What's up guys and welcome to one take I'm gil and today we're talking about the expanse season 5 episode 7 This will be a full recap and review So it'll be full of spoilers through episode 7, but no book spoilers So nothing from any future episodes right at the top I'll say this was one of my favorite episodes of the season on par with episode 4 where we saw the asteroids hit earth I say that because this episode gave us not one But several very powerful and emotionally effective character moments for Naomi All of that culminated in a betrayal, which I did not see coming and an intense Hail Mary pass from Naomi Which I also did not see coming but both felt organic and believable All that made this a great episode Which is also a testament to Dominique Tipper's performance as Naomi with that let's get into the recap But first just a quick reminder if you're enjoying these videos Please go ahead and hit the like button hit the subscribe button and hit the bell icon So you get notified the next time we do a video Including our next expanse review and other expanse related content Let's start with Holden Alex and Bobby Monica asks Holden what they'll do once they find the protomolecule And he assures her that they'll destroy it She also lets Holden and bull know that she's speaking with inside sources And if they don't get to the Zamiah before the protomolecule is handed off she should hear about it And in that moment I was sure they were not going to reach the Zamiah before the handoff Then Bull and Holden discuss Fred Bull discusses his respect for Fred and the integrity he had Holden confesses he never trusted him and always thought Fred was working some angle Bull points out how alike Fred and Holden are including Holden's tendency to always think he's right The season began with Fred trying to convince Holden to stay out of the fight And essentially retire since Fred's death I think it became clear that part of Holden's reason for staying in the fight now will be to carry on Fred's legacy I don't know that Holden will become an opa leader like Fred But I do think he'll become even more of an advocate for them I think hearing that he's like Fred and recognizing that Fred's motivations are pure He wasn't playing an angle are both further signals that Holden will continue to fight for Fred's dreams to be realized Alex and Bobby get a message from Holden letting them know he's no longer on taiko And for some reason it cracked me up when Bobby says they can't be on taiko anymore Right before Holden says the Ross. He's not on taiko anymore And she gives a shrug as if to say yep They reply letting Holden know and Naros is buying martian warships and includes profiles for those ships Holden immediately recognizes one of them as Naomi's and surmises that Marco has kidnapped her He messages back asking Alex and Bobby to follow and keep an eye on them at this point Alex and Bobby have spent about half the season on the razorback basically observing and evading So honestly, I'm ready for them to get off that ship. I don't know if there's a way for them to intercept with Naomi But one way or another I'm hoping this finally gets them into the battle And to do something a little bit more interesting Holden and Monica talk She points out that for inaros to acquire warships Someone high up in the martian food chain must be involved Further marco wouldn't have the funds to buy those ships So he must be offering something else the protomolecule and cortisol the protomolecule scientist who we know was kidnapped earlier Holden also mentions the in case something goes wrong message from Naomi But before he can say any more about that they're interrupted because they've located the zamia I'm really curious to find out where we're heading with the protomolecule I can't imagine the season ends with the protomolecule being destroyed Especially since cortisol has been brought back into the fold I have to think he'll have a chance to perform more experimentation with it And I wonder if we'll see it do something new similar to the reveal of the rings a few seasons back They go after the zamia evade a bunch of missiles in a pretty thrilling sequence They corner the zamia and intend to board it for info on Naomi But the zamia suddenly explodes In what I imagine is the spaceship equivalent of a spy budding down on a cyanide capsule once they're caught I assume those were marco's orders in case someone tried to capture the zamia I also assumed that means the protomolecule was handed off at some earlier point speaking of marco Let's talk about him, Naomi and philip this episode marco pays Naomi a visit and they discussed their past He claims that he kept philip because he thought it would make Naomi stay He also claims that had he known taking down the augustine gemara would have driven her away He wouldn't have done it. She tells him he's doing the same thing to philip now And philip doesn't deserve to die for marco's dreams This scene was like an emotional appetizer for what comes later in the episode Since it didn't strike me too much on an emotional level like the scenes for philip did later Part of that is because marco is such an enigma to me that when he's on screen I don't know what emotions are real and what is just manipulation His eyes definitely teared up when he discussed the augustine gemara So he seems to genuinely regret losing Naomi at the same time the words are meaningless He clearly has no trouble killing innocent people So if it wasn't the augustine gemara, he would have attacked something else And maybe it would have been done in a way where Naomi didn't feel culpable But she would never have stayed with marco after seeing the horrors he's capable of So it was an interesting scene and felt like one more puzzle piece in understanding marco Finally marco lets Naomi once again roam the ship But if she does anything wrong again, she's dead and marco says philip will know you for who you really are This scene told me that marco does want to kill Naomi But not at the cost of his relationship with their son So part of his motivation in letting her go here is he wants to give her a chance to betray them So philip will understand when marco ultimately executes her Of course, Naomi heads right to philip's room She tries to bond with him a bit before they get into the crux of their conversation Philip asks her what she meant when she said that she knew what he was going through She explains that marco manipulates you and makes you blindly go along with him He does that by making you feel like the center of the universe and crave his attention That blindness made her write the gamara code and marco is doing the same thing to philip now She asks philip if he feels any remorse for what he did He does not in one of the first emotional bombs of the scene Naomi tells him that she used to dream of all the things philip would do and become Now she only dreams that he'll one day regret all the things he's done Finally, he asks her why she left him. Naomi explains that she didn't intend to she had to leave marco But she searched months for philip and eventually accepted she wouldn't find him Then she reveals that after giving up the search she walked into an airlock and contemplated taking her own life This is the conversation i've been waiting for all season I wanted Naomi to have a chance to explain the whole story of how she was separated from philip I thought we mostly knew the story already. We've heard versions of it before But it was important for us to hear it again and experience it through philip's eyes And we did but on top of that we learned about the airlock which was new I thought dominique tipper's delivery of it was incredibly effective And the phrasing of why she decided not to take her own life was also interesting because it was all about philip I was going to open the door and then I realized that person that button Wouldn't change anything for you Either way a life or death you Will go into court without a mother. She's essentially saying that the choice of whether to live or die Hinged on her calculation of what it meant for philip So I don't think she could have made a stronger case that she truly loves him And he is the center of her universe and I think philip believed it all which ultimately actually worked against Naomi Because Naomi was so effective I think philip did start to forgive her and did start to feel a little bit of regret Which means internally he probably started to feel doubt about marco But we can't forget that he spent his entire life with marco. So that's where his core loyalty lies So it won't be hard to convince philip that his mother is emotionally poisoning him against his father Because that's exactly what she's doing Her story was effective and that rattles philip. So when he reasserts his loyalty to marco He turns against her hard Physically assaulting her if Naomi hadn't been as effective and hadn't been able to sway philip at all Then I think he would have been able to just brush the conversation off and wouldn't have felt so betrayed by her Like I said, I've been waiting for this scene all season and it did not disappoint I love Naomi's emotional revelation and philip's complicated reaction to it The revelations continue as we next see Naomi with sin He tells her the story of the last time they spoke on palace Naomi said she was going for a walk, but he noticed a look on her face Falling her He saw Naomi get me airlock and knew what she was thinking of If I had known it would come to that he says I would have helped you Then he confesses that she never found philip because he helped marco hide him from her her response and his defensive it crushed me He was my son. I'm so sorry. I thought you loved me. I loved all of us We were family I thought I was doing the right thing. I thought one day you will come back to marco This was another great emotionally effective scene. I loved sin's line I thought I was doing the right thing that encapsulates part of what makes this show so great We typically don't have mustache twirling villains. Everyone thinks they're doing the right thing There's no one that's just pure evil It also made me feel bad for sin and others like him because you really do see the hold marco has on people He's a charismatic leader and so effective. He's able to sway people to do monstrous things Which if they eventually wake up like sin, they come to regret So this was a great character moment between niomi and sin But also a nice way to show more collateral damage from marco's leadership As promised sin attempts to help niomi and asks marco to let her go marco chastises him for being weak And promises niomi will never be free Then philip stops by and asks for command of a ship He wants to show people what he can do and for people to know who he is marco replies by pointing out the many plans foiled thanks to philip's screw ups Essentially saying you're not ready yet Then he points out that people are chanting his name not philips and adds you are nothing without me Though he wraps up by telling philip you are my heir and one day you will lead the belters after i'm gone This was another interesting puzzle piece in understanding marco and aros Niomi continuously points out that marco only cares about himself I believed her to an extent, but at the same time I had to imagine that marco does believe in the fight for the belters at least to some extent But watching him tell philip they're chanting my name Makes me think the ego maniacal self-centered part of him really is his primary motivation In this conversation, he seemed much more interested in who is recognized for their accomplishments Than what is best for the opa also the fact that philip seems to be concerned with people knowing his name He must have gotten that desire from somewhere and I think that's him learning from his father So i'm starting to suspect that marco doesn't care too much about the belters He just saw this whole conflict between the belt earth and mars as an opportunity for him to gain power and notoriety And if that's true, I look forward to the veil being lifted for philip Perhaps philip will see who marco is and realize who he is becoming just in time to help stop marco But we'll see finally niomi is brought to see marco He informs her that she'll be free to go just as soon as they use her ship to lure the rossinante and destroy it He also tells her philip inspired the idea philip wants the belt to know that he is the one who destroyed the rossinante I think that's a slight bending of the truth in the opening of the episode Marco asks philip if they can use niomi's ship for an unspecified purpose And we saw him tracking the flight plan at the end of last week's episode So it is marco's plan, but I think he's decided they'll credit philip with it That's what philip wants so people start to know his name But more than that it's one more way for marco to stab at niomi Now she gets to watch her own son betray her and kill some of her loved ones Niomi pleads with philip, but he slaps her and accuses her of trying to make him weak And poison him against his family This was a particularly effective moment because of the earlier scene When it looked like there was hope for philip and the funny thing is he's not wrong She is trying to poison him against his family But the party leaves out is that she's doing so with the truth This was also a particularly painful moment because it felt like there's no coming back from it It's really hard for me to imagine philip and niomi ever fully accepting each other again After everything they just went through niomi is dragged away as she screams for philip and tells marco How much she hates him they prepare to launch her ship But sin notices she's at the airlock as he goes after her philip sees a security feed sin left up and follows I loved the somber music that kicked in as niomi heads for the airlock After hearing the story twice this episode They wanted us to think she was contemplating taking her own life here I didn't think that was going to happen But that somber score and sin crying after her both were so effective the scene definitely moved me Sin begs her not to do it, but niomi responds. You shouldn't have followed me Then he notices the needle in her hand She hits the button killing sin while philip watches and launching her into space without a suit She holds out as long as she can then injects herself With hyper oxygenated blood Which the show cleverly seated earlier in the season when holding injected monica with some when she was losing air in the shipping container Finally barely alive niomi reaches the ship. This was an amazing sequence It was the perfect blend of thrilling and emotionally effective Niomi has been backed into a corner all season and we've been wondering how she'll get out of it Finally she finds a way It's clever and physically challenging But not just that it came at a great emotional cost as well Sacrificing her old friend sin. There was also a lot of emotional buildup that had to happen to make this possible for her She's leaving her son possibly for the last time And I don't think she would have had the strength to do that had philip not betrayed her And maybe convinced her that he's too far gone and too much like marco now Also without sin's confession that he hid philip from her Maybe niomi wouldn't have been able to so callously let him die So it was an emotionally effective and complex moment Wrapped in a suspenseful thrilling escape sequence a great way to end a great episode Anyway, I think we can wrap it up there. Like I said, I loved the episode Let me know what you thought of the episode in the comments Let me know if you agreed with my take where you disagreed and we'll keep the conversation going And if you enjoyed this video, please go ahead and hit the like button Hit the subscribe button and hit the bell icon so you get notified when our next video drops We'll continue to review the show every week and have some other expanse related content on the way So stay tuned. Thanks for watching and see you on the next one take


I'm Carlos Picari. I'm not a software developer by profession, but I do this for a hobby. And this is my project filmulator, which is a photo editing specifically for raw camera photos that simulates the development of film. It's not a new project, but it may be new to many of you. And I started it way back in 2012. So, what is filmulator? It's a raw photo editor with library management, including importing and moving files around. It emphasizes three things, simplicity, over-flexibility, ease of learning for new users, and the streamlined workflow for experienced users. And in addition to that, it uses a tone-napping algorithm that simulates the chemical action of film development to achieve great results. So, it's different in many ways from existing photo editors. So, for example, I only have like 20 or so tools total in filmulator compared to pages and pages and pages and pages of tools that may do the same thing multiple different ways. So, I try to strike a new balance between flexibility and ease of use. Other tools might compare to flexibility. I prefer ease of use in filmulator. One thing that, when I started the project, I was very insistent on was having a very polished editor view. So, it has unconstrained, smooth zooming about the mouse cursor anywhere in the frame. Back when I started this, a lot of photo editors had kind of janky zooming, and panning is very slow in other editors, although they've great improved since. But I can have 60fps full resolution 4K screen panning around at any zoom level in filmulator. And it also has a fast preview of the same pipeline, so you get responsiveness to the sliders. And then eventually it recomputes at full resolution. Another difference with many of the popular raw editors like Rawthair Paint Darktable is that I actually support importing from CARD. So, I like to have it all in one tool. I don't want to have to use a rapid photo downloader or DigiCam before switching over to a separate image editor. I like to have it all in one program, and so filmulator lets you copy from a CARD or import in place, and it does simultaneous backup with checks and hash in the files after it writes to verify secure copying. And also, you can have it automatically create a directory structure for your photos so that you don't have to organize them manually. Another thing that I try to emphasize is that a lot of these other applications prefer to keep very minimal user interface help, I would say. Like tool tips that are entirely unhelpful sometimes. Like on the right it says vibrance, the amount of vibrance. Frankly, I would say that doesn't mean anything. Whereas in filmulator I try to explain every tool in clear language. Even if it's a little verbose, I also try to make the tool tips stay out of the way. So, in real use by power users they never get in the way, but for a new user, they're there to help. There is a manual too with explanations of all the tools and when to use them. So, it's not like I'm stamping on that aspect. But what might be the most interesting part about filmulator is the film aspect. So, when I started photography, I learned on actual film with that camera you see there in high school. And when I went to college I got a DSLR for the first time and I found that I was rather disappointed by the photos. I really couldn't put my finger on why I didn't like the digital photos. Something about the color, something about the way they rendered the skies. And so I racked my brain for like two years over what isn't about film that just looks good. And so what I realized was that after a few times when I developed film myself, I asked myself why is there an agitation step. If you're not familiar with film, you pour liquid into a tank that contains the film. And every few minutes you shake it. And I was wondering what the shaking was doing. And I realized that the aspect of film development that this shaking does is, it causes the diffusion of the film, of the developer around to make it uniform again. So what happens when film is exposed is that silver grains are activated in different parts of the film. In brighter regions more silver grains are activated and in darker regions fewer are. It's a stochastic process. And what happens when you put the developer in a liquid chemical is that the parts with more activated silver grains consume more of the developer and that slows the rate of development in the bright areas. And this depletion reduces the global dynamic range. But at the same time, because it's in a liquid, the liquid diffuses between adjacent regions of the film and the local contrast is enhanced by the bright regions stealing the plentiful developer from the nearby dark regions. The dark regions stay darker because they lost the developer to nearby bright regions. And so all I had to do is mimic the process instead of having to try and make a stab at the end result. So by literally simulating film development, it just makes the images look better. So what does it do? It lowers global contrast. In this image, I've raised the exposure but the film aspect has reduced the highlight brightness so that the overall global contrast is much lower. Although that's an extreme example and typically I wouldn't push it that far in real use. It also raises local contrast so you can see the clouds have more detail, the building has more pop and if you look in the tight crop, you can see that the tiles have more contrast and more color. And additionally, it naturally boosts the color in a way that will never induce clipping. What happens is the three color channels are basically three layers of film and if one of the layers is significantly brighter than the other, it does the same stealing of developer basically from the other two layers. And so in the case here, the red channel steals from the blue and green channels and enhances the color. And in this particular case, the actual flowers were just red and the weird thing is that no matter what I could do in other programs it's very difficult to remove the orange and yellow that appear when I take a photo of it. I have another all sorts of very interesting touches in the user interface. For example, I expose the pipeline which makes it easier to learn what each tool does. So at various points in the pipeline, which the tools are in pipeline order from top to bottom, you can see before the film step we have a histogram and of course we have the end result histogram at the top. And so you can see in a linear space what white balance is doing in exposure compensation. You can see how your highlights are behaving. It's the highlight recovery working. Did I clip a channel without needing to guess at it from the end result? In addition, in the organization view, I have a histogram of photos taken per day. So it's very easy to find a trip you went on or a photo shoot you had where you took a lot of photos. Although recently I've seen this in dark table, so it's not unique to me. And I also put a lot of effort into a very nice cropping tool and filmulator that you only press one button and it enables you to choose aspect ratios as you wish. And it's just super polished. You hold control to lock the aspect ratio and you can press shift to snap to preset aspect ratios. And you'll just choose the nearest one and size accordingly. So a little bit about how I got here. Back when I first started in 2012, a friend and I started just with a MATLAB prototype. And this was extremely slow. It took minutes and minutes to process a single 1 megapixel image. And then over time we enhanced it with speed. We implemented the C++, we multi-threaded it, changed memory accesses and stuff. And then we also changed it so that the workflow is smoother. So instead of you having to feed it tips, it would generate them. I created the GUI and that's how we've gotten here. However, recently the Libraw project which we were relying on for loading and demosaicing removed the better demosaicing algorithms from the demosaic packs. They discontinued them. So in order to support this functionality in filmulator, I started the libRT process which is a name that might be subject to change. And we took GPL licensed algorithms from Roth Therapy and now are sharing this with any other project that likes to use this library. And this is better than what Libraw had, which were 10-year-old versions of these algorithms. Now they're maintained, now they are much faster. And we have more stuff too. So these filmulators are very usable right now, but there's a lot of things that it's missing. Things I'd like to add in the future, noise reduction, sharpening, distortion correction for lenses, deleting images, tagging images, pulling images as you import, and building for Windows. But there are things that I don't plan which is basically anything with not very much return on user interface complexity. So if you want split toning or more local adjustments, I'd ask that you just use them in another tool. So who's filmulator 4? Filmulator is for people who find post-processing to be chore, more or less. That was my approach to it. I didn't like spending 15 minutes on a photo to make it look good. Now I spend 20 to 30 seconds per photo. But at the same time I don't want to use presets. If you want the final creative say in every image you output, filmulator can give you a result quickly. On the other hand, it's only for people who want a natural looking result. If you want the most capable flexible program, if you want cross-processing emulation or glitch art or something, or if you like spending an hour dodging and burning each image, this is not really the program for you. Or if you want technical accuracy, it's generally designed for pleasing this over accuracy and simplicity or flexibility. So if you'd like to, please check it out and join us on the Pixels Forum where I have a subcategory. I'd like to thank my friends, Omer, for starting the project with me, and all sorts of other people from the community for helping me out, including making an effort to continue some integration from the last minute. And I'd also like to thank the whole open source community for inspiring me and encouraging me to get back. Any questions?


Welcome to lecture number 22 on measure and integration. If you recall, in the previous lecture, we had started looking at the properties of Lebesgue measure and of Lebesgue integrable functions. We started looking at analyzing, when does a function which is Lebesgue integrable on the interval a, b and its relation with Riemann integral of the functions on the interval a, b. Let us, we had started looking at the proof of the theorem namely that, if f is a function defined on an interval a, b to R which is Riemann integrable, then we wanted to show that it is also Lebesgue integrable and the Riemann integral is same as the Lebesgue integral. We will continue the proof of that theorem and then go on to analyze some more properties of the space of Lebesgue integrable functions on the interval a, b. So, today's lecture is going to be mainly concerned with Lebesgue integral and its properties. So, the theorem we wanted to prove was that, if f is a function defined on an interval a, b to R and it is Riemann integrable, then it is also Lebesgue integrable and the Riemann integral of the function is same as its Lebesgue integral. So, to prove this theorem, we started with this idea that, since f is Riemann integrable, there exist sequences psi n and phi n of step functions on the interval a, b such that this sequence psi n is monotonically increasing and the sequence phi n is monotonically decreasing and the function f is between these two sequences phi n and psi n for all points x belonging to a, b and the Riemann integral of psi n converges to the same value as the Riemann integral of f and it is the same as the limit of the Riemann integrals of the step functions phi n. So, let us recall these steps which we had proved last time.  So, what does the Riemann integrability imply? The Riemann integrability of the function implies the following namely, there exists a sequence P n of refinement partitions of the interval a, b such that the norm of these partitions goes to 0 and the upper sums of f with respect to these partitions that decreases and the upper sums and the lower sums of f with respect to P n increases and the common value is the integral. So, limit n going to infinity of upper sums is same as Riemann integral of f and that is same as the limit of the lower sums. So, this is because f is Riemann integrable. Now, let us see what are the upper sums and what are the lower sums. We need to analyze them slightly more carefully to look at. So, this is, let us draw a picture of the function say the function looks like this. So, this is a and this is b and we get the partition. With respect to a partition, let us say this is the general interval say x i minus 1 and x i. So, in this interval look at what is the smallest value of the function. So, what is the smallest value of the function? That is this. So, look at this height and look at the largest value of the function in that interval. So, largest value of the function is somewhere here. So, look at that height. So, lower sums consist of the areas of these rectangles with height as the blue line and the upper sums consist of the sums of all the areas which are the green lines. So, mathematically what this means is the following. So, let us write mathematically what it means. So, mathematically these things mean the following namely. So, look at consider the function. So, let us write. So, consider let us define define.  So, let us say that is the partition. So, define let us say m 1 to be the supremum of the function f x x belonging to a that is less than or equal to x 1 x 1. And let us write m k to be the supremum of the function in the general interval. So, f x for x between x i minus 1 and x i. So, keep in mind here I am taking left open and right close here at the end point is both sides close. So, these intervals are disjoint intervals. So, what I am doing is in the first part I am looking at this, then I am looking at left open, right close, left open, right close, left open, right close. So, I am partitioning the interval a b according to the partition points p n and then looking at the supremums in the respective intervals. Similarly, let us write m k to be equal to infimum of f x in x x i minus 1 less than or equal to x i and m 1 to be the infimum in the first interval. So, that is f x x in x 0 x 1. So, what is this value? This m 1 and m k's are corresponding to the height which is the green line. So, that is the maximum value of the function in the interval x i minus 1 to x i and the blue ones correspond to small m k's. So, once we have done this mathematically, let us define the required functions. So, let us define phi n is the function which is summation m i indicator function of x i minus 1 to x i i equal to 2 to n and in the first one, let us put that value as m 1, the indicator function of A x 1. Similarly, let us write psi n to be sigma i equal to 2 to n capital m i the maximum value in the interval x i minus 1 to x i and capital m 1 in the first interval. So, that is indicator function of A to x 1. So, these are the functions we defined. So, they are corresponding to the function which is phi n, small phi n will look like the minimum values like this and it will look like this. And the capital and psi n's, they will look like maximum values.  So, quite clearly, these functions phi n and psi n are step functions and phi n of x is less than or equal to f of x and less than or equal to psi n of x. So, as a first step, the Riemann integrability of the function f over the interval a, b gives us a sequence of functions phi n and psi n, where each phi n is a step function, each psi n is a step function and phi n is less than or equal to f of x is less than or equal to psi n of x. And since our requirement was that Riemann integrability implies that the sequence p n of partitions is a sequence of refinement partitions. So, that implies that the sequence psi n will be a decreasing sequence and phi n will be an increasing sequence. So, let us write that observation namely that, so we have phi n's. So, each phi n psi n is a step function, phi n's are increasing and psi n's are decreasing. Moreover, further, let us look at the Riemann integral of the function phi n x dx a to b. So, because phi n is constant on each sub interval of the partition, this is nothing but equal to m 1 times the length of the first interval.  And similarly, the Riemann integral of the function psi n x dx is equal to capital M 1 in the first interval times the width of the interval that is x 1 minus a plus k equal to 1 to n the areas of the other rectangles, so that is capital M k times x k minus x k minus 1. So, those are the Riemann integrals. And by the definition of the upper and the lower sums, this is precisely the lower sum of f with respect to p n and this is precisely the upper sum of the function f with respect to the partition p n. And saying that the function is Riemann integrable implies that the upper sums and the lower sums converge to the same value. So, this and the Riemann integrability implies that the Riemann integral a to b of phi n x dx limit n going to infinity is same as the Riemann integral a to b f x dx and that is same as the Riemann limit of the upper sums, so that is limit n going to infinity the Riemann integral a to b of psi n x dx. So, that proves our first step. So, as a consequence of the Riemann integrability of the function f, we have constructed two sequences of step functions psi n and phi n, where psi n is monotonically increasing and phi n is monotonically decreasing and limit of both the integrals of both of them converge to the Riemann integral of f. Now, let us observe at this stage. So, in some sense the step functions and the Riemann integrals are the building blocks for the Riemann integral. Now let us observe that the lower sum of the function f with respect to the partition which was the Riemann sum which was the Riemann integral of phi n is also nothing but the Lebesgue integral of the function phi n with respect to the Lebesgue integral, because this is this function phi n is a simple function, is a simple measurable function and its integral is nothing but this integral. So, the observation is that for every n integral a to b of phi n x dx, the Riemann integral is same as the Lebesgue integral of the function phi n with respect to the Lebesgue integral over the interval a b and this observation is simply by the fact that phi n is a step function. So, hence it is a simple measurable function that is integral is nothing but the value times the Lebesgue measure of the portion on which that value is taken and that being here sub intervals. So, it is same as the Riemann integral and similarly the Riemann integral a to b of psi n x dx is equal to integral over a b of psi n d lambda. So, this is the observation which is going to play an important role for us. So, now let us define, let us consider the, because we have got the observation that the function f n, the function phi n is always dominated by f x is less than or equal to psi n. So, let us look at the function psi n minus phi n. So, look at the function. So, consider the sequence psi n minus phi n. So, look at the sequence of these step functions. These are step functions as well as they are simple measurable functions and they are non-negative. So, they are non-negative simple measurable functions and by Fertu's lemma. So, we are going to apply Fertu's lemma to this. Consider this sequence and apply Fertu's lemma. So, what will that give me? So, that will give me that limit inferior of psi n minus phi n d lambda limit n going to infinity integral over a b. So, the Lebesgue integral of the limit inferior is less than or equal to limit inferior of the integral psi n minus phi n d lambda. So, that is by Fertu's lemma. But, let us observe here that integral of psi n over a b minus integral of phi n over a b, the limit inferior of that is equal to 0, because the Lebesgue integrals of psi n are same as the Riemann integrals of psi n and Lebesgue integrals of phi n are same as the Riemann integrals of phi n and those Riemann integrals converge to the Riemann integral of f. So, this right hand side is equal to 0. So, that means that the limit inferior of psi n minus phi n, that function is a non-negative function and its integral, Lebesgue integral is equal to 0. So, that we know implies that the function must be 0 almost everywhere. So, this implies that limit inferior of the sequence, which is psi n minus phi n x must be equal to 0, almost everywhere x. But, we know that psi n's are increasing, psi n's are decreasing and phi n's are increasing. So, this limit inferior exists. So, that implies that limit n going to infinity of psi n's is equal to limit n going to infinity of phi n x almost everywhere x. But, we know since f of x is between phi n and psi n of x, this implies along with the earlier fact, this implies that limit n going to infinity of psi n x must be actually equal to f of x, actually equal to limit n going to infinity of psi n of phi n of x for almost all x. So, this must happen. But, that implies because each psi n is a measurable function, each phi n is a measurable function, this implies f is measurable. But, recall f was remain integrable function. So, obviously it is a bounded function. So, implies that f is Lebesgue integrable because f bounded. So, by boundedness of f, every bounded measurable function and this is defined on AB, which is a finite measure space. So, that must be integrable. That we had observed earlier. So, f is Riemann integrable. So, only we have to prove now. So, claim that integral f d lambda over AB is equal to integral a to b of f x d x. So, this is the only thing left to be shown. So, what we have shown till now is f is Lebesgue integrable. So, this integral exists. Now, let us observe one thing. Not only f is Lebesgue integrable, it is a limit of a sequence of functions phi n's. Phi n's converge to f of x. So, the sequence phi n is converging to f of x and psi n's are decreasing to f of x. So, whichever fact we require, you can use. So, let us use the fact that psi n's are limit of psi n's converge to f of x. They are decreasing and each psi n is a integrable function. So, we can apply Lebesgue's dominated convergence theorem to conclude. So, by dominated convergence theorem, since psi n x converges to f of x, almost everywhere x and psi n's are decreasing and integrable psi n's decreasing psi n's integrable. So, implies by Lebesgue's dominated convergence theorem that integral of f d lambda over A B must be equal to limit n going to infinity of the Lebesgue integral of psi n d lambda. So, that is the observation we have already made that the Lebesgue integral of the step function psi n is same as the Riemann integral. So, n going to infinity. So, that is A to B of psi n x d x. And this Riemann integral we have observed is the upper sum and which limit is equal to… So, this is the limit of the upper sums of f with respect to p n and that converge to integral A to B f x d x. So, that will prove that integral, Lebesgue integral of f is same as the Riemann integral of f over d lambda. So, that proves the theorem. So, let us go back and recall the proof. What are the first step? As a first step in the proof, using the Riemann integrability of the function, we construct two sequences of step functions, psi n and psi n, so that f is trapped in between them. And the upper sums are nothing but the Riemann integrals of psi n and the lower sums are nothing but the phi n. So, that means the Riemann integral of psi n converges to the Riemann integral of f and which is also equal to… So, here is the equality sign equal to the Riemann integral of phi n. So, that is this construction is purely from the fact that the function f is Riemann integrable. And the second observation is that each phi n and psi n being a step function is also measurable and Lebesgue integrable. And the Lebesgue integral of phi n is same as the Riemann integral of phi n and the Lebesgue integral of psi n is same as the Riemann integral of psi n. So, that is the second observation we will make. So, these two Riemann integrals of the step functions are same as the Lebesgue integrals. And now because of the earlier consequence that the Riemann integrals of phi n and psi n can work through the Riemann integral of f, look at the difference phi n minus psi n. So, look at that sequence of measurable functions phi n minus psi n that is a measurable non-negative measurable function. And an application of Fatou's lemma will give us that this psi n and phi n both must converge to the same value and that is f of x almost everywhere. So, that will imply that f is measurable and being a bounded measurable function on a finite measure space it becomes integrable. And now the psi n's are decreasing to f of x. So, an application of Lebesgue's dominated convergence theorem gives that the Riemann integral of f is same as the limits of the Riemann integrals of psi n's which are equal to the Lebesgue integrals of psi n and that dominated convergence theorem gives you that is the Lebesgue integral of f over a b. So, that proves the theorem completely namely. So, this is the step we wanted to this was the beginning of our lectures namely we wanted to say that to remove the defects of to remove the defects of Riemann integral namely that the fundamental theorem of calculus may not hold and that the space of Riemann integrable functions may not be complete under what is called the L 1 metric we wanted to extend the notion of integral from Riemann integrable functions to a bigger class. So, we have constructed here a class of functions on a b which are called the Lebesgue integrable functions on a b and we have shown that if the class of Riemann integrable functions is a subset of the class of Lebesgue integrable functions and the notion of Lebesgue integral extends the notion of Riemann integral beyond the class of Riemann integrable functions. So, that was that is the first step in our extension theory. So, Lebesgue integral is an extension of the Riemann integral. So, as a next step we want to look at that. So, the space of Riemann integrable functions are inside the class of Lebesgue integrable functions and there is here is a observation which one can observe from the proof of this theorem that if a function is Riemann integrable then it must be continuous almost everywhere. So, to conclude this observation from the proof itself basically what we have to look at is that the function f is the limit of those step functions. There is a limit of the step functions. So, if we leave aside those partition points. So, remember we concluded that f is limit of those step functions phi n's and psi n's. So, with that we concluded namely that here. So, we concluded that this is the fact that we proved in our theorem that the limit of the step functions phi n and psi n is f of x. So, that almost everywhere f is limit of psi n's and psi n's are piecewise continuous functions. So, the points where psi n's may not be continuous are possibly the points of the partition points of p n's. So, if we pull together all the points partition points they will be at the most countably many and if we remove them along with this almost everywhere set. So, outside a set of measures 0 this function f will become continuous. So, I am just indicating the possibility of a proof of that. So, those interested probably should look into the text book and in fact the converse of this theorem is also true namely that if f is a bounded continuous function which is bounded function which is continuous almost everywhere then f is Riemann integrable. So, that means there is a characterization of Riemann integrable functions in terms of continuity namely a function f is Riemann integrable if and only if it is continuous almost everywhere. So, we are not given the proof of this. So, those interested probably should look into the text book as mentioned above the in an introduction to measure and integration in which the complete proof is given. But what we have wanted to indicate that the proof of the theorem proof of one part of the theorem namely for a Riemann integrable function it should be continuous almost everywhere is already included in the proof of the fact this now we proved that Riemann integrable implies it is Lebesgue integrable. So, that is one part of the properties of the space l 1 a b that R a b the space of Riemann integrable functions is in l a b. Now, let us look at a metric on l 1 of a b.  So, it is a linear space. So, it is a vector space over the field of real numbers. So, on this we are going to define a notion of a magnitude.  So, this is called the l 1 norm of the function f which is in l 1. So, clearly it is a number finite number because f is integrable. So, this right hand side exists and is finite and you are integrating a non-negative function. So, the first property namely the norm l 1 norm of a function is bigger than or equal to 0 for all functions f in l 1 of a b. So, that is obvious. The second property namely supposing this function f is 0 almost everywhere then clearly integral of the function will be equal to 0 that we have already observed. So, norm will be equal to 0 and conversely if the l 1 norm is equal to 0 then the function absolute value of f of x being a non-negative function its Leverk integral 0 that implies that the function must be 0 almost everywhere. So, the second property namely the norm is equal to 0 if and only if the function is 0 almost everywhere and the third property which is that if you multiply the function f by alpha the norm of alpha f is equal to the absolute value of alpha times norm of f and that is obvious because in the definition if you replace f by alpha f then this being a constant the property of the integral. So, the integral of alpha f is equal to mod alpha times integral mod f.  And finally, the triangle inequality property namely if f and g are integrable functions then we have already shown that f into g is also a integrable function and integral of the absolute value of f plus g will be less than or equal to integral of absolute value of f plus integral of absolute value of g by the triangle inequality of the numbers.  So, these are the properties of this magnitude or this norm of f 1. At this stage I just wanted to point out that this is very much similar to the Euclidean metric or Euclidean norm on R n. See on R n for a vector x with components x 1, x n we normally define the norm to be equal to we can take the norm to be equal to sigma mod of x i i equal to 1 to n. So, this is what is called the l 1 norm on R n. And now, so what we are saying is that if x is a vector with n components then this must be the norm l 1 norm. Now, treat a function f defined on an interval a b to R. So, treat this treat as a vector with components with as many components as points in a b. So, I want to treat this f as a vector with components as many components as points in a b.  So, you can treat f of x, x belonging to a b as a vector. So, if you treat that way then what is the l 1 norm of f you would like to define. So, keeping in mind, so take the absolute values of the components. So, take the absolute value of the components. So, this is the component take its absolute value and you want to sum it and the summation is nothing but integral d lambda. So, this is in that sense this is the perfect generalization of the ordinary l 1 norm on R n. So, the only problem in this is that we do not have the property that if l 1 norm is equal to 0 if and only if f is equal to 0. So, only we have got that the l 1 norm is equal to 0 if and only if f of x is equal to 0 almost everywhere. But, let us keep in mind that the l 1 norm does not change if we change the function on a null set on a set of measure Lebesgue measure 0. So, with that observation in mind from now onwards what we do is in l 1 of a b we identify functions which are equal almost everywhere. So, if two functions are equal almost everywhere if f and g in l 1 are same are equal almost everywhere lambda then we treat these functions to be as same.   So, that is an observation which you should read from that textbook already mentioned. So, this was one of the defects of Riemann integral that motivated the development of Lebesgue integral namely the space R a b under the l 1 metric is not a complete metric. So, this is not a complete metric under the l 1 metric. So, but there is a theorem namely every metric space can be completed. So, there is an abstract theorem in metric space is that if every metric space can be completed for example, the look at the set of rational numbers that is not complete under the usual distance of absolute value as a distance and its completion is the real numbers and that is the important property of real numbers that it is complete under that metric.  What we are going to show is that that completion is nothing but l 1 of a b. So, we are going to prove that l 1 of a b the space of all Lebesgue integrable functions on a b can be realized as the completion of the space R a b under the l 1 metric.   So, that will show that l 1 of a b is a realization of the completion of the space R a b like rationales are dense in the real line reals are dense real the field of real numbers is complete that is why we say that real numbers is the completion of the field of rational numbers. So, in the similar way we want to prove that l 1 of a b is the completion of the space of R a b.  So, the completion part is called the Ries-Fischer theorem. So, the Ries-Fischer theorem states that l 1 of a b is a complete metric space in the l 1 metric. So, let us look at a proof of this. So, the proof that to prove that it is a complete metric space what we have to show? We have to show that every Cauchy sequence f n in l 1 of a b converges to a value in l 1 of a b. Every Cauchy sequence in l 1 of a b is convergent and convergent to a point in l 1 of a b. So, that is what we have to show. So, for that let us show that. So, this is what we have to show that there exists some function f in l 1 of a b such that f n minus f l 1 norm converges to 0 as n goes to infinity. So, to prove this fact here is an observation what we will show is it is enough to show that there exists a subsequence of f n which is convergent in l 1 norm. So, what we will show is to show that f n is convergent in l 1 metric it is enough f n is a Cauchy sequence to show that a Cauchy sequence is convergent it is enough to show that there exists a subsequence of the Cauchy sequence which is convergent that will prove that the sequence is convergent. So, to do that so we have to produce a subsequence of f n which is convergent to a function in l 1. So, let us look at the first step of our construction to construct that subsequence we are going to use the Cauchyness of the sequence f n. So, f n is Cauchy. So, the first step is that saying that the sequence f n is Cauchy implies that I can pick up a subsequence f n k of f n such that the norm of f n minus f n k is less than 1 over 2 to the power k for all n bigger than or equal to n k. So, to do that we start with so what is Cauchyness means? So, saying that the sequence f n is Cauchy saying that the sequence f n is Cauchy that means it is same as for every epsilon bigger than 0 there exists some stage n naught such that norm of f n minus f m is less than epsilon for every n and m greater than or equal to n naught. So, that is Cauchyness. So, to start our construction, take epsilon equal to 1 and find n 1 such that norm of f n minus f m is less than epsilon equal to 1 for every n and m bigger than n 1. So, in particular when m is equal to n 1 that will give me so that is f n minus f n 1 will be less than 1 for every n bigger than or equal to n 1. So, that is the first stage. Now, suppose n 1 less than n 2 less than n k have been constructed have been found. So, now use Cauchyness. So, find n k such that so how do I find n k?  So, the next one we have to construct n k plus 1. So, I will find n k plus 1 such that n k plus 1 is greater than n k and this property holds.  So, I can put it k plus 1 also that does not matter k plus 1 for every n bigger than or equal to n k plus 1. So, by induction there exists n 1 less than n 2 less than n k less than so on such that norm of f n minus f n k is less than 1 over 2 to the power k for every n bigger than or equal to n k. So, that is step one we do that. So, once that is done we go to step two and the step two is showing that this subsequence that we have constructed has the property that the sum of the l 1 norms of f n 1 plus the l 1 norm of 1 to infinity of this is finite. So, that the sums of the l 1 norms of f n 1 plus the l 1 norms of f n j plus 1 minus f n j j 1 to infinity that is all finite and that is that follows from the effect that just now we looked at this.  So, if I specialize n to be equal to n k plus 1 then I have this property for every k.  So, that will prove that the required property step two namely sums of norms of these quantities f n 1 and this is finite. Once that we have that now I can apply my series form of the Lebesgue's dominated convergence theorem.  So, that is precisely follows from the series form of the Lebesgue's dominated convergence theorem. So, if I look at this series then I know that L 1 norms of this series is finite. So, that is precisely the perfect situation where the series form of the Lebesgue's dominated convergence theorem applies and says that these functions they must the series must converge almost everywhere. So, this sum must exist almost everywhere and if you denote the sum by f of x then f of x equal to this exists almost everywhere and it also says that that function is actually a integrable function and integral of f is equal to integral of f n 1 plus integral of the sums of the corresponding series. So, this integral of f is equal to integral of f n 1 plus this series. So, we have located a function f and now was only to claim that the difference f minus f n j goes to 0 that the f is the limit of that subsequence. So, let us look at. So, note that if we look at f minus f n j that is precisely equal to summation k equal to let me n j.    So, that goes to 0 as j goes to infinity. So, that will complete the proof that hence the f minus f n j goes to 0 as j goes to infinity. So, that will prove that the subsequence f n j is convergent. So, let us just go back to the proof once again. Basically, the proof requires one observation namely to show that a sequence a Cauchy sequence is convergent. It is enough to produce a subsequence which is convergent and that subsequence is produced in such a way that by using the Cauchyness we produce that subsequence with the property that the norms of the consecutive terms of that subsequence are less than 1 over 2 to the power j. Once that is done, we apply the series form of the lab-examinated convergence to conclude that the sum of f n 1 x plus summation f n j plus 1 x minus f n j that exists almost everywhere that is a integrable function and the integrals converge. Once we have that, it is obvious that norm of f minus f n j goes to 0 because once we subtract that the remaining thing is a tail of the series 1 over 2 to the power j and that must go to 0. So, with that we prove the Ries-Wischer theorem. So, today we analyzed two important things namely one that the space of Riemann integrable functions is inside the space of Lebesgue integrable functions, Lebesgue integrable on the interval a, b and the notion of Lebesgue integral extends the notion of Riemann integrable. So, that was one property and the second property we observed that the space of Lebesgue integrable functions on the interval a, b under the L 1 metric is a complete metric space. So, and we will continue this analysis tomorrow and we will show that the space of Riemann integrable functions which is inside the space of Lebesgue integrable functions sits inside as a dense subset and that will prove that L 1 f a, b is the completion of the space of Riemann integrable functions. Thank you.


Hi, I'm Alex Bannack-Brown, based at the Quest Centre at the Berlin Institute of Health, and today I'm going to discuss research ecosystems and the role of R in effective evidence synthesis, how we can build bridges between researchers. To give you some background, I work in evidence synthesis in translational biomedicine. We take evidence from preclinical research and synthesize it to inform decisions for clinical research and to refine and improve our own experiments. Preclinical reviews and preclinical research are not very common, primary research reports are not reported in very standardized ways, and of course the evidence synthesis process is a very resource intensive one. Our aim is to create research ecosystems in biomedicine to increase good quality research and to improve the translation of biomedical findings to improve human health. Where preclinical research is informed by systematic reviews and where preclinical research is synthesizable. So what are research ecosystems? Open research ecosystems are communities of researchers, evidence synthesis, tool makers, information specialists, data managers, etc. that collaboratively recognize evidence synthesis as the end goal of research. Research ecosystems support researchers to design, undertake and report primary research and evidence synthesis in a way that optimizes reuse, translation and sharing of data and methods. And research ecosystems are based on shared, open principles, transparency of research methods and data, both in evidence synthesis and primary research. On the left here we've got the current evidence synthesis system. Reviewers are separated from the research process. Data could be missing if it is not published and then does not get synthesized. Synthesis is a resource intensive task and evidence synthesis also may be delayed in relation to when new data is available. On the right we've got our future goal that systematic reviewers are embedded within the research process, supporting researchers to conduct evidence synthesis in their own domain. Researcher is available for synthesis and may even be directly available for synthesis by passing reports in the traditional published manner. And the processes of evidence synthesis and the reports of evidence synthesis are also open to the public and stakeholders. To realize this idea we are working to build research ecosystems in translational biomedical research. A project excitingly we've recently got some funding to kick start. We're working to increase education about systematic reviews in biomedicine. We're working to provide widespread infrastructure for researchers, both to conduct systematic reviews and also to conduct reproducible primary research. We're bringing together stakeholders to support this, both preclinical researchers, systematic reviews, systematic review methodologists, statisticians, information specialists as well as patient advocates and others. We're working to create a community code of conduct for what it means to be part of such a research ecosystem and how we can best work together, including the best structure and format for this ecosystem and for the communication. And we're exploring additional infrastructure that may be needed in future in order to allow for the growth of the ecosystem. And infrastructure here is really key to supporting the widespread growth and uptake of evidence synthesis. And Brian Nosek's cultural change pyramid really highlights this. Infrastructure is the foundation allowing it to be possible and supporting all other steps so that we can build communities to make these practices normative. And R is a wonderful infrastructure framework and existing community that already supports and is closely linked to the principles of open evidence and open research ecosystems. And the number of tools that we already have available is highlighted in this amazing conference. We're building, testing, validating and integrating new tools all the time. We have tools to support the evidence synthesis process and tools to automate the steps in evidence synthesis process. We've got tools to engage with external databases and other tools. And we've also got tools to export our synthesis and share these results and findings with others. But surrounding this more broadly, we have groups and tools that support evidence synthesis frameworks and support these communities. We also have education and tools to support education, both for systematic review methodology, but also education on how to use these tools themselves. And most importantly, we have tools to support integrating primary research into the evidence synthesis pipeline. Existing tools for cleaning experimental data, building reproducible analysis code, and tools to help us disseminate our data and our research. And just wanted to draw attention to the talk that Emily Hennessy gave yesterday about making primary research synthesizable. And we can use our existing overlapping communities to build pipelines to make best use of the existing tools to collectively identify gaps for new tools and to share these best practices that we've got. On top of infrastructure and tools, it's important to build a strong community based around clear shared values. And that's something that we're working towards in translational biomedicine. Transparency of methods, of data, of research processes, ensuring quality that we foster open reproducible research, both primary as well as meta research. And that research and data are open and fair, findable, accessible, interoperable, and reusable. And that we have these best practices of workflows and best practices in data sharing in practical solutions. And that's something that relies on effective communication, using existing platforms for optimizing how we communicate. Slack, forums, conferences, et cetera. How we can set clear standards, values, and how we can shape our role as community members by setting codes of conduct to ensure that the community that we're a part of is fair for all. And support, how we can support each other in realizing these goals. A starting place that we're working with is fostering sharing and learning. For example, with introductory workshops to reproducible research in R, introductory workshops to systematic reviews and evidence synthesis. These are just some of the workshops we deliver at Charité in Berlin. And I think support is a great place to finish up. Because support both within the community, supporting each other. But also support from out with the community, out with the immediate community, engaging with other communities that can help us grow. And I think support really underpins a strong community and helps us achieve the goal of open research ecosystems. Not just in biomedicine, but for everyone. And just briefly, I've presented some of the work today that we're applying a research ecosystems and this approach in biomedicine. This is really work in progress. Thank you very much for listening and I'm really looking forward to hearing your thoughts and engaging in discussions on Slack. Thank you.


Hey, what's going on guys picture prime here once again with another exclusive Transformers review now This was a figure. I was not going to pick up But everybody and their brother is posting about her on Facebook and I figure hey since I'm an Amazon Prime member I might as well pick up the exclusive siege Greenlight and Dazzle star Dazzle star is probably one of the worst Transformer names that has come out. That's That ranks right up there with eight face. So anyway, here you have green light in robot mode Dazzle star, which is a Recaller of lionizer now since I skipped out on lionizer. I thought this was a pretty good deal They got a nice flame effect. So it looks pretty cool There's your front of the box side of the box with the siege artwork This side really cool artwork of both figures on the back Vehicle mode robot mode lion mode sword mode and she's wielding the different battle masters bottom's got the UPC top says Transformers war for Cybertron siege So let's go ahead and get her ripped out of the package and see if she was worth my prime membership in that two-day shipping and Welcome to Patriot Prime reviews Now once you get green light and Dazzle strike out of the packaging This is what you're going to get. There is the instructions right here These are the fantastic siege instructions that make everything very easy to follow and You just can't open them Easy to follow and see how to do the transformation There is micro masters and battle masters on the back. So there you go. There's the instructions. You also get the Combiner fist fanny pack that all the combiner Wars figures get so there is her fist So that should alleviate many questions where people are wondering if she is a combiner or not She is you also get this awesome flame effect. I really like this this attaches to Dazzle strike now Dazzle strike. I swear.  I Hate that name Dazzle strike is a repaint of Lionizer now I skipped out on lionizer. It just didn't look like a good figure to me So getting both of these for one price and not too bad I'm still not really impressed with this figure from what I could tell from pictures The difference between this character and lionizer is she I guess it's a she has the green inside the blade And there's like white paint Above the eyes she's got eyebrows Transformation she turns into a bladed weapon you take the back gun Flip down snaps into place for a blade.  So there you have the sword This is what I really like. This is cool. You attach this flame effect to the sword. Check that out Whoosh, I dig it. That looks really really cool So yeah, there's one there's one thing. It's really impressed me already with this set Now, let's take a look at green light herself She is a repaint remold of Moon Racer and Nova Star So what I'm going to do since those figures have been reviewed countless times Instead of doing a full review of this figure. I'm going to show you the differences between her and the other two Okay, here we have the three ladies all together now the first thing I'm going to show you is the Hand Fanny pack thing Every one of these is the exact same mold except with different colors and different clear pieces You have Moon Racers here clear blue Nova Star clear clear and Green lights green lights I swear this looks like a key lime cookie the colors with the white The tan and the green This this looks like a dessert. That's or maybe I'm just hungry. So anyway, there's your fanny packs all of them Have the exact same mold not fanny packs prime armor. I got quick calling them that so there is your prime armor all the same Now green light as I stated before is a remold slash Recaller of the Moon Racer Nova Star mold and the main difference is the head sculpt and the torso Okay, here we now have a close-up where you can take a better look at the head sculpts and Torsos of the figures first thing, of course, you'll notice is the different head sculpts Moon Racers right here She is my favorite. She's the most Feminine looking of the trio. Then you have Nova Star. She looks really good. I love the painted in eyes They have actually the face paint on these two Nova Star and Moon Racer is fantastic Her face Not so much. I guess she's not a fan of makeup. She doesn't look that feminine compared to the other two Now as far as the torsos you have Moon Racer with this clear stomach You have green light with the stamped Autobot logo Then you have kind of a different type of abs here. Actually, she's got a six pack four pack She's got well sculpted abs. She's got more of a Robotic look to hers which makes sense Autobot symbol up there on the chest But right here these are the big differences with the figures aside from the paint the heads and The torsos other than that the molds are exactly the same Now vehicle modes are pretty much identical. There's a few mold differences and the paint applications But other than that transformation is the same and the vehicles are The same for these figures except for one glaring problem. Let me go ahead and remove the Back portions off the vehicles so I can show you If you look at the rear section of both Moon Racer and Nova Star These are where the arms transform. Let me go ahead and pop this open so you can see You've got the arm and the fist. There's a little peg right here. That slots into this section. So that goes up Slots in and then the fist Folds in out of the way. So that is a fairly clean looking Transformation same thing with Nova Star here fists fold up And there's a little peg that slots right there to attach it and Make it a clean transformation. So I'm transforming green light. I know how to transform these guys I'm transforming her and for the life me. I cannot figure out why the arms won't work They are molded completely different. There's no little tab. You cannot line this up I have tried and tried. There's no slots nothing to line in the fist are Molded in place so they don't flip in at all So you have to kind of mold it over and around and I think that looks really sloppy. I Mean and the fists kind of drag along too. So you know for an exclusive figure and If you're going to copy a mold, let's go ahead and copy every aspect of it There's really no sense why she doesn't have fists that fold in or why the arms are Molded so different whoops those popped off Or why the arms have to be molded so different that they just don't work So there is one complaint for this figure I mean, that's they drop the ball on that. I mean vehicles. All right It's different enough from the others But that kills it for me that sucks and I've went through the instructions trying to figure out And it's the same way for the others take the arms over fold them in place and there you go But that's what you're stuck with. I guess I could Know that that sucks come on hasbro So if I'm doing it wrong, let me know in the comments, but that seems to be what I'm stuck with So there we go. There she is in vehicle mode the Amazon exclusive Transformers war for Cybertron siege green light with dazzle strike is a pretty good set I really like the dazzle strike sword Battlemaster not a fan of the name the flame effects really cool and I actually like the weapon I may go back and grab a lionizer now that he's pretty cheap It's really cool that we now get more of the fem bots to add to the collection and for you guys who use them as Combiners, there's you another limb But the QC issue. I mean the problem with her transformation.  So there we go guys There is the Amazon exclusive siege green light with dazzle strike Okay, once again, I didn't go over the combiner limb modes because I'm really not going to display her that way Plus, I don't have an elite of one just yet.  I really don't think she's really that worth it She does not look very feminine at fem. That's a hard word to say this early in the morning She doesn't look that girly at all compared to the other two. I do like the Dazzle strike figure with the flame effect. That's really cool But you get to thinking this is a 2499 set. You got a 1699 power of the primes figure You got a 599 battle master. You know, it's not a bad deal But not highly recommended if you're just after this figure. So That's my thoughts on it and guys. I appreciate you stopping by and checking out my video Don't forget to like and don't forget to subscribe. I'm trying to reach 2000 subscribers by TF con at the end of October. So hashtag 2000 by TF con also check out my series the sit rep I sit down and talk to other transformer collector youtubers And we have an absolute blast talking about our favorite plastic robots and check out the Patriot Prime merch store I've got some brand new merchandise including this awesome Patriot Prime salute shirt. It's got Patriot Prime reviews on the back I also have one that says Patriot Prime reviews on the front and the who are on the back So that's in the description below. Also, if you would like to donate to the channel I have a PayPal link in the description also guys. This is Patriot Prime signing out


Hello, welcome to the e-lecture Predicate Logic 1. Predicate Logic is the most widely used meta language for the representation of the internal structure of simple propositions. The topic is too complex to be covered in one e-lecture. Thus I will split it into two parts, into Predicate Logic 1, this part, where I am going to explain the basic machinery of Predicate Logic and into a second part, Predicate Logic 2, where the principles of quantification will be discussed and where the combination of propositional and predicate logic will be exemplified. But why do we need predicate logic in the first place? Couldn't we say that truth conditional semantics is sufficient for the description of sentence meaning? Well, not really. Propositional logic treats simple propositions as atomic, that is, as if they had no internal structure. However, this assumption limits its usefulness as a tool for the description of meanings. Here are two examples. The first one is concerned with quantification. Propositional logic treats propositions as either identical or totally different. However, it may be the case that two propositions are only partially different, as in these two examples which differ in terms of quantification.  Now, all versus some is the key issue here. Since there is no way of expressing quantification, all or some, in propositional logic, it is not possible to point out the differences between these two propositions and to simultaneously capture what they have in common. Note that I've already used some symbols used in predicate logic, for example the universal quantifier, the upside down A, the existential quantifier, and here some variables that are part of my examples. The second problem for propositional logic can be referred to as the problem of relations. Since propositional logic has no access to the internal structure of propositions, it fails to notice important relationships among them. For example, if we look at the following compound statement. John is taller than Mary, and Mary is taller than Paul, and Paul is taller than Linda. From such a compound statement, we can conclude that John is in fact taller than Linda. But this conclusion is based on our logic of the meaning of the relation X is taller than Y, holding inside each component proposition. It cannot be drawn from the corresponding expression in propositional logic. To handle such phenomena successfully, it is necessary to consider simple propositions not as unanalyzable units, but as having an internal structure that corresponds to the structure of the state of affairs in the external world. The machinery that describes the internal structure of propositions is referred to as predicate logic, also called predicate calculus or first order logic. It shifts the focus from the logical relations that hold between sentences to those that hold within sentences. The essential idea is that each proposition can be defined as a predication. Predications themselves consist of a predicate, and the predicate itself always occurs with an initial capital letter, so it is capitalized, and a set of arguments represented with small initial letters. Well, and you can read it as follows. So, here we have the predication Px, and it can be read as X is a P. So, let's look at an example to illustrate this in more detail. The proposition John loves Mary can be broken apart into the following components, into a predicate love, and into two arguments John and Mary. So, X would be John and Y is Mary. Whereas the corresponding predication would look like this, love John Mary, or with variables love X, Y. As we can see, predications consist of two basic elements, predicates and their arguments. Each predication may have only one predicate, but it may have one or more arguments. So, let's look at predicates in more detail. A simple predicate is one that assigns some property to its argument. So, here we have the predicate country with one argument Great Britain, and it can be read as Great Britain is a country. Other examples would be something like John is tall, Mary is pretty, and so on. More complex predicates represent relationships between the entities denoted by their arguments, if there is more than one. So, here we have a predicate, love, and two arguments, John and Mary, and the proposition that can be associated with this predication is John loves Mary. Or take this one, Jane sends Paul a letter, that's our proposition R, and the predication would be send with the predicate send, and three arguments, Jane, Paul and letter. As already mentioned by convention, the labels for predicates always start with a capital letter. And according to the number of arguments required by a predicate, often a distinction is made between one place predicates with one argument, two place predicates with two arguments, and three place predicates with three arguments. Well, and if there are more arguments, you could call them n place predicates with n, with any number of arguments. The argument structure itself specifies not only the number of its arguments, the number of the arguments of a predicate, but also their order. For example, the proposition the hunters shot someone can be represented by the predication that you can see here. The predicate is shoot and hunters and someone are the two arguments. But what about the proposition Q, someone shot the hunters? Well, this different state of affairs is represented in the order of the arguments of the predicate shoot. So in order to represent this adequately, we would have to swap the arguments. And this is our new predication, same predicate, same arguments, but different order of arguments. So the order of the arguments of a predicate is highly influential with regard to the meaning of a predication. Well, and what about the argument types? Well, the arguments of a predicate are entities minimally involved in the property or relation expressed by the predicate. If one is missing or unspecified, the predication is incomplete. The arguments of a predicate themselves may be any logical term. The simplest argument type is referred to as individual constant. An individual constant is a term that refers to a particular individual in the world. And the range of individuals includes the people, things and places of everyday life that can be recognized as distinct and identifiable. For example, cat, dog, Great Britain, John and so on and so forth. It should be noted that the task of giving a name to each individual is much easier in simplified artificial worlds than it is in the real world. And then there are so called individual variables. While individual constants stand for particular individuals, an individual variable stands for an arbitrary individual. In other words, variables range over all individuals. And variables are denoted with a lower case characters x, y, z and so on. With variables, we can form expressions such as teach x. So something like your going to teaching. Or we can create this predication, read x, y. So in this case, the children are reading a book. By themselves, these predications do not express any proposition because the variables x and y have no fixed reference. Well, finally, arguments can be more complex than simple constants and variables. In fact, they can be whole predications themselves, each with its own predicate argument structure. Let us construct such a predication. Here is a complex proposition. The teacher saw that the children were reading a book. And in fact, this complex proposition can be broken down into two propositions. P, the teacher saw something and Q, the children were reading a book. And both P and Q can be translated into individual predications. Here is the first C teacher. So the teacher saw something, C teacher. And here is the second. The children were reading a book, read children book. In putting them together, we now use the second predication as an argument of the first. So this is what we have to do. Here is our first predication C teacher. And then we need a second argument. Well, the second argument is the entire second predication Q. So this is now our complex predication with two arguments. The first argument is an individual constant. And the second argument is a predication. So predications can be arguments of predicates. Shall we practice a little bit? Okay, let's look at some examples. Here is the first. John is a linguist. The predicate is linguist. There is one argument, John. And this over here would be the predication linguist John. Another one, Mary snores. Again, a one-place predicate. Snore. One argument, Mary. And the present predication. Well, you should now understand the system. Let's take a two place predicate next. Admire is the predicate with two arguments, Bill and John. And the predication admire Bill John. And what if we reverse the situation John admires Bill? Well, then we virtually have the same. We still have the same predicate, but the order of the arguments has to be reversed. So now we have admire John Bill. Let's take a three-place predicate next. Linda gave Paul the book. Predicate give. Linda Paul book, three arguments. And here is the predication. And finally, here we have a complex predication with one predicate, C. And the predicate itself has two arguments where the first argument is John and the second argument is what John saw, namely that Mary left. So we have the first argument a constant and the second argument is a predication in its own right. So you should have understood the system I think. So let's stop here and let's summarize this first part. We first showed the limitations of propositional logic for the description of sentence meaning and introduced the idea of splitting up propositions into predications, which in turn consists of predicates and their corresponding arguments. Having understood this basic formalism of predicate logic, we can now integrate principles of quantification, as well as the set of logical connectives that I introduced in my e-lecture on propositions. How this can be done will constitute the focus of my second e-lecture on predicate logic. So see you there.