Hey, welcome back everybody. Jeff Frick here from theCUBE. We're at our Palo Alto studios, having a CUBE conversation today with Susie Wies. She's the VP and CTO of DevNet at Cisco Systems. So Susie, great to see you. Great to see you, Jeff. So before we jump in, DevNet, what is DevNet? DevNet, DevNet is Cisco's developer program. You probably didn't know that Cisco had a developer program. I didn't, but that doesn't surprise me because everybody's looking to engage developer these days, not a surprise. Yes, excellent. So yeah, with DevNet, we founded DevNet about three years ago. So Cisco had different products where they wanted to create developer and engage developers around them. But three years ago, we actually started a Cisco-wide developer program to really create good resources, solely focused on developers. And it actually spans all of Cisco's products. So starting from the infrastructure, with networkers that we've had going a long time, taking our networking equipment, our data center, our cloud products, getting into the internet of things, our collaboration products. So we really eat security. We go all the way from infrastructure up through applications. And really DevNet is all about giving developers the resources to learn. A lot of times they just want to learn coding 101 if you want to write a networking app. If you're a networker trying to get up there, or if you're already a coder writing a network app, you need networking 101. And then we deep dive into our APIs around network automation and orchestration and things there. We help people learn. So we actually have coding resources. Like if you want to write an application for a contact center, you would have to buy a contact center to test it out. But we have a sandbox, a DevNet sandbox, where we have all the kit running live so that a developer can test their app right in there. Or if you want to do something for software-defined networking, we actually have LiveKit of routers with a product called APIC-EM, which is our SDN network automation software. And you can have that running live and write your apps there. So the coding's really important in our sandbox. And then on the Inspire side, what we have is DevNet creations. Once someone's built something cool, then they can share what they've built and just kind of publish it. Say, this is a project I wrote. Here's the source code. Here's some demos. And then finally, we have allowed people to connect and connect through in-person events, through online communities. It's really about bringing the community together to solve the big problems of like, how is IoT really going to work in this next generation? How will networks really move to network programmability? How will collaboration take it to the next level? So why did you have to set up a separate thing, DevNet? I mean, I'm sure you've always had developer tracks. At Cisco Live and other Cisco conferences. Obviously, big investment you've got to see in your title for this. Why did Cisco, why did you guys decide that you had to do something different above and beyond to kind of having a developer track in your standard conferences? Yeah, well, before what happened was actually Cisco didn't even have a developer track in its conferences. Oh, they didn't. No, before three years ago. But we had a certain product and the product team would get really excited. Like, you know, Cisco had Jabber and said, hey, we're going to create it, we're going to have a hackathon, right? Or, you know, so just products there. So we created DevNet and then we started to have developer conferences at Cisco Live, our big event where, you know, 25,000 people come to Cisco Live US, you know, 20,000 in Europe, we have it in Mexico and in Australia. So we have these events around the world. And then we for the first time did have developer conferences there, all about Cisco's APIs, Cisco's products, teaching networkers about programmability and software so that the world of software-defined networking didn't just pass them by. So actually we've been getting quite a lot of momentum there and that's all awesome. So that's the DevNet zone at Cisco Live. But what we want to do now is we're creating a new venue, something that we call DevNet Create, which is our first standalone developer conference. And what we're trying to do is not actually just have this be about Cisco, but we're creating an industry-wide developer conference and the theme that we're focusing on is what I think is this big transformation going on in the industry right now about where applications meet infrastructure. Right, right. It's interesting, was there a catalyst that suddenly said, oh my gosh, we need to do more for developers, you mentioned about three or four years ago. I mean, what was the catalyst? It was kind of the wake up call that some smart people that maybe don't work inside Cisco's four walls that we want to engage. Well, is there a specific moment, a specific thing that happened? Well, what happened was Cisco was going around saying, and acknowledging that we need to really double down on a software strategy. And so it's all about software. We acknowledge that networking was going on and they're saying networking is moving to software to find networking. Does Cisco want that to happen or do they not? So there was kind of all of that question. And so, myself, I started in Rick Tawaniak, my co-founder of DevNet, we just started lobbying and just saying, okay, Cisco, you want to have a software strategy? Awesome, keep going on that. And yes, software with recurring revenue, that's all great. But the real reason you have a software strategy is because it's about the ecosystem. It's not just about your product, it's about how you interact with other products that are going on and how does that interaction happen? It happens through APIs. So you can't just build a product, build some APIs and they will come. You need to then really cater to developers or to networkers who want to use APIs, IT and OT guys. So it's really about providing resources for them and that's that whole learn, code, inspire, connect. As then we created DevNet and really provided a full set of resources for folks and it's actually changing people's lives. It's interesting because we cover a lot of shows, right? And everyone has a developer track in their show. That's pretty standard operating procedure because everybody wants to get to the developers and they're hard crew to get to, right? This is a competitive world. And last year we covered the GE Pritx Transform Event which was their first ever developer conference. So who would think GE is basically hosting a developer conference, but same thing, right? They wanted to get an ecosystem built around the Pritx cloud which is their little special IoT cloud. And it was a very successful thing and a key part of their strategy. So very similar to what you're talking about, right? You need to have an engaged development community. It's all about developers. And what happened is in the Fortune 100, I think it was something like 35% of Fortune 100 companies are now having developer sites and published APIs, which is incredible. So these are things like Visa and MasterCard, GE and others. So it's just real business, right? Right, so getting together for this, doing a little homework, I see you got a blog that you just recently put out talking about really the change in the way this whole world is working really. Where before you had your infrastructure and the app team had to build to that infrastructure, but now it's kind of flipped on its head right now. The apps are kind of dictating what happens to the infrastructure. And as you point out here, and we always joke about this too, that with IoT, all right, people are things too. So now you've got a whole different way to interact. The application has to interact beyond the simple kind of three horsemen of classic IT, which is storage, compute and networking, right? Because now you have things, you have people, IoT's coming down the pike. Mobile World Congress was last week. It's all about 5G, it's a big IoT enabler. Everybody loves seeing autonomous cars drive through the neighborhood. So it's a very different world, a very different application world that these developers are entering into. It's amazing, yeah. And I think that we haven't even reached the potential of what applications can do. Oh, barely guys. And it sounds so mundane because you're like, okay, an application. I use it on my computer, I have a keyboard and a mouse. Or then it got really exciting, like mobile apps. I have mobile apps on my device, which is awesome. I can take them anywhere. And you have that whole social mobile and all of everything changed there. But now you get to this world of IoT and cloud and apps take on this whole new meaning. So where, as you said before, an app just ran on top of the infrastructure. Now with cloud it changed because you started to get to DevOps. You're like, wait a minute, okay, so now an app develops but they develop and deploy and that has some kind of interaction. But you go even further and then what you have now is you have apps interacting with the infrastructure through DevOps and through APIs as well. And before, as you said, all the network, all the infrastructure did for you was provide network compute and storage. But when you think about the internet of things, all of a sudden things come on board and then you can all of a sudden get, create entirely new apps using the sensors and everything, you take this building and once this building gets digitized, then you have your HVAC system, your badging, your security cameras, that's all cool stuff, but imagine how to write an app on top of all that. So you have tons of kind of things and data and then with the place you can actually start to get indoor location, wireless access points are giving you location data. So you're in a shopping mall, you know where people are just because their wifi, even if you're not connected, the wifi network knows where you are just because it's searching for MAC addresses and things like that. You can all of a sudden get information that's really, really interesting for business. Where are people hanging out? How much time are they spending in different places? That's information any app developer would die for. So the infrastructure's not just providing connectivity, but it's providing really interesting information that an app developer wants to use. And from all over the place, public databases, proprietary databases, APIs here, APIs there, and... Absolutely, and that's crazy. Like so just the data is from all over the place, it's not just this nice contained here's the sensors on my device, but you're now bringing together data from around the world, you're working on a cloud infrastructure. There's data sovereignty issues in terms of where the data can be, there's kind of security issues. But you want, like the app developer just needs access to all of this, but you need to be very careful. And you need to architect your system so that it can really work well. And it has to be software-defined, right? Because sometimes you might not have a good connection, sometimes you might not have access to that data. There's so many parameters that define this kind of software interaction. That just a hardcore machine-to-machine wire connection isn't going to get it done if there's not software to be able to buffer and deal with all these various conditions. Absolutely, and so you think about, okay, why do you need software-defined networking or software-defined infrastructure? It used to be that, let's say that you're, again, taking a shopping mall and IoT enabling it, right? You're digitizing, you're putting in all these sensors, very cool. When you go home, you just kind of put it up and you put on your baby cam and all that kind of stuff, but you go to work and then all of a sudden you're like dealing with proprietary systems and things there, you have to really worry about security. If you go to a Tesla manufacturing plant, you need to worry about security, like who has access to the data. So when you start to put these things online, what matters is, you put a picture, your video surveillance cameras, your badging system, your HVAC system, and then just your video conferencing systems, they have very different security requirements about them. So how do you put them on your network in a secure way? You want to segment your network so that each of these is on different network segments. They have the right access, but an app developer doesn't want to deal with all that. So what you want is to be able to put them on, configure your network.  But with the software-defined, you can just say, hey, create a secure network segment with this group of devices, get the data going across, right? And then now allow my applications to access it. So you can actually start to use all of these capabilities of software-defined infrastructure to help app devs, right? So this is such a huge category of stuff going on. I want to say attack surface, because we were at RSA a couple of weeks ago, but even really just opportunity surface in terms of the developers and where they can add value. What are you guys focusing on at DevNet? And we'll talk about it in a minute. You've got an event coming up in late May, which we're excited to bring to theCube there. I think it's your first one. But of all the things we've talked about, what are you and your team and what should people that go to DevNet create? What is your main focus? So our main focus there, it's actually two areas, but it's IoT, so the Internet of Things, and then just app developers wanting to create new IoT apps. But then we're looking at, how does that hit the infrastructure, right? So again, is how can you have IoT developers, cloud developers come together to really get the most out of this next generation of apps? We actually break that down in a few ways. So you said there's the Internet of Things. So it's kind of like, where do applications meet things? But in addition to me, it's where do applications meet people? It's where do applications meet places? It's all about, to me, the Internet of People, Places and Things in terms of how these things come together. So if you just kind of dive into each of those, it's, again, it's not easy to figure out how to write an app for a business that, again, is instrumented with IoT, that has location capabilities, that has kind of analytics throughout. But we want to talk about how to truly expose all that to app devs, so that you can really get not just kind of vertically closed proprietary system of apps, but you can really have the full world of app developers hacking on and building on all of this stuff. Right. Okay, so how do people get involved? So let's get to the full plug. So it's May 23rd and 24th, San Francisco. Yep. Do you have a venue? Yes, so DevNet Create is May 23rd, 24th, San Francisco at Beespoke, so it's in the Westfield Mall. Okay. It'll fit about 450 people, so it's a little bit more of a cozy atmosphere, but we're super excited because we want people to come, we want people to submit talks to be speakers in areas that you think are critical here. And we want it to be one where you can interact, right? You can interact with the speakers, you can interact with each other, because we totally want to jam on this area of where applications meet infrastructure and figure out together as a community. Okay, so what do people need to do to get involved? They can, you're looking for speakers? We're looking for speakers? Okay. You can actually go to devnetcreate.io, and that's where our whole site is. You can submit a talk, actually you can do more. You can submit a technical talk if you want to present, say, hey, here's a cool thing that I built, or here's a key technology issue that I solved, here's an API and platform that I used. Also, because we wanted about learning and hands-on coding, you can submit a workshop about your API or your platform that you think is really critical to make this work, and we'll actually have stations set up so people can do hands-on coding on your API if you want. You can create learning labs, so these are online learning labs that'll then be available to everybody forever. So to just get people up there and teach them about the platform and the API and teach them about some new technology topic, so all of those are possible for the venue itself. In addition, though, we actually want to start the conversation now, and so what we're doing is we've created a medium blog post, a blog publication on devnetcreate, and we actually invite everybody to submit their thoughts on where applications meet infrastructure and what it means to them. So just everybody's going to have different ideas. What's the hard technical problem? Is it changing? Do you believe that it's, you know, should they just continue to be separate? You know, what do the boundaries look like? Where does it matter? So I would love to get thoughts from you and from everybody about where apps meet infrastructure. We want to continue the conversation on theCUBE, but we'd love to get that conversation going now online as well, so if people can write some stuff, we'll bang around at it, we'll include your publication in our, you know, devnetcreate publication. Okay, great. And then when May comes, we'll continue talking in person. That's right, we've got a couple months. So have you already been collecting data or are you still kind of kicking this off so people get an opportunity to get in the door early? We're kicking it off now where you can submit your, you know, tech talk or workshop or learning lab now. You can submit a medium publication now, like just share your thoughts with us now, yeah. Awesome, all right, so we'll look forward to watching the content grow pre-show and then that'll really set us up for an awesome show there on late May. Excellent. All right, Susie, well thanks for taking a few minutes of your time to stop by and give us kind of the breakdown of devnetcreate. Should be exciting May 23rd, 24th at San Francisco. We'll be there, hopefully you'll be there. I know Susie'll be there. I'll be there. All right, thanks for stopping by. Thanks, Jeff. All right, Jeff Rik, here at theCUBE. Thanks for stopping by.


Good morning, let us continue our discussion of drop and velocity size distributions as applicable to sprays. We are going to define these distributions in the x v space where x is the drop size and x is any number between 0 to infinity. It is a positive number and v is will just stick to one component of velocity and because the component of velocity can be either positive or negative it goes between minus infinity to infinity. Those are I mean without knowing anything about a given spray this is sort of the limits I can set on it right. So, now I define a function f in these two variables f of x comma v is a probability density function if it satisfies two properties one f of x comma v is greater than 0 for all x and v that are admissible. And the second condition is simply that if I was to integrate the probability density function over the set of limits that has to add up to 1 and just to recap this second condition comes from our basic definition of a probability density function that f of x comma v times dx dv is the actual probability that is the size of the drop falls in this range x to x plus dx and so if f of x comma v is a probability density function this probability density function multiplied by dx and dv. So, if you imagine x and v as being two orthogonal axes describing this x v space dx comma dv is like a tiny area elemental area in the space probability density function at that point x v multiplied by that elemental area gives me the actual probability that a drop falls at that point. Now, if I add up these actual probabilities over the entire range of admissible values of x and v that is supposed to add up to 1 that is our law of simple of probability. Now, just to set things in perspective if I take a spray I have a spray nozzle that is got this spray I have in the most general description three spatial coordinates describing this spray. So, if I draw an axis there is a radial if I just use cylindrical polar coordinates there is a theta and there may be a z coordinate. So, I have an r theta and z describing this. So, if this is my origin point every point in the spray has a position vector I will write it more compactly in this coordinate notation that is easier. So, this is a position vector in three coordinates and in each of these three coordinates at the velocity vector may have a v r v theta v z. And if I simply take the size and if I say size is one scalar quantity that describes the physical measure of the volume in the drop and t is time. So, if I take a very simple unsteady spray at every point p the point p itself is described by r theta and z its spatial coordinates at that point I have a probability density function in x v r v theta and v z. So, the pdf is essentially a function in x v r v theta v z these are the arguments of the probability density function. So, if I integrate it appropriately over these four independent parameters independent coordinates now my the space in which the spray is characterized is this x v r v theta v z space. And the physical space is r theta z and time I use a semicolon to separate the list of arguments in the pdf. So, list of arguments I will say describing the pdf space or in which the pdf space is this would be the most complete description of a spray. If I can come up with this function f that is going to tell me the probability density of finding a given size of drop with a given set of velocity components at a given physical point in the space and at a given point in time. I can as time varies at that same physical point in space the pdf could evolve if I have a real unsteady spray right. In this case let us say a diesel injector puts out large drops in the beginning of the injection cycle and large drops at the end of the injection cycle. In the middle there you may have a real fine atomization. So, this f at one point sees a variation in time and even if I take a steady spray like the one we saw in the video earlier at different points in the spray I will have a different probability density function in the size coordinate and the velocity coordinate. So, just to set you know we started to talk of f of x comma v as a probability density function in this two parameter space. What we really should be looking at is a probability density function in the four parameter space of x v r v theta v z that itself varies as a function of r theta z and time. This is like the most general description we can think of in a statistical sense. So, we are still looking at the moment we say probability density we are suggesting that there is in some sense a local stationarity over some period of time or over some ensembles of cycles. We will look at that when we look at experimental techniques because we will take advantage of this in making some measurements of these sprays. But this is our understanding of what it is. So, let us now go back to I do not want to sort of just to understand what the most complicated way of looking at a spray, but we will simplify it just to understand some of the physics of these distributions. We said integral this is just coming from the idea of probability. Now if f x comma v dx is the probability of any velocity. So, this here is a function of velocity if I perform this integration from 0 to infinity this becomes I will put this in curly braces. So, I want to see if I can define like a mean velocity I want to find a mean drop size in the this thing. So, let us first simplify this if I define a mean drop size x times f of x comma v dx dv integrated from 0 to infinity and the v integral going minus infinity to infinity. This gives me the mean drop size over all the velocities. What I want is a mean drop size of all the drops that are moving with some velocity v to v plus dv let us say. So, if I ask myself the question what is the if I ask myself this question then x f of x comma v as first of all f of x comma v dx dv is the probability of finding a drop in the size x to x plus dx. So, if x is the size then you know the probability multiplied by the size added over all the limit gives me a differential probability of all the drops in the range x to x plus. So, this is now all the drops, but having velocities v to v plus dv. Now, this is really this dg is a probability because I have taken the probability of the f f of x comma v dx dv is a probability then I have taken all the probabilities and added them up, but I have not added up all the possible probabilities over all the range of v going minus infinity to infinity. So, dg is basically a probability of finding a drop of any size of any size of any size let us do one thing we will even erase this x. So, just to get our argument straight with the probability part and then we will look at the mean part. So, if f of x comma v dx and if I am only integrating in the limits over x that is giving me a differential probability of finding a drop in the range v to v plus dv. So, let us first define that. So, this dg d over dv is integral 0 to infinity f of x comma v dx this is the velocity probability density function. So, what we have on the right hand side here is only a function of velocity. So, I will call this some h x plus dv plus h as a function of v h is a velocity pdf why is it it is not just a function of v it is actually a pdf because this is automatically satisfied. This is actually coming from our basic definition of this the integral of f of x comma v dx dv equal to 1 over both the ranges. So, if I just take the if I just take this part and if I call that some new function h the integral still remains 1. I can likewise define another function we will call this p of x which is minus infinity to infinity f of x comma v dv. So, this p of x is where I have integrated out the probability in the velocity space. So, I do not care what is what it this is a mathematical statement what it physically means is that I do not care what the velocity is tell me what the probability is of finding a drop in the size x to x plus dx probability what the probability is of finding a drop in the size x to x plus dx and that that probability divided by dx gives me the probability density that is what this p of x is likewise h of v is is is physically saying I do not care what the size is just tell me what the velocity distribution looks like at that at some point in the spray or the whole spray will get to that little bit. So, these are in some sense two simplifications of the full f of x comma v in one coordinate or the other only. So, let us look at some real experimental data to see what what this actually means this is data that was obtained using an instrument this is experimental data at one spatial location in the spray. Now, what we see here mean there is about 10000 dots on this graph each dot is one drop. So, this was an instrument called the PDPA will it is called the phase Doppler particle analyzer we will look at that again and later on in the class, but let us just say it is a particle counter. So, I have a way of counting every particle going through that instrument at that point and figuring out what its size is as it goes through there. So, I took a sample of 10000 drops at one point typically this may be like half a second of real time in a in a reasonably you know we looked at these numbers right a simple perfume with has about a million plus drops. So, to sample 10000 drops is mean is hardly any time. So, what we did is we took the each drop and you see each drop and its size you can see how the size never really goes to 0. Let us say the smallest drop I know in this sample is probably about one micron the largest drop is slightly less than 250 microns actually it is slightly greater than 200 microns you can see that is the largest drop the smallest drop may be somewhere here. So, if I now take the probability density of this and I am going to draw it on this axis you can see how the density is 0 at 0 the density quickly rises the reaches a maximum and then in fact since this is experimental data it actually becomes 0 let me just make that line a little straighter. So, if I now look at what I have essentially done is I have taken the drops all of the drops and from essentially creating you can imagine a histogram first. So, I have created a histogram and from that histogram I have constructed what looks like a continuous curve which is my. So, this is my probability density function in the drop size space we will look at a stepwise procedure of doing this in an example as well but for now that red curve that I have drawn on top of these blue dots you can see sort of qualitatively indicates a density of these drops in this vertical coordinate called diameter that the vertical coordinate is like a diameter and how densely are these drops packed in that space is this red curve is an indication of that you can also see that it satisfies all of the general criteria we set out for an actual spray pdf which is saying that the probability density should be nearly 0 should be 0 for drop size being 0 the probability density should tend towards 0 as the drop size becomes large the probability density should achieve a maximum at at least one point. So, for example, you know I could for all I care have more drops at another point. So, that would give me two peaks on the drop size distribution that would be perfectly acceptable it would just be called a bimodal distribution and you know I could go on and you know there is nothing that precludes as from having more and more maximum but in a real spray a bimodal distribution is about as complicated as we get typically a single mode single maximum point on the pdf is what is more commonly observed. So, now if I move on to the velocity now in this case I have not plotted the velocity this is actually a plot of speed the speed is slightly different from velocity in that velocity is allowed to go from minus infinity to infinity speed is only a positive number. So, without going into much details you can see how if I were to draw a pdf of this shows a graph that looks something like that. Now, we look at functional forms of these graphs a little later on but essentially you can see again that it is hard to find a particle that is of 0 speed meaning there are hardly any dots near the bottom of this vertical axis it is hard to find a very fast moving drop either. So, 30 meters per second is about as fast as this sample of drops had but most of the drops are moving right about 10 to 12 meters per second this is again one spray at one point a distribution of 10000 drops a sample of 10000 drops at that point. Now, if I take the size and velocity as the two independent axes now. So, look at it this way I have the diameter on the x axis and real axial velocity now on the y axis believe me there are 10000 little triangles on this graph. So, every drop that we sampled that we showed in the previous two graphs where you know the x axis in the previous two graphs was a number called the particle number it is like a it is imagine I slap on an id to every particle that is coming through 1 to 10000. So, it is just like some way to distinguish from drop to drop in this particular graph in this graph what we have done is we have ignored the particle id that is I do not know when the particle came in the previous two graphs the id was to show like a sequence of arrival as a matter of fact. So, let us go back to that graph and look at it a little more carefully if I took a sample of the first 1000 drops and constructed a pdf just like this and then took the sample of the next 1000 from 1000 to 2000. Similarly, if I constructed 10 separate pdf would the 10 be approximately similar or would they be totally different from each other they are all going to look approximately similar I can take all the all the drops in that little strip or this little strip they are all going to look approximately similar I have about 1000 drops in every strip there right. So, what that says is if the pdf constructed from any point any sample of the population is the same I can call the spray as being stationary that is at least in the time that I have investigated it which is this half a second nothing drastically is changing over that time I can call this spray as being statistically time stationary that is if I now were to extrapolate this belief that I have all I can say is I can take a 10000 drop sample tomorrow on the same operating condition spray and I can expect to get a pdf that is approximately the same it is a very important belief to have without which you cannot do experiments right or for that matter go further in any fashion right. So, this idea of stationarity that is if I bring on the same supply pressure same air flow rates etcetera I can get the same spray from a pdf sense the exact arrival times of every drop could be different, but I am not concerned to that microstructure of the spray the macro structure in terms of this pdf I say it is not really a macro structure the statistical structure of this spray is repeatable I am able to reproduce it tomorrow same thing if I now come here if I throw out the time stamp or the id id and time stamp are interchangeable right I can look at every drop in this size. So, essentially this is x in our old description f of x comma v if I now construct a mound in this if I now construct a mound in this f of x comma v space that mound is going to be my f of is my two dimensional probability density function in the previous graph what we could draw as one line curve now becomes a surface. So, in this f of x comma v you can clearly see that right about this middle region there is a real peak density and in this little ring around here there is less of a density. So, I have a peak essentially it is like a little hill you know that is sloping away from this peak that is going to be the nature of this f of x comma v now I want you to pay close attention to one thing the diameter scale here is logarithmic that means in the log of the particle size I get what to me looks like a Gaussian curve Gaussian or a normal distribution curve in the diameter space the velocity coordinate here is linear. So, the f of x comma v this is now real experimental data right f of x comma v tends to show a Gaussian like behavior in the log of the particle size and Gaussian like behavior in the linear in just v. So, if I were to do this if I was to create a probability density function of this graph is a real essentially I can see this is my p of x from the previous graph the probability this is my f of x comma v. So, these dots in some sense if I was to process them appropriately I will get f of x comma v if I ignore the velocity coordinate and only do the binning in the x coordinate what I get will look like that top red curve that is my p of x if I ignore the diameter coordinate and only do the binning in the velocity coordinate you can see how I will sort of get something that looks like this this is my h of v. So, this is a graphical representation from a real data set of what p of x is what h of v is and what f of x comma v is. Now, when can I say that there is no size velocity correlation in this data set that that is a physical question to ask and there are mathematical implications associated with it. If I if all of these points that you see in this graph are sort of oriented along the coordinates meaning if I was to draw a best fit straight line and different levels of confidence interval on that best fit straight line. If the straight line is going to be a horizontal line if the best fit straight line is horizontal then on average the mean velocity of a given drop is not dependent on the size that is the real conclusion you can draw that is saying on average the velocity of a given set of drops does not depend on the size. You can take any sample from any size part you will get the average velocity to be about the same that is the actual precise meaning of size and velocity correlation. I can do the same thing to the velocity axis if I draw a best fit straight line of the diameter as a function of the axial position that is to say what is the average size of all the drops that are moving with a given velocity and if that also happens to be a vertical line then I can say that I can take any velocity let us say if I ask the question what is the average size of all the drops that are travelling with let us say 0 to 1 meter per second versus 10 to 11 meters per second versus 20 to 21 meters per second. If these three average velocity average drop sizes were all the same that means the essentially a best fit vertical line through this data is a straight line the best fit straight line that is vertical is nearly 90 degrees. So, these two straight lines being oriented along the axis is effectively like saying that there is no size velocity correlation. The average velocity of any given sample of drops does not depend on the size or the average size of any given velocity sample does not depend on the velocity itself. So, these are two different ways of looking at size velocity correlation. Now what does this mean mathematically? Mathematically what this says is f of x comma v because they are oriented along orthogonal directions the mean the best fit are oriented along orthogonal directions I can write the function f of x comma v simply as a product of two functions in each of the two independent variables. So, this simplifies my mathematics significantly I can if I can do this if remember in the most general case I have f of x comma v r v theta v z instead of dealing with the function in a four dimensional space if I can deal with four one dimensional functions is so much more simpler. So, except this thing called size velocity correlation I can actually deal with four functions in four one dimensional functions as opposed to one four dimensional function in the most general case in this specific case instead of dealing with one two dimensional function I can look at two one dimensional functions and that would I can then reconstruct the two dimensional function from from the two one dimensional functions. Now mind you this p of x is approximately Gaussian as you can see from this and v of h of v is also now really speaking it is not p of x that is Gaussian it is p of this is p of x, but remember it is in the log coordinate. So, it is Gaussian in the log coordinate. So, now with this let us go back and look at some very simple functional forms. So, if I have to take this kind of data and actually generate p of x or h of v what I need is a mathematical function for p of x or for h of v that I can find a best fit to this data set. So, some of those mathematical functional forms are listed here the simplest is called the normal distribution. So, this is like your h of v I have just h of v is given by this 1 over root 2 pi times sigma n in the denominator exponential of v minus v bar squared by sigma n squared. So, I have two parameters in this functional description v bar and sigma n. So, this is called a two parameter probability density function and for any given spray say for example, if I go back to this gives me the value of v bar this gives me the value of v bar. And like a spread an extent of the spread gives me sigma n. So, this is a by if I have an average faster moving spray all it means is that v bar is a higher number. On average if the distribution has a wider range of velocities then sigma n would be a higher number. So, this is a functional form that I can fit to any sort of a p d f. You can imagine how at different points in the spray because the sample of drops are moving with different velocities and different spreads in the velocity v bar and sigma n would be a function of the spatial coordinates.  So, the reason I put the semicolon in that seven parameter in that eight parameter description is the p d f itself is only in the variable v, but the parameters in the p d f v bar and sigma n can be functions of r theta z and t. Now, so this is one simple p d f that occurs quite commonly we will see this. The second is the log normal distribution. So, it is essentially a normal distribution as you can see here except it is normal in the log of the diameter. We saw this in the previous slide where if I was to make the particle size if I was to plot the sample of drops in the log of x space the spread this is now my p of x looks approximately Gaussian. So, again this is a two parameter description just like the previous case with d bar and sigma g squared as being the two parameters sigma g being the two parameters and d bar and sigma g in this case could be functions of r theta z and t. So, that would be the way to give like the most detailed level of information and there are others that we will see that follow that look like the same spatial that look similar in form one is called the Weibull distribution. This is also two parameter description with d bar and k as being the two parameters likewise the two gamma distribution with d bar and k as being the two parameters. So, these are just examples of functional forms that you can use for either the p of x or h of v in the previous case and as long as you have no size velocity correlation you can choose to describe f of x comma v as simply a product of p of x and h of v. We will stop here and we will continue this in the next class.


Welcome to Tilburg University, home to the School of Catholic Theology. My name is Reggie and I'm currently in the second year of the Bachelor of Theology. The programme focuses on the interaction between humanity, society, faith and reason. It deals with existential issues on the meaning of life, the forming of identity, traditions and values, both in the past and the present. One of the exciting and challenging parts of this programme is the studying of important religious texts in their original language such as Hebrew, Greek and Latin. The programme offers a broad scope of fields from biblical sciences to spirituality and you'll become competent in dealing with topics from history, philosophy, literature and social sciences. This variety in perspectives helps you to approach topics from different angles to reason logically and to write creatively. Theology deals with fundamental questions such as how does faith give meaning to people's lives? How are universal values such as tolerance and justice determined? That is why theology offers you a great opportunity to develop and enrich your personality and character. You'll learn to deal with different dilemmas which in turn will help you determine for yourself what truly matters in life. You share your classroom with people from different countries, denominations, age and life experience. For example, I myself am from a Pentecostal church. The atmosphere and campus is very personal. Students and professors help each other and has always room for conversation and counselling. The programme in Tilburg is entirely in English. You can also choose to study in Utrecht where the Dutch taught programme is available. When you've finished your bachelor you're an expert on existential issues and cultural and religious diversity. You can then choose to proceed with one of the master's programmes that are available in Tilburg. Theology, Christianity and Society or Religious Education. With a degree in theology there are plenty of impactful jobs to choose from. We often see theologians in professions such as journalism, education or in spiritual counselling in prison, the army or in healthcare. You can also choose to pursue a professional career at an NGO or in academic research. By choosing theology you will be equipped with a broad range of knowledge and skills which will help you to contribute to societal solutions. So will you take up the challenge and give new insights into all forms of faith in today's world and choose theology in Tilburg?


Welcome to this video. Today, you're going to learn how to use the advanced structure having plus past participle. This is a question that a student had submitted and it's a great question, so I'm happy to explain this. Of course, I'm Jennifer from j4senglish.com, and this channel is dedicated to helping you feel confident speaking English in public so you can take your career and your life to the next level. Now, before we go any further, make sure you subscribe and hit that bell icon so you're notified every time I post a new lesson. Now, let's dive in with this video. Let's talk about how to use the structure having plus past participle. The past participle is your third form of the verb. Now, we use this structure when the action is complete. So whatever the action is, if the structure having plus past participle is used, you know that the person has done that action. Now, as for sentence structure, this is commonly used to start a sentence. So in that case, notice your sentence starts with the verb having. It doesn't start with a subject. It starts with having, and it's just implied that whoever is talking is the subject. So for example, one of the most common ways to use this is having said that. Having said that. So said, of course, is the third form of the verb say. Having said that. Now, when somebody uses this expression, they're letting you know that they're going to reference something that they've previously said. In this expression, having said that, the that is the words that the person previously said. Now, normally they just said it. It was the what they just said. It is possible that it could be something they said a while ago, but generally it's they just said it. So for example, you could be in a meeting and your boss is praising everyone saying, awesome job guys. We really did a great job this week. Our sales are up. Our performance is up. And those are the words. Now he wants to transition. And he could say, having said that. So he's referencing the words he just said. Remember, the words he just said were positive. Okay, so you could say, having said that, we still have a lot of work to do. So he's giving you all this praise, but he wants you to keep in mind that there's still work to do. So he's balancing it out. Having said that, we still have a lot of work to do. So that's a very common way to use this expression, but you don't have to only use it with the verb say, you can use this with pretty much any verb. But remember is to show that the action is complete. Let's say my friend and I are talking about marathons and my friend wants to run a marathon and it's talking about training for this marathon. Now I could say, having run a marathon, having run a marathon, I can give you some tips. So I'm letting my friend know that this action of running a marathon is complete for me. I've done it. I've run a marathon. Having run a marathon, I can give you some tips. So we commonly use this just to show the experiences that we've had that are complete for us in order to educate or in order to inform or maybe even in order to show sympathy or empathy for someone to show that you understand their situation because you've experienced it as well. Now I talked about how most commonly it's used to start a sentence. This isn't the only location. You can use it as the second part of a sentence and it's going to follow a comma. So for example, I could say New York City is known for its busy streets and having lived there, I can confirm that this is true. So notice it starts the next part of a sentence after a comma and I'm just using and to show that connection between the two ideas. Of course, I can divide these into two separate sentences and say New York City is known for its busy streets, period. Having lived there, I can confirm that is true. So the choice is yours. It doesn't really matter. It probably just depends on the sentence, but you will see this most commonly at the start of a sentence. And the important thing to remember is that the action is complete. So now you know how to use this advanced sentence structure. Of course, it's your turn to practice. So I want you to leave three different examples using three different verbs. So you also really get comfortable with the past participle because you need the third form of the verb, which is the least common verb used. So I want you to get comfortable with that as well. So leave three different examples in the comments below. And if you found this video helpful, please hit the like button, share it with your friends, and of course, subscribe.  There you'll find a free case study. In this case study, you'll learn how to feel confident speaking English in public so you can impress your boss and your clients with your message in only 30 days. Simply click the button, enter your name and email, and you'll get instant access to the case study. And until next time, happy studying. Awesome job learning this new advanced structure.  And I'll see you in my next video. Bye.


What's up everybody, I'm TheBangooz, you are awesome and today I'm going to be covering everything I know about Metabuff and Core. I'll probably do one of these for all the games I cover, but we're going to start with Core. Right up front, if you have zero idea who Metabuff is and what Core is, then let's just get that out of the way. Metabuff is a company that is creating a sequel to Paragon using the free assets made available by Epic and they are calling the game Core. Now let's get started on everything I know about the company and the game. Before there was Metabuff, there were two companies trying to achieve pretty much the same thing. Brain Dead Games and Unleashed Games. Both were working towards the same goal and recruiting people from the same pool of talent. They decided to combine their efforts and begin working together. Around this time is when Unleashed brought Sylphon to the team. While I have no idea what kind of skills Sylphon has as a GDA, I do thank him as a generally trustworthy dude whose content I always enjoyed, so this step greatly increased my personal interest in the game. Before long the two companies completely merged into Metabuff. Metabuff officially incorporated on 5 September of 2018 in the state of Delaware. Along with the incorporation came the first big update from the company in the form of their 6 part proof of concept. This is when the hype train for Core really took off. Mainly due to this shot from the first video in the series in response to the ever present Will It Be On PS4 question. However, as I've stated many times, this isn't a guarantee that the game will come to PlayStation, it's simply proof that Metabuff agreed to Sony's terms and conditions. Still personally a little irked by the way this was presented. The first video also let us know that they intend to have 10,000 slots available for their alpha and they released the planned date which was April 27th of 2019. That day has of course come and gone that was a bit of a romantic deadline with it being a year from the date that Paragon closed. Metabuff was unable to meet this deadline with a product that they were confident in and decided to delay the alpha. It is currently unknown when the alpha will now be released. The rest of the proof of concept series turned out to be more of a proposal of concepts instead of a proof of concepts showing us some of the possible mechanics planned for the game. That isn't to say that they didn't prove anything, they did show us some of the work that they've done so far and a bit of insight into how they would be moving forward. The exception to this was the final video that covered the UI. This was arguably the truest proof of concept video where they showed us how they were designing the UI, why they were designing it that way and backed it up all with concrete data. You can no longer view the proof of concept videos that were taken down at the urging of another notch. I'll link the impressions of each video in the description below if that's something that interests you. The next major news from Metabuff was the Grayscale AB map testing. Several influencers in the community, content creators, competitive players, and other known members of the Paragon community were given access to two separate gray box maps created for Core. The goal was to get the opinions of not only which map was preferred but what features from both maps were good or bad. They allow people to create content about the map testing and then conducted surveys of not only their participants but also the general community. This gave everyone their first look at the ideas for the map and was a great way for Metabuff to gather community feedback. After the map testing core announced their proposed roster of 15 heroes scheduled for the alpha with an attempt to have three heroes for each role. I'm not going to call out the heroes at this time as the list has changed a few times but if you want to see what they have planned now for now you can head over to metabuff.com. The first change to the roster was replacing Revenant with Sparrow with the reasoning being that the community was asking for it. I did see many people calling for the inclusion of Sparrow at that time however the next change to the roster was a little off. They replaced FaZe and Kuang with Decker and Fengmiao. Again the reason provided was that the community had asked. While some community outcry may have factored in I personally think the real reason is that Decker and Fengmiao have an easier to implement ability set. This is the first inkling I got that the alpha probably was not going to be on schedule. That announcement was made a month prior to the April 27th deadline which is not enough time for them to onboard two new heroes. Metabuff then informed us that they had a wise license for sound engineering and would include multiple announcer packs for the game. They would also work on creating some interesting doppler effects and more ominous music for the jungle. We saw during the full map testing that they were indeed able to achieve some nice sound design. Then came the fully realized map tests. This is when the community got a real look at the design choices for Influencers were once again invited to use our girl Kalari to test out a concept map. This time it was one map with the assets fully implemented. Once again testers were encouraged to create content and share it with the community. This time however changes were made almost instantly. As many people pointed out various flaws with the map, Metabuff quickly updated things to accommodate what was perceived as solid critiques. They made changes to the prime dunk pit, adjusted lighting and added or removed geometry as necessary. Unfortunately this is when things started to go a bit south. Metabuff announced that they would not be able to release the alpha on the planned date of April 27th. Along with the announcement they showed us their planned UI that had some nice hidden nuggets of information such as a planned clan system, ranked mode and a ban system. But that was all overshadowed by the delayed alpha. Since then Metabuff has been rather quiet. They've provided very few updates and decided to focus on the game. We haven't been completely devoid of information though. They have since told us that they would be making more changes to the map based on information received from the map testing. Mid-May they let us know that they're well over 50% completion of the alpha. This is kind of a generalization. Some people say some people in the company said like 90% while others said about 60%. I decided to just go with well over 50%. They indicated that they have no more plans to swap the alpha roster and they showed us a video of Subrog using his abilities. So they aren't dead just laying low. My personal opinion of Metabuff has swayed back and forth quite a bit ever since learning about them all the way back when they were still separate companies. When they picked up Sylphen I was elated. However when I started for the minions my opinion for them dropped significantly due to a perceived lack of transparency. This was not their fault though.  When I personally reached out to the company they were very friendly and forthcoming. I made a few negative statements about Core in some of the first episodes of my little show. I would like to apologize to Metabuff as a whole for that. The fault all that time was completely mine. The proof of concept also gave me a less than positive impression of the company and that one's kind of on them. There's good reason they took those videos down. The release of the AB map testing restored my faith in Metabuff. Not because of the work they had put into the map but because how they included the opinion of the entire community. This was reinforced with the full map testing. I also felt that the map was pretty damn good. I wasn't nearly as devastated as the rest of the community seemed to be with the announcement of the alpha delay. I kind of expected it in fact. They were making those roster changes like a month prior to the pro's release date. I just didn't think it was going to be possible to implement two brand new heroes in time to meet the April 20th of the deadline. I support their decision to push the alpha back. If they didn't take the game was in a state that will satisfy the community then you know work on it somewhere I get it that's fine. I actually applaud them for delaying the alpha. Currently though the lack of any significant updates some of the rather wonky ways they've resented information in the past and the fact that we haven't seen self and do anything correlated in a while has got my spirits to a low point per core. I will do my best to keep the faith though and keep sharing them on. Madeabuff has been able to restore my faith in the past and I really hope they could do so again. But for now this is the Magoo signing off. You stay classy Agora. MANGOOOOO