 years after that how much the landscape has changed but i know it's going to be amazing um go out there and do some more research you guys figure it out and um pave the way and you guys will you know just better the profession for those coming up behind you all right thank you guys so much for watching and thank you for requesting this if you have any other questions go ahead and leave it in the comment section below and i will be sure to get back to it thanks talk to you later bye