We're going to take a look at the final aspect of vector algebra that we need in this course. And that is specifically another kind of vector multiplication known as either the vector product or the cross product. The key ideas that we will learn in this section of the course are as follows. We will revisit the idea that vectors have two kinds of multiplication, only one of which we have seen up until now. The one we've already seen is the scalar product or dot product, which takes as an input two vectors and it returns a number, a scalar. But in this section of the course we're going to take a look at the cousin of the dot product, the vector product, or also known as the cross product. It also takes as input two vectors, but it returns a third vector and so the utility of the cross product is that it gives us a special kind of vector that results from the input of two other vectors. We will not get a number, we will get something that has both direction and magnitude from this product. Now the cross product or vector product is a bit more complicated than its cousin, the dot product. Like the dot product, it involves multiplying two vectors, which for the purposes of this portion of the lecture I'll label as v1 vector and v2 vector. Now unlike the dot product, the result of this new multiplicative activity is a vector, not a number. We represent this special product as follows. Vector v1 and vector v2 are cross multiplied and the symbol for cross multiplication is the classic arithmetic times symbol, an x or a cross. Now the cross is crucially important here because when you write v1 cross sign and then v2, you mean very explicitly the vector product or the cross product. The dot product or scalar product is independently represented by placing a dot symbol between these two. It is really important to keep your notation straight here and also to know what notation you are seeing when you read about the product of two vectors because you need to be able to distinguish when you should be doing the scalar product from when you should be doing the vector product of two vectors. This symbol is the symbol for cross product and you should accept absolutely no substitutions. Now I've drawn over here in a three-dimensional coordinate system with an x-axis, a y-axis and a z-axis, these two vectors v1 vector shown in blue and v2 vector shown in red. Now it's perhaps a little bit difficult to see as it almost always is in two-dimensional representations of three-dimensional spaces but v1 and v2 have components that lie only and entirely in the plane defined by the x and y-axes. They have no third component in z and I emphasize that now because when we do the cross product you'll see that something very interesting happens with these two vectors. Now before we proceed, it's important to know the rules involving the cross product of unit vectors that lie along the coordinate axes. So for instance, i hat lies along the x direction and only along the x direction, j hat lies along the y direction and only along the y direction, k hat lies only along the z direction. These three unit vectors, i hat, j hat and k hat stand in for vectors that point only and entirely along one coordinate axes and they are all at right angles to each other. i hat is perpendicular to j hat, j hat is perpendicular to k hat and i hat is perpendicular to k hat. So they are very special vectors and that's why it's important to learn the rules of the cross product for these vectors first. They're the building blocks of all other vectors. So these rules for i hat, j hat and k hat are as follows. The cross product of i hat and j hat in that order, i hat cross j hat gives you k hat. In other words, the cross product of a vector that lies only along the x direction with one that lies only along the y direction gives you a vector that points only along the z direction and you can already see the utility of the cross product. If you have two vectors like i hat and j hat and you need a third vector that is perpendicular to those two, the cross product will help you. It's a very nice mathematical operation. So i hat cross j hat equals k hat. Now how do we get the rules in general for the unit vectors? Well, the trick to getting the rules for all of these unit vectors and how they multiply each other is to sort of think of i, j and k as laying on a conveyor belt, a belt where when one symbol falls off the right hand side of the machinery, it comes back and becomes part of the left hand side of the machinery and the other symbol shift forward in this system. So for instance, I can conveyor belt i, j and k so that k is now on the left, i takes the place of j in the middle and j takes the place of k on the right. So again, compare the first line to the second line. What's happened? The symbol k has fallen off the end of this equation and reappeared at the beginning. i has shifted over one position and j has shifted over one position. The symbols remain in the same places. The cross product symbol and the equal sign have not moved. So you can think of this equation as a machine where the pieces that fall off the right hand side reappear on the left and all the other pieces shift to the right by one space. This is known as a permutation. A permutation of these symbols yields the second equation. k hat cross i hat is j and then we can permute them or conveyor belt them one more time. We put j at the beginning, we shift k to the right, we shift i to the right and we get j cross k equals i. Now I'm dropping the hats here to speed this up a little bit but you get the rhythm of this. i cross j is k, k cross i is j, j cross k is i. Now if you conveyor this one more time, what equation do you get? Well if you noted that if i falls off the right hand side and then reappears on the left, j shifts over one, k shifts over one, that you get back to i cross j is k, then you're correct. In fact, this cyclic permutation of these three symbols will yield automatically from the first equation all of the rules that I've shown you so far. But these aren't the only rules you can imagine. For instance, if i hat cross j hat is k hat, well then what is j hat cross i hat? Notice that j hat cross i hat appears nowhere in these three equations. What is that cross product equal to? Well the answer lies in the following. If you swap any of the two symbols on the left hand sides of the previous equations, so i cross j, k cross i, j cross k, and change them to j cross i, i cross k, and k cross j, then you will get a negative sign appearing in front of the symbol on the right hand side of the equation. So if i cross j equals k, j cross i is negative k, and so forth. So again, if you can remember that i cross j equals k, and that simply conveyor belting or cyclically permuting those symbols in their positions in the equation will yield you three of the equations, the next three can be obtained by taking the first three, swapping the order of the multiplication on the left, and a minus sign appears on the right hand side. In other words, if you have j cross i, you get a negative k hat that points in the negative direction along the z-axis, not the positive direction that i cross j yielded, and this makes some intuitive sense. If I swap the order in which I multiply these two vectors, and I'm getting a vector out of them, it makes sense that if I swap the order of the vectors, I flip the resulting vector, right? There's some sort of intuition there that you can imagine geometrically. But we're not done yet. We have the rules for i cross j, k cross i, and j cross k, and then from this we derive the rules for j cross i, i cross k, and k cross j, as shown on this slide. But what about i cross i? What about j cross j? What about k cross k? They haven't appeared anywhere in here so far. These are maybe the easiest to remember. The cross product of any vector with itself is zero. i cross i, j cross j, k cross k, all zero. And you'll begin to see why this isn't a bit, but this is the rule for this multiplication, and this is not so bad, it's easy to commit to memory. Now notice that the cross product rules are slightly different from the dot product rules. In the dot product, i dot i yielded the number one. j dot j yielded the number one, and so forth.  When you have the cross product of a vector and itself, it completely goes away. When you have the dot product of a vector and itself, you basically get back its length squared. So this is a little bit different than the dot product. And you can almost imagine that sort of the rules that apply to the dot product are the sort of reverse of the rules that apply to the cross product. And that might help you to remember this stuff as well, but practice is the best way to build memory. Now with those rules in mind, let's actually do the cross product of v1 and v2 shown over here on the left side of the slide. Now this involves the product of the two vectors, and we're going to distribute the cross product multiplication terms, and then keep using those aforementioned rules to simplify. Now I'm going to keep this in algebraic notation. I actually haven't given you the numbers that represent these vectors, but I'll show you how I drew them in a moment. I'm going to keep this algebraic. I'm going to substitute numbers in at the very end, so we can actually get a number for this vector, and then I can draw it for you. So the cross product is v1 cross v2. If I substitute in with the x and y components of v1 and the x and y components of v2, remember I told you, neither of these two vectors has a component in the third dimension, z. Then I would get an equation that looks like this. vx1 i hat plus vy1 j hat is how one would represent in unit vector notation the first vector v1. It's got an x component along the i hat direction. It's got a y component along the j hat direction. No real surprises here. This is going to be then cross, multiplied cross producted with the components of the second vector v2. So here we have vx2 i hat plus vy2 j hat. Okay, well, again, these are the sum of two terms, multiplied by the sum of two other terms. This is just polynomial multiplication. We can bust out our algebra at this point and start multiplying components through this to get a four term polynomial. It's not pretty. We get vx1 i hat cross vx2 i hat. That's the product of these two terms. We get vx1 i hat cross vy2 j hat. So that's the multiplication of this term with the second term and the second vector. And so forth. The remaining two terms just come from repeating this exercise with the vy1 j hat distribution into the second vector.  Each term is the cross product of two components of these two vectors. And so we wind up with four total terms. Now, I can play the old game that scalar numbers like vx1 and vx2, they don't play a role in the vector product, either dot or cross. So I can pull them out in front and then isolate the cross product itself. And that's what I'm going to do in the next line of this equation. I pulled, for instance, vx1 times vx2 out in front. And this leaves me with i hat cross i hat here in parentheses. And repeat that for the second term, vx1 vy2. And I get i hat cross j hat, vy1 vx2, and I get j hat cross i hat. Again, order here is important. You must preserve the order in your cross product. Don't start swapping things around in the cross product without thinking. Or you'll get yourself into a lot of trouble very quickly. Keep the order in the cross product the same as the way you wrote it in the earlier line. And then finally, we have vy1 vy2 and j hat cross j hat. Now, this is where we need to bust out our rules for the cross products of unit vectors in the coordinate system. What is the cross product of i hat with itself? Well, the cross product of any unit vector with itself is always zero. So this term will vanish. And also the last term will vanish, j hat cross j hat is zero. I can indicate that here in the next line of this equation. Now we've eliminated two of the four terms. That's nice, but we're left with two terms. So let's see what we can do to simplify and group these. Well, I notice that this term in the equation involves i hat cross j hat. Think back to the rules, i hat cross j hat equals k hat. So this can be replaced with k hat, a vector that points only and entirely in the positive z direction. I have your j hat cross i hat. Well, that's this, but reversed. What happens when you reverse the order of cross multiplication? Well, you get that third vector, but with a sign flip. So we don't get k hat here, we get negative k hat. So we wind up with an equation that looks like this. Vx1 vy2 k hat plus vy1 vx2 negative k hat. Well, I've got k hat and I've got k hat. I can group these terms one more time, pulling the k hat out in front of everything, and I will get this final, and pretty much as far as I can take it simplified equation, which is a number out in front of a unit vector. The number is vx1 vy2 minus vy1 vx2. That's the number I get, where each of these is the number that represents the length of the component of that piece of the vector. And then finally, I just have k hat, which indicates the direction of this cross product vector. Now, again, notice something remarkable here. We started off with vectors that only had components in the x and y direction, and we end with a vector that only has a component in the z direction. This hints at a key property of the cross product, which I hinted at earlier. It returns a vector that is exactly perpendicular to the other two. I'll come back to that and re-emphasize that in a moment. But that is one of the key aspects of the cross product. If you have two vectors and you need a third vector perpendicular to those two, the cross product is your friend. So indeed, we've obtained a vector, as promised from the vector product or cross product in the first place. Now, what vector do we actually get? Well, for the drawing at the left, I actually used some specific numbers to draw v1 and v2. v1 is 1 comma 2. It has one unit of length along the x direction, two units of length along the y direction. And you can see that reflected here in the blue vector. v2 was 2 comma 1. It's sort of the reverse. It's got two units of length along the x direction, one unit of length along the y direction. And if we insert these numbers into our cross product, which I'll rewrite here from the previous slide, the magnitude of this cross product out in front, vx1, vy2, minus vy1, vx2, plug in the numbers there. We get one times one minus two times two, which yields negative three. So numerically, the vector that I drew here over on the left, the cross product of v1 and v2 is negative three k hat. And so if I draw that here, this is the resulting vector capital V from the cross product. It points in the negative z direction. It has a length of three, and I've represented it here in this three-dimensional coordinate system. So again, I wanna emphasize that the angle between big V and v2 is 90 degrees. And the angle between big V and v1 is 90 degrees. Big V is exactly perpendicular to either of v1 or v2. So we have obtained a vector that has no components in x or y. It lies purely along the negative z axis, and it has a length of three. That's a lot of algebra gymnastics. Is there a quicker way we could at least estimate, for instance, the magnitude or the direction of the cross product? Well indeed, let's take a closer look at some of the properties of the cross product, and these answers will come up. So what the heck is the vector represented by the cross product? It's great that we got one, but what exactly are its properties and what sort of physically does it mean? Well, the cross product always returns a vector, and that vector is always perpendicular to the two vectors used in the product. So go ahead and check this for yourself. Take the vector I just got, big V, negative 3K hat, dot product it with either v1 or v2. If you have two vectors with a 90 degree angle between them, the dot product always yields zero. Remember the magnitude of the length of a dot product goes as the cosine of the angle between them. The cosine of 90 degrees is zero. So if indeed there's a 90 degree angle between big V vector and either v1 vector or v2 vector, the dot product should yield zero in both of those cases. Go ahead and check it, and you'll see that it does. And that's because the original two vectors v1 and v2 involved only i hat and j hat. The third vector, its cross product involves only k hat, and k hat dotted into i hat is zero. You'll see that it's exactly true. But in general, you'll find that this is always true of any vector, big V, that results from the cross product of two little vectors, v1 and v2. The dot products are exactly zero. Now what about its length? Well, its length in general is given by the following equation. The length of the cross product, that's what this symbol here on the left represents, is equal to the length of v1 times the length of v2 times the sine of theta, times the sine of theta, where theta is the angle between v1 and v2. That's just as in the dot product, it's the angle between v1 and v2 that enters into this calculation. Now in the dot product, v1 dot v2, the resulting number represented the physically the following. It was the length of one vector, say v1, multiplied by the component of the second vector, v2 cosine theta, that lies along the first. That's what v2 cosine theta was. It's a projection of v2 onto v1. That's what the dot product physically represented. The vector product represents something slightly different. It returns, first of all, a vector. What's the length of the vector? Well, the length of the vector is given by the length of one vector, say v1, multiplied by the component of the second vector, v2, that is perpendicular to the first one. v2 sine theta is the length of the piece of v2 that points at a right angle to v1. Do some trigonometry and play along with this a little bit and you'll see how this feels a bit more. We'll practice this, of course, as we go forward in the course. This will come immensely in handy for rotational motion, deeper aspects of rotational motion, especially rotational forces and rotational momentum. Now, is it possible to determine the direction of the cross product without doing all of those algebraic gymnastics? The answer is yes. There is a helpful rule that you can use to aid in finding the direction of the cross product and it is another kind of right-hand rule. Now, when we looked at rotation earlier in a more general sense beyond uniform circular motion, we encountered quantities like angular velocity and angular acceleration and they indeed can be represented by a vector, but that vector is perpendicular to the plane of rotation of the object. So, the cross product has a right-hand rule in the same sense that finding angular velocity or angular acceleration has an associated right-hand rule. So, let's go ahead and talk about this. It's depicted here over on the left and I'll walk you through the stages of it in a moment. But let's imagine that we have two vectors, A and B, and we want to take the cross product, specifically in the order of A cross B, A first, then B. We want to get C and we want to know the direction that C points in. So, take your right-hand, take the index finger on your right-hand, also known as the pointer finger, so it's this first finger next to the thumb, pointed in the direction of the first vector in the product. Well, the first vector in the product is A vector here. So, take the index finger, the pointer finger on your right-hand, the one closest to your thumb, and point it right in the direction of A. Now, you're going to take the middle finger on your right-hand as depicted here. That's the next finger on your right-hand. And you're going to try to point it in the direction of B while maintaining your index finger pointing along A. Don't start rotating your hand randomly. You do need to reorient your hand, potentially, but your goal is to keep your index finger pointed in the direction of A and orient your middle finger so that it indicates the direction of B, the second vector in the cross product. To do this, you're going to have to tilt your hand around and we'll do an exercise in this in a moment because your goal is to comfortably point your index finger along A and your middle finger along B. Remember, your fingers really only bend in one direction and so please do not try to crack your knuckles to make your fingers bend in directions they were not intended to go. Just tilt your hand, rotate your wrist so that your middle finger points in such a way that it comfortably indicates the direction of B while maintaining the index finger pointing in the direction of A. Now, stick your thumb out, perpendicular to both your index and middle finger and that's indicated in the picture here. The thumb now indicates the direction that the cross product C vector points in. You now have C hat, the unit vector that indicates the direction where C or A cross B points. That's the right hand rule for the cross product. Point your index finger in the direction of the first vector while maintaining that pointing get your middle finger to point in the direction of the second vector. You may have to rotate your hand, flip your hand over so that you can comfortably do this, that's okay. Flipping is okay. And then stick your thumb out perpendicular to both of those fingers and the result is that your thumb points in the direction of the cross product. It's not too bad but you should practice it and we're gonna practice it right now. So, to practice the right hand rule for cross product multiplication I want you to try to answer the following question and after I ask the question I want you to pause the video and play around with this keeping the rules of the right hand rule for cross products in mind. So, the question is the following given the vectors A and B shown below A here in blue, B here in red what is the direction of the cross product A cross B is it into or out of the screen? So, keep the rules of the right hand rule for cross product multiplication in mind. You're gonna take your index finger you're gonna point it in the direction of A now you may have to flip your hand over from where it's currently oriented but your goal is to now get your middle finger to point in the direction of B stick your thumb out perpendicular to the two your thumb indicates the direction of the cross product A cross B or C vector if you wanna call it that. Now, once you've done that I want you to answer the question does this resulting vector of the cross product point into the screen or out of the screen? So, pause the video here and try this out for yourself and resume the video when you're ready to see the answer. The answer is that you should be forced to flip your hand over so that your thumb points down into the screen and I'm indicating that direction here with a circle with a cross through it. Vectors are like arrows and if you think about an arrow in the sense of an archery arrow where you have a long stick with a point on one end and some kind of stabilizing feathers on the backside you draw the bow back and you fire this arrow it's difficult to represent three dimensions very easily in a two dimensional surface like the screen and so the way that we do this notationally is if we wanna indicate a direction in the third dimension into or out of the screen in this case we use a circle with an arrow in it for a vector that points into the screen and we use a circle with a dot in it to indicate a vector that points out of the screen and this is analogous to the stabilizing tail feathers of an archery arrow flying away from you so into the screen the tail feathers would make a little cross and that's what the cross is kind of meant to represent but if the arrow is coming out of the screen at you you see the point of the arrow and that would be the circle with the dot in the middle of it so that's just a mathematical graphical notational trick let me write that down here if I indicate a circle with a cross through it like I've drawn here it means a vector pointing into the screen here's that symbol written out for you separately from the coordinate system here if instead I had drawn a circle with a dot in it it means a vector pointing out of the screen and that's indicated here now for this problem again in order to answer the question where does the cross product point you have to point your index finger in the direction of A you're forced to flip your hand over to get your middle finger to point roughly in the direction of B your thumb then points down into the screen and so to represent that direction down into the screen I use this symbol a circle with a cross through it now as a bonus question you could answer the following what direction does the cross product B cross A point in so you could try that as a variation on the above question so A and B still are as drawn but now calculate the direction of B cross A using the right hand rule you should find that now your thumb points out of the screen toward you so B cross A points in the opposite direction of A cross B and again that makes sense whenever you flip the order in which you do the cross product you flip the result in cross product vector just as we saw with the unit vector rules earlier in this video so let's review the key ideas that we have learned in this section of the course vectors as we have now fully emphasized have two kinds of multiplication we've reminded ourselves that the scalar product or dot product takes as input to vectors but it returns a number just a scalar number could be positive or negative but it's just a number however we now have the second kind of multiplication for vectors the vector product or cross product and this can be used to construct a third vector from those two original vectors and we've seen some of the properties of this we've learned the formula for calculating the length of the result in cross product so if we have two vectors A vector and B vector the length is AB sine theta where theta is the angle between A and B and we've learned a right hand rule for this in addition to all the algebraic rules for the actual unit vectors to help us find the direction of the third vector very quickly the right hand rule can be used to very quickly check a calculation where you have ground through the algebra of I cross J, J cross I, I cross K and so forth it's good to help build some intuition to use the right hand rule in conjunction with a full algebraic calculation so that you have a comfort zone by calculating these things we're going to use this cross product going forward it's a necessary ingredient in understanding rotational motion and more to the point describing the vectors associated with rotational momentum and also forces associated with rotations


Hello. My name is Sanjay Pujare. I am in Google Cloud Engineering and I am a lead in the GRPC team. So in this session, I'm going to talk about what GRPC is and some history behind it. Then I'll discuss microservices and service mesh and GRPC's role in that evolution. One of the main stages in the evolution of service mesh is proxy service mesh and I'll cover that. Then there are a few slides about main tenets of proxy service mesh, traffic management and security. I'll mention XVS and how traffic management and security works in the proxy service mesh with XVS. I'll describe how to use proxy service GRPC with an example in Java. Then I'll talk about one of the main developments in GRPC, observability and what's happening there. And then we'll end with question and answers. So what's GRPC? GRPC was created by Google based on their experience of and the next version of study. Study is the internal RPC framework Google has been using successfully to operate Google scale of microservices. One of the numbers I heard mention is something like order of 10 to the power of 10, about 10 billion RPCs per second. One of the improvements of GRPC over study is use of HTTP2. And the benefits we get are binary framing, multiplexing, streaming and HVAC compression for headers. I'll also talk about protocol buffers in a later slide. Protocol buffer is also known as protobuf and that's the term I'll use in the service presentation. Protobuf is used as the serialization framework with GRPC. So how does one use GRPC? At a high level, you define your interface using the protobuf IDL in a .proto file. .proto is the extension for such files. I use the protoc compiler to generate client and service apps. By the way, protocol buffers is a separate project and the protoc compiler uses a language specific plugin to generate code for a target language. So for example, there is a Java plugin for protoc and that's how protoc generates Java code. So anyway, after the code is generated and steps are extended or implemented, you can use the client step to simply make a call to the server. Strictly speaking, GRPC can be used with another serialization framework. Protobuf is not strictly speaking mandatory but is the most popular and de facto framework for GRPC. So what's protobuf? Protobuf predates GRPC since Google has been using it with stubby for quite some time. As you can see, its advantages are that it is strongly tied. It has a binary format for compactness and is highly extensible in a backward compatible way. I had already mentioned the code generator plugins for various GRPC languages like Java, C++ and Go. There are code generators for other languages as well. I have shown here a sample snippet of protobuf ideal that shows a struct with string, enum and n fields. This like captures in a nutshell why GRPC is so good. Most of these things follow from what I have discussed so far. Now just a couple of things I would like to add. GRPC is not only used for unary RPCs. A unary RPC is where you send a single request and get a response. But it is also used for the streaming paradigm where you do client streaming or server streaming or bi-directional streaming RPCs. A stream is an unbounded stream of messages. For using streams, GRPC provides an asynchronous framework for processing streams. Another thing that I would like to talk about is extensibility and customizability using what we call interceptors. These interceptors are present both on the client and the server side. Using an interceptor, a client or server can intercept RPCs to decorate the calls or it can perform some cross-cutting functionality such as authentication or authorization or logging. I'll talk more about using interceptors for logging when we get to observability. Now this wraps up the introduction to GRPC part of the presentation. In case you want to know more about GRPC, here are some of the links or resources you can look up. The first one is a link to a very useful presentation covering introduction to GRPC in a previous QCon conference. Let's move on to the next section of the presentation. Now GRPC enables remote procedure calls to make them almost as simple to use as in-process direct calls. This has enabled the microservice architecture where a monolithic application is broken up into multiple microservices. What used to be in-process communication inside the monolith is now RPCs over the network. In this picture, the yellow layer talks to the red layer which talks to the green layer and these RPCs cross network and infrastructure boundaries. The dotted lines in the cloud-like shape show the various boundaries the RPCs have to cross. One advantage of microservice architecture is the ability to scale. Various infrastructure resources such as VMs, clusters or networks are added as the application scaling requirements go up.  So how can all this be automated or managed? So this is where the service mesh comes up. The service mesh has a control pane like Istio shown here in the yellow box that is managing the data pane. That is the bunch of microservices that make up an application. The control pane maintains and manages policies for traffic management and security. These policies are enforced or implemented by data pane entities called proxies. Now this is the proxy mode. In this picture, GRPC traffic flows through these proxies and the proxies are responsible for offering the traffic and enforcing security based on policies from the control pane. The proxy is transparent. That is the GRPC application is not aware of their presence and communicates as if the proxies are not present. The proxy is also used for HTTP and other application level traffic such as Redis or MySQL. But with GRPC we can do away with the proxies if we implemented the same functionality in the GRPC layer. So this is the so-called proxies model. We enhanced GRPC to have the same traffic management and security functionality as the proxy or specifically the on-white proxy. That is most commonly used in Istio or XPS based service meshes. The control pane Istio in this case sends the same policies to GRPC instead of the proxies and the GRPC client and server enforce these policies within the GRPC library. The services in the mesh talk to each other directly without the proxies. So this is of course true for GRPC traffic, but if you have other kinds of traffic, say HTTP or Redis, then proxies might still be needed in your service mesh. So let's look at the advantages of the proxy service mesh. In this slide, you can see the latency gains as the result of the proxies mode. Here are some background on this experiment setup. This was set up using Forteo, which is a Go-based load testing app. The infrastructure resources used are as follows. In the GKE cluster version 1.20 with three E2 standard 16 nodes, these nodes have 16 CPUs and 64 GB memory each. This experiment uses the Forteo client and server apps in the application container, which has 1.5 virtual CPU and 1000 MB memory allocated to it. And we also have the sidecar container for the Istio agent and the on-white proxy, which has 1 virtual CPU and 512 MB memory allocated to it. The experiment included both the with and without MTLS enabled modes and with and without the on-white proxy. Now, a little bit about the sidecar container. If this is proxies mode, why is there a sidecar container? Note that we did the experiment to measure the performance for both the cases. In case of proxies, there is no on-white proxy, but we have the sidecar container for something called an Istio agent. So even though we don't need the on-white proxy, we need the Istio agent. Now let's compare the performance. Now compared to the on-white case, there is a massive improvement with MTLS at 64 connections. The latency improvement is from 6 to 16 times. That is about 500% to 1500% improvement, depending on whether you are looking at a P15 or P99 latency numbers. Note that this still supports advanced traffic management and MTLS, but without the on-white proxy. Let's also look at the social research. As mentioned earlier, the proxies experiment still requires an agent called the Istio agent. Even if we still require an Istio agent, the agent uses less than 0.1% of the full VCPU and only 25 megabytes of lemmery, which is less than half of what on-white requires. Note that these metrics don't include the additional resource usage by GRPC in the application container, but this serves to demonstrate the resource usage impact of the Istio agent when running in this mode. I think I had mentioned XDS before, so let me expand on that a little bit. XDS is a protocol for control plane to talk to the data plane entities. That's why it's called a data plane API XDS. Now XDS where X stands for some data plane entity like X in algebra, and DS is discovery service. For example, CDS for discovery of clusters, RDS for routes, LDS for listeners, and so on. XDS was developed for on-white, but it's pretty open and extensible for any kind of service mesh. GRPC adopted it and extended it for the proxy-based service mesh. This slide mainly shows how XDS works for traffic management in the service mesh. The LDS, which is the listener discovery service, is used to discover the configuration route for any GRPC service a client is trying to reach, such as payment-service.mydomain.com. LDS is the route of the configuration and it points to other artifacts, specifically RDS for routes. Now RDS contains the routing information, things such as how to process the host, path, and other HTTP headers to route a request. So this is the place where routing and traffic policies are enforced. RDS further points to CDS. CDS has cluster information. A cluster is a set of backends that are part of the same infrastructure, such as the same geography or the same network, and all the backends in the cluster share the same security configuration, such as certificates and keys. Now CDS has references to what is called EDS, endpoint discovery service. EDS has the actual backends that a client connects to. So CDS and EDS together are used for load balancing. Having covered traffic management, let's look at security. So why is security so important in a service mesh? Remember that a service mesh is the result of breaking up a monolithic application. What used to be in-process communication inside the monolith is now RPCs over the network, and as a result, they need to be secure. These RPCs are routed or load balanced as part of the service mesh orchestration. We need security that's well integrated with things like routing, load balancing, and service discovery. For example, each endpoint needs to be able to validate its certificate and identity using the control frame provided information. Security also includes authorization where a server authorizes a client before accepting the RPCs. So how is all this done and who does it? The answer is service mesh with security. This is a diagrammatic representation of how it all works. You have the client in the yellow box on the left sending RPCs to the server in the red box over a secure channel. The blue lock on that line indicates a secure channel. Both client and server are XDS enabled and get the security configuration from the XDS control frame shown in blue at the top. The client and server need certificates and keys that are provided by the certificate and deployment infrastructure to make it all happen. The green box represents the various infrastructure components which include certification authorities, also known as CAs, to make certificates. A process to continuously generate CSRs and use them to make the certificates. A mechanism to make the certificates and keys available to GRPC workloads using the GRPC's plugin feature. Now, for implementing security, we implemented a certificate plugin feature in GRPC. And we also added the required extension points for the plugins in XDS. When all of these things are in place, the client and server secure their GRPC traffic. Let's recap service mesh security. The control frame uses a transport socket abstraction within a CVS or a VS to consider security in GRPC. But there are external components like the security infrastructure to provide certificates and keys. When MTLS is involved, GRPC uses the provided certificates and certain other bits from the transport socket configuration to create the MTLS configuration or to create MTLS connection. We get authentication, encryption and something called server authorization with MTLS. Server authorization is somewhat like the host name check in HTTPTLS. Then as part of security, we also have regular authorization or client authorization implemented on the server side. Where a user can use authorization policies, also known as RBAC, to authorize RPCs based on the various things including client identities. So how does one use this stuff? Say in Java. The example in this slide is from the security GRPC mentioned here, 829 XDS TLS security.md. Now a GRSC is an RFC or a proposal in the GRPC ecosystem. This example is in Java, but the usage in C++ and Python and Go is similar. There is something called XDS channel credential and that you supplied to your channel builder and this credential tells GRPC to use XDS supplied security configuration. And there is something called server credential on the server side, which instructs GRPC to use XDS supplied security configuration on the server side. And I wonder what the insecure channel credentials used inside create is doing. This is a fallback credential. And what is that? I will come to that in a bit. Now that XDS channel credential is, note that the XDS channel credential is a way for a caller to obtain the use of XDS security config. Note that a caller can use a different credential. For example, a TLS credential with a channel in which case the XDS supplied security config is ignored even if the rest of the configuration from XDS is used. And now back to fallback credential. And XDS credential also takes something called a fallback credential, which kicks in if XDS doesn't supply any security configuration. So instead of choosing this, choosing to treat this as a plain text or insecure communication, a caller can tell GRPC to use fallback TLS credential. If they had used TLS credential in this particular XDS credentials. This wraps up the GRPC and service mesh part of the presentation. For more information, you can look up a previous KubeCon presentation that talks about professional GRPC service mesh in some detail. I have also included another KubeCon presentation last year that focused on security in professional service mesh. Both of these talk about using the professional GRPC service mesh in Google Cloud using Google service mesh products. I have also included an Istio blog that talks about professional service mesh in Istio. Now let's look at another aspect of microservices or the service mesh where effective use of this paradigm could be hampered by what we call observability or lack of it. Observability in simple words is visibility into the internal goings on in your service mesh to the extent that you need that visibility for reliability and efficiency. For example, if something breaks in your complex service mesh or it is performing poorly, how will you figure out where the problem is? Is there any way the infrastructure or the software components can provide that required visibility? So let's talk about GRPC observability and how that comes into play here. We in the GRPC team are about to release GRPC observability which consists of logs, metrics and traces. The three main pillars of observability. I had talked about GRPC interceptors before. We use the GRPC interceptor framework to inject our observability interceptors which generate the required raw data for the three pillars. This part is then integrated with exporters and backends so that the raw data is massaged and sent through the exporter pipeline to an appropriate analytics backend. This integration provides the end to end GRPC observability. Some more information about GRPC observability or O11Y as we like to call it. You have the app developer, the character, the icon on the left-hand side in green. The developer is building GRPC applications using the latest GRPC artifacts that support observability. The running apps are provided with appropriate observability configuration by the developer or the SRE. The GRPC interceptors pump the relevant raw data, I mean the logs, metrics and trace information through the related exporters into the respective backends. Here you see a logging backend, a metrics backend and a trace backend. These backends then produce the required dashboards that are used by the consumer. In this case, the SRE to get the visibility into the internal state of the application, specifically as it is related to GRPC traffic. The GRPC observability product runs in Google Cloud platform. On the producer side, it has plugins for logging, metrics and traces. On the producer side, you also include the required exporters in the application, namely the stack driver exporters configured to send data to the Google Cloud apps backend. The product also has an admin console to enable or otherwise administer the feature. And then we have consumer dashboards that provide some popular canned views or allow you to configure or customize the views with customizable queries. Let's see how all this works in Java. In Java, there is an artifact called GRPC GCP observability that you use in your application. The artifact also pulls in other required dependencies such as the stack driver exporter. In your Java app, you call an init function at the beginning. When the application is running GCP and an appropriate configuration is provided, it automatically sends the required raw data to the Google Cloud apps backend and you have observability. Let's look at the Java code snippet for an actual example. In your main application class, there is a main method. You call GCP observability.grp init to start observability. In this case, we are using try with resources so when the try block exists, close is also is automatically called. The whole application execution is inside the try block. Now you may choose to call close explicitly if you don't want to use try with resources. This is what the GRPC observability configuration looks like. There are enabled disabled flags for the three pillars. For logging, there are filtering options to limit or filter the kind of RPC you want to log. We also have provided a filter to filter the kind of events you want to log. And finally, there is a probabilistic sample configuration where you specify the sampling rate. So with 0.5, it will send only 50% of the calls to which are randomly selected to be for generating the trace data. Now one more thing about observability, there is something called tags which are labels attached to the lot and methods data. We automatically attach location tags which identify the location or sold information of where the data was generated. For example, the VM name or the Kubernetes cluster name or the namespace. We also allow the user to provide additional custom tags that could be used to provide additional identification information such as the app ID or the data center and so on. This is a screenshot of the consumer dashboard. As you can see, we automatically provide suggested queries based on the ingested data and clicking on a suggested query will generate that dashboard. For example, log records of GRPCs that had errors. This is a screenshot of a log record of one of the GRPCs that failed with the deadline accident error. The screenshot of a log record shows the location and custom tags called labels are here. The location tags have the cluster name, pod name, project ID and so on. The custom tags contain the app ID and data center as supplied by the user's environment or the configuration. For GRPC observability, we have already released the logging feature in private preview. The metrics and traces are coming soon, almost as we speak. These will be integrated with Google Cloud monitoring entries. This is a screenshot of the upcoming metrics part of observability. This is done by specific workloads such as the VM name or VM instances or by location or custom tags. So that wraps up the whole presentation. Before closing, I would like those of you who are interested to know more about anything I mentioned here. If you just want to meet the GRPC maintainers, you can go to GRPC.io to submit a form and to get started. GRPC.io is a good starting point to get more information about GRPC. Thanks everyone. So let me know if you have any questions.


Comme vous pouvez le voir, je ne suis pas Alicia. Alicia est ici, c'est mon étudiant. Nous travaillons dans l'application laboratoire, mais nous faisons une théorique astrophysique pour longtemps pour moi. Comme vous le voyez, c'est un problème très difficile parce que les observations sont très difficiles à obtenir. C'est très difficile. La numérique est très puissante, mais vous pouvez faire ce que vous voulez. Vous devez le mélanger avec tout ce point. Et pour le temps, j'ai envie de présenter un summary de la situation, si vous voulez. En tout cas, j'ai donné à vous des idées, j'ai envie d'avoir une bonne idée de ce qui se passe dans ces systèmes. Au début, je parlerai des factures en astrophysique. Notre problème est concerné par les clusters globales et les galaxies. Ce n'est pas une large-scale structure, comme Michael Joss m'a dit. C'est un autre problème. Vous devez inclurez la relative générale. En ce cas, vous êtes sur une petite scale de l'univers, la scale galactique et la relative générale. Ce n'est pas important. Le deuxième problème que j'ai voulu évoquer, c'est le problème de l'équilibre état, dans lequel l'équilibre est observé par ces systèmes. Ce n'est pas un problème très simple, comme vous le voyez. Après, je présente des instabilités, parce que je pense qu'il y a quelques instabilités qui s'occupercent dans ces systèmes. Et ils sont très intéressants à faire un bon scénario, qui je présente à la maison. Il y a quelques factures. Le modèle standard de la dynamique stelaire est très bien connu. C'est un système avec des n-compagnons en interaction gravitationale. Comme l'n est très large, vous êtes dans un limiter. C'est un problème dans lequel l'équilibre état est associé à une fonction de distribution, qui s'évolue dans le potentiel gravitationnel. Et les équipements dynamiques sont les systèmes de Vlasov Poisson. Il y a une grande densité, qui est l'intégral de la fonction de distribution sur les villes. Et il y a deux constants dans ce problème. Un petit temps, qui est un temps dynamique, qui est obtenu de manière différente. Mais vous avez toujours une diminuie de l'homérité. Un sur la route square de G, le constant de Newton, et la grande densité du système. C'est le temps d'aller par une star, d'aller sur un côté à l'autre côté de la galaxie, si vous voulez. Et il y a un autre temps, qui est un temps long, un temps considéré comme l'infinité dans des systèmes. C'est le temps qui est pris par une collision, pour changer d'une manière ou d'une magnitude, la vitesse dans le système. C'est une très grande calculée par Chandra Sekar, dans le milieu de l'année dernière. Et vous avez beaucoup de controversies sur ce résultat, mais tout le monde est presque dans la connexion avec ce formulaire, il n'y a pas de détails. Et vous voyez que ce temps est N, ce temps-là. Donc, si N est equal à des billions, comme dans la galaxie, puis, comme ce temps-là, il y a des millions, des centaines de millions de années, vous comprendrez que ce temps-là est très, très long, en comparaison entre l'âge de l'univers. Donc, parfois, vous pouvez considérer que ce temps-là est infinit. Mais pour la cluster globale, il n'y a plus de stars, il n'y a plus de stars, il n'y a plus de 1000, 10 000, 100 000 stars. Vous pouvez avoir l'effet de la collision dans la cluster globale. Let's see this point. So, here you have two representative cluster globale. We are a lovely object in the sky. If you've never seen a cluster globale in a telescope, let's try. It's very impressive to see in the reality. You can do this with a small telescope. It is very possible. So, you are here the two kinds of globular cluster. This one, with a large core, and this one with a collapsed core. The difference is very remarkable. So, when you plot the density of stars in function of the radius of the system, in this kind of system you are a large core, and after a low, in this kind of system you are no more a large core, and as we said, a cusp in the core. So, they said, astrophysicists said that this kind of globular cluster are core collapsed. And you have almost 80% of the globular system, the system of the galaxy. In our galaxy, there are almost 100 globular clusters, and there is almost 80 in this state and 20 in this state. And we can say that this effect is an evolution effect. How we can say this? This is very simple to say, to easy to say. You plot all the globular cluster in a diagram, which is, here you are the globular cluster, the alfamast radius, RT, the limit of N, here an estimation of the radius of the core. And when you plot all the globular cluster of the galaxy in this diagram, you see that there are repartition. When you identify what, where there are collapsed core by this symbol, they are all here. And why I said it is an evolution effect is because when you make a color which represents the time, the dynamical time of the system, you see that all the collapsed core are the blue one and the blue one are the one that have the smaller dynamical time. So during the evolution of the galaxy, the evolution of the galaxy during 10 billion years, they are affected by collision and the effect of collision makes this core to collapse as we see in a moment. The model for globular cluster is very old. There is no more explanation but it is very old. There is an explanation but the explanation is not so good as well. This is the king model. The king model it is fine tune heuristic model. You consider an isothermal sphere. You will see why. And you cut it because you have some problem at the end of the distribution. So king said there is no problem. We have to cut and there is no more problem. And you obtain this model. And with three parameters you can fit very well. This is two globular clusters with a core and you can see that you can fit in a very good, with very good accuracy the data and the model. And the collapse core are rather like an isothermal singular sphere. So the density profile is only a low radius to the power minus 2. For the galaxy, the situation is rather different. In fact you have two kind of galaxies. You have LSB which are large, low surface brightness galaxy. We are small galaxy, isolated galaxy. And which are corallaux fashioned. You can see here such of LSB. Which LSB represent in fact 90% of all the galaxy. We can see. It is not very seeable. But when you plot the density if you can of such an object, it is very recent 10 or 20 years we are able to do this. We obtain a corallaux structure. A core with no slope here and minus 2 in the power and the slope. So this is for LSB galaxies and for high surface brightness galaxy. We have such profile for such galaxy or for galaxy form in the large scale structure simulation by cosmologies for example. You obtain such for example, they say this is NFW profile or NSTO profile. And in fact there is a study by Merit some years ago, 10 years ago, which said that NFW is not the same, the better but the best. But rather equivalent profile, it is pruniel simian which is here. And this is a deprojection of the famous Devocouler law. And in this deprojection you see an exponential and you can think that there is some thermodynamics in back in front. The difference between these two kind of galaxies is not an evolution of the system like in global cluster. It's what I think. I am not only the one to think this. The difference between these two systems is between the history and the evolution, the formation of the galaxy. So now what is the problem with equilibrium? If you want to describe a galaxy by thermodynamics, it is a no problem with no solution. A solution by Lindembell in 1767. This is a violent relaxation. So you split the phase space into two energy macro cells. You divide these macro cells into micro cells of the same old. Macro cells contain all the particles with the same energy. And after you compute to maximize the number of complexions and their contents. But there is a lot of problems. They are not distinguishable or not. What are the actual constraints, the energy, the mass, the angular momentum or whatever? Can we use, this is not a simple remark, can we use the steering formula at first order? Like everything do in thermodynamics, statistical thermodynamics. Is it a Vlasov equilibrium and over question I don't know it. So let me present for the person who don't know this, the Lindembell result. So in this calculation, Lindembell suppose that particles are distinguishable. But in fact if you see in detail, he suppose that all the particles are the same mass. So it is a little bit contradictory to use. The constraints imposed are the total mass, the conservation of the total mass and the conservation of the total energy. And as you see, as you know, gravitation impose a classical poly principle because you can put two particles at the same place due to gravitation. So when you compute the number of complexion you obtain this way, which is a Fermi Dirac with distribution with distinguishable particles. And when you compute the distribution, when you look for in this set, so the set of distribution with a finite mass and a finite energy, when you compute the maximum of the entropy, of entropy like, you obtain a Fermi Dirac distribution. As the gravitational system are not degenerate, you can consider that any is very smaller than GE, the degenerate sense of the state, then this distribution reduced to the Maxwell-Boltzmann distribution. So this is the conclusion of Lindembell. But it is good because in the thermodynamic limit when n goes to infinity you obtain Maxwell-Boltzmann distribution. When you integrate this distribution over the velocity you obtain a density exponential of minus an inverse temperature times the potential. And when you plug in into the Vlasov equation you obtain such an equation. And when you use Gidas and Nuremberg theorem of pure mathematical theorem it is said to you that such a system is spherical. So you are happy because everybody thinks that all the gravitating systems are spherical. For example all the globular clusters are spherical. Very few not spherical globular cluster but there is a slow rotation we can explain it. You say to me the spiral galaxies are not spherical but if you have only a disc galaxy, the disc is unstable so around the disc you have a spherical dark material. So in this context all is spherical. So it is a good result but you have a lot of problems with this result. I speak with two problems. First of all this is a classical problem of this kind of calculus. The result is not in the set where you are looking for. Because when you can compute the behavior or the density you obtain in the outer region and you obtain that at the limit when air goes to infinity the density goes like air to the power minus 2. There is a minus here. So when you integrate to obtain the mass over R3, R3 you obtain a divergence. So this system has not a finite mass and you are looking for a system with a finite mass in the basic hypothesis. So it is a problem. A less classic problem perhaps for me you are looking for like a maximum of the entropy in a system which is described as a glass of equation. And glass of equation conserves the entropy. What does it mean to search the maximum of the entropy when it is conserved? For me it is a problem but perhaps it is not a problem. The classical solution like king model we have a cut of this problem.  So the cut, the king cut or box there is a large theory in which people put isothermalsphere in a box so you haven't such problems. But what is this box?  And there is two modern ideas to solve these two problems simultaneously. The first is a paper by a Brazilian guy and I when this famous trimester when Jihad was in Paris two years ago. We have, I will present to you and our idea six years ago by Orge and Lili Williams. They said that at the end of the system larger the concentration, the number of stars are not so sufficient to use the sterling formula cut at the first order. And when you consider over terms, second order terms and more complicated terms, this gives a finite mass to the system. It is so simple, why they don't think to this before. And I show you what it gives when you do this change. So the distinguishability problem, this is the idea with Beraldo et Tall two years ago. The violent relaxation of self-gravitation, self-gravitating system is not able to produce a full mixed state. It is well known and collision are needed to to to fully mixed the system, but collision takes a long time. So when the system is collapsed, the system is not in a full mixed state. After a few dynamical states, the system only is partially mixed and the phase space contains isolated mixed in Iceland. Particules in mixed regions are indistinguishable among themselves, but distinguishable between the over islands. So in fact you can consider that all particles are the same property in regards to the distinguishability. There are a set of particles we are distinguishable and a set of particles we are indistinguishable. So when you do this, the number of complexes using these remarks becomes this way. And when you do the same calculus, you obtain this distribution. And when it is Maxwellian, you will see it. But this kind of hypothesis assumption breaks the Vlasov symmetry because to obtain Vlasov equation, you know that you have to stop the BBGKY hierarchy. And you have to suppose that all the particles are the same law in this improbability. And in this case, they don't have the same law. So this gives the possibility to the entropy to grow during the violent relaxation. To obtain this kind of distribution function, this kind of density profile, so it is always interesting. You have a core and a halo, but you are still faced to the problem of the mass here. This is the slope of the halo. So you see that including this remark of distinguishability, the slope is always minus 2 at the end of the system. So when you consider the new sterling approximation, as I said in this paper, the situation is changed and this is the same.  And in this case, you see that the slope is not longer 2 and it is for depends of parameters. So this kind of system has a finite mass, so you don't have any problem and you don't have to cut it before doing the job. Let's me now speak about instabilities quickly. The first instability, which fashion self-gravitating system, is the jeans instability, it is very well known. It is a lot of name, it is very simple. When you consider a new system with velocity dispersion, with constant density and with radius, when the radius of this system is greater than a certain radius, which is the jeans radius, the jeans length, then the system collapses. And what you obtain after the collapse, in fact, you obtain a cor-halostructure. It is always the same thing. And not a general cor-halostructure, in general you obtain a cor with a slope with minus 4. And what we do with Alicia, we remark that this model you obtain is an Isochron model. Let me say a few words about this Isochron model because it is very interesting and fabulous model by Michel Enon, the one of Enon Health. It is in 1968. And the idea of this model, you know that when you have a sphere, I don't resist to write on this marvelous blackboard.  And you know that this star is characterized by an energy and a square momentum. You know that the orbit of this star in this system lies in a plane. It is a first-year problem, first-year university problem. And you know that the orbit in this plane. And so you have the distance to the center of this star is periodic. And you can compute the period. And it is very easy between the peri-center to the apocenter. This is very simple. If you don't know, you can find it in classical books. The energy minus the potential minus the square of the momentum. So you can see that in general this period of the star depends on the energy and on the square momentum. Michelinot asks the question, what are the more general potentials for which this period do not depend on L2? And the names of these potentials are the isochron potential. And he obtains the formula. The formula is very simple. It is minus. So you can see that when B is equal to zero, an isochron, it is a Kepler potential. When B tends to go to infinity, you can show that this potential is equal to the harmonic potential. And in between it is an isochron potential. And what you obtain after the genes, the genes instability, you can see here, you can see here, it is this potential. And I think I understand why. It is not in two years ago in the middle of this amphitheater. So here you are the collapse. And in blue and in black you are the density. When you put it into the Blasov equation, you obtain this formula with only one parameter. And when you fit the data with the model, it is okay. So the isochron model is a product of the violent relaxation in this sense. The second instability is well known by the people like you. It is Antonov instability because it is a thermodynamical problem. When you put an isothermal sphere in a box with four parameters, an energy, a temperature, a mass and a radius, we can show that when air goes to infinity, the mass goes to infinity too because it is an isothermal sphere. But when you cut the system, you put it in a box, there is no problem with mass. But you cannot put any isothermal sphere in any box. So you have constraints. If you fix the temperature, then the good parameter is the density contrast. It is the ratio between the value of the density at the center of the system and on the edge of the system. And when you want to put an isothermal sphere fixing the temperature with a density contrast larger than this number, it is impossible. And when you fix the energy, the density contrast for the instability is less, this is well known. This is at the basis of the ensemble in equivalence. And I make the remark that this instability, Antonov instability, the parameter of instability is much more or less, is less, is very, when you add a thermostat to the system, is the problem of caloric curve. I think you know this kind of problems. And the result of an isothermal sphere in a box, it is a Corallo system. And the result, the product of the Gravothermal instability, of the Antonov instability, is the collapse of the core. So we think that it is what happens for globular clusters. Such systems have density contrasts we grow during the revolution. And when density contrasts go up to the limit, the core shrink and collapse and you obtain, this is the common explication. Less known instability, this is radial orbit instability. When you have, we have done a proof some years ago, this is a very strange instability. This is an instability which needs dissipation to develop. This is very interesting, I refer to the paper to see it. And this instability transforms a sphere into a triaxial system. The mechanism is the following. When you are a system which reaches in the velocity space, and when you add a non-radial perturbation with a direction which is non like the overs, there is, you pull one, this is radial, this is pencil, this is radial orbit. And this extends one of the orbits. And there is a torques existing between this orbit and the over. We are close to this. And after, there is a strange. And this is at the end, you obtain a stable equilibrium, which is no more spherical. I can show this mechanism is very, very complicated. What you have to keep in mind is you can produce this instability, not only in simulation but in reality. How to do this instability in reality? You have to make a collapse of something onto something. Let me show something about this. Here you have a plumber sphere, which is a spherical galaxy. And around it, you have a homogeneous system. And this homogeneous system is a gene unstable. And the gene's instability is parametered by the initial virial ratio. When you are far from one, minus one, the instability is very strong. And when you are near one, the instability is not so strong. So when you make a collapse of a system onto another system, you can obtain this instability. This instability is evident on the simulation and you can prove it. In this case, the system receives a lot of radial velocity in this phase space. So it develops the radial orbit instability and develops a bar. In this case, it receives not a sufficient amount of radial velocity. And the instability cannot develop. We think that this kind of instability is at the origin of a primordial elliptical galaxy. In a few years ago, 10 years ago, 20 years ago, when they do simulations, cosmologists, they don't can't explain why there is a primordial elliptical galaxy. They think that all the elliptical galaxies are the product of the merging of two spirals. And so there is no reason to have elliptical galaxies at the beginning of the universe in the simulation. Using this kind of instability, you can produce such a galaxy when you want. But in fact, when you have produced such a galaxy and if it is not isolated, the merging process, something goes on to it, et cetera, et cetera, and it loses its possibility to remain elliptical. But in fact, there is a footprint of this instability in the slope of the density. It is a very interesting paper by Katz, you see it. And this instability is very important to observe what we observe. OK. So let me finish. I finish by putting all these things together. What is the paradigm to explain the formation and evolution of globular system, globular cluster system? At the beginning you have an initial homogeneous cloud. It suffers a violent relaxation, genes instability, it forms an isochron. If the collision on a very few time, dynamical time, on a less, on a more and more longer time, there is a collisions who produced a system like a king. And after the evolution can make the core of the king collapse to form the 20% of the globular cluster you obtain. In the galaxy context, it is different. If you have a hierarchy scenario, so you can idealize by two systems, a smaller into a bigger one. For dynamical reasons, this is a smaller which collapse first. So the first collapse on the gene stem scales to form an isochron. But in this context, the bigger one is a thermostat. And in this case, the critical radius, the critical density contrast is very smaller than 700. And it is equal to 244. So the Antonov instability occurs at the very beginning of the formation of the system. And you have all this part of the system is pushed towards the center. And it is a good hypothesis, a good, a good mechanism to explain why there is object which is in the scope of GAD. Because it is a good possibility to form a supermassive black holes. Which are not present in the over paradigm.  After the big system collapse onto this and you can produce such thing with a black hole at the center. Or, always with the black hole, but if the collapse is violent, as we see in the simulation, you can obtain a triaxial structure like an elliptical galaxy.


We are very happy to have with us today the pianist Marc-André Amelain. Welcome to the Hineverlag. You've just given a concert here in Munich last night and we'll play in Belgium tomorrow, so thank you very much for taking the time to visit our publishing house for this interview. It's a pleasure. It's wonderful to see the offices, you know, what your facility looks like here. It's wonderful.   It's great. We at Hine have just published three Urtext edition of works by Rachmaninoff, the 24 Preludes, the Attu Tableau and the Coralli variations, and the fingerings for these volumes have been provided by none other than you, Marc-André Amelain. I remember when we met in December 2012 to discuss this project, you were at first a bit hesitant to take on the job. Were you skeptical about the idea of adding fingerings in general, or maybe was it because of Rachmaninoff in particular? For example, how well did you know the works that I mentioned before? Well, I think at first I was hesitant because I didn't know whether editions really needed fingerings because, and I still think that there are quite a few passages and sections of works which are so obvious that they really don't need any commentary or fingering elucidation from anyone, really. But there are actually, after examining these works closely, I can say that there are indeed suggestions that are possible to be made. Above and beyond what Rachmaninoff has already provided. So that's what I set out to do. In a few places Rachmaninoff added fingerings himself, and they are very original sometimes. Have these fingerings been illuminating to you in some way? Does it tell you something about the way he wanted his pieces to be performed? Well, first of all, when I saw that he provided some fingerings, of course I wasn't going to change them. I don't think, I mean this is a little bit long ago that I did these fingerings, but as far as I remember I did not suggest any alternates when he provided his own because I figured that he had specific results in mind. In one particular case which I think is one of your questions, it's very, very clear that the fingering that he indicates, it's in the 4th etude tableau, opus 39, really has an influence on the musical result. And it's a very, very simple thing. So it's a simple descending scalar passage. But it's sort of a very marcato sort of style of music. So what he indicates is thumb and second finger. Even with a thumb on the black key, which in music of the classical period is considered taboo, but here it's perfectly acceptable and there's an accent at the end of the scale. So it helps the rhythmic contour of the piece. And I think that is better than if you just fingered it to the conventional way, 1, 2, 1, 2, 3, 4, 1, 2, 3. It wouldn't be quite as effective. So that's a very, very intelligent suggestion and I wasn't about to change it. So that's just one example. He did not provide a lot of fingerings overall, only when he felt it was absolutely necessary. My role in there was to supplement these suggestions. Not with anything terribly personal, although I was thinking that there are places which perhaps need clarification, depending on your level of pianistic ability in order to tackle these things. Another interesting question, of course, is what kind of hand do you write fingerings for? Because Rachmaninoff had very large hands. I think he could span a 12th. I myself can span an 11th, so just from C to F. And generally I try to stick to fingerings which would benefit a large hand, even though there are many pianists who tackle these things, who happily tackle these pieces, who have very, very small hands. But I've found that pianists who do have small hands somehow find a way to get around the writing and find solutions through creative peddling or whatnot or certain other devices that I'm not aware of, because I have a large hand and I don't have to worry about these things. But I decided to really stick to the large hand philosophy, the large hand sort of canvas in writing these fingerings. So with regard to your own fingerings that you have provided, maybe you could show us an example of a passage where you felt it was necessary to give a hint to the pianist? I think in most cases the solution, when there was no fingering, was so obvious that I didn't feel that I could add any fingerings without making the performer feel like an idiot for not thinking of it themselves. But in certain cases, I guess there's more personal things such as this little passage here in Opus 39, No. 902 Tablo. It's a simple pattern in thirds and it's within a D major sort of scale, a diatonic scale. If you would follow the sort of accepted concept that you shouldn't have too many thumbs on the black keys, then you would finger it taking care to put second fingers on black keys. But personally I find that it helps to have as much of the same movement as possible with each of these thirds. So I put a thumb and third finger on every eighth note. It helps establish the rhythm, the regularity of the rhythm and also the regularity of the accents. Instead of... is pretty much how you would finger a scale in thirds. So that's just one example really. Are there pieces that you got to know better while working on the fingerings and perhaps would consider playing them now more often in your concerts or maybe for the first time? I have to say that I haven't played all of these pieces, but working on these fingerings would definitely encourage me to explore this literature further. I don't think I would necessarily play all of them, but there are some which I hadn't been as attentive to as I should and which would make a perfect addition to some of the programs that I offer. And to answer another possible question, I think it is perfectly possible to offer fingerings for things that you haven't played before. You approach this sort of thing in the same way as you would when you were learning a piece. Finding fingerings is part of that process, whether you are playing the piece or not. What would you say? Which place does Rachmaninoff occupy in a repertoire in general? I think I'm very likely to play more Rachmaninoff in the future. I added a few preludes in my repertoire a couple of years ago and I'd definitely be interested in looking at more of the etude tableau. I can't tell you how many people have actually said that you should look at the first sonata, because they really, really love it. The couple of times I've heard it, I have to say that it did not make an immediate impression, but that doesn't necessarily mean anything because I can think of other composers, Metna, for example, which don't make an immediate impression at first hearing, but then gradually the music takes hold of you. And I'm sure that in some of Rachmaninoff's works it's the case as well. On the other hand, I think that something like Rachmaninoff's Chopin variations is a very appealing piece, but it hasn't really received its due. Pianists are much more readily tackling the Corelli variations, but I think the Chopin variations, even though it's an early work, is very, very worthy of anyone's attention. In a concert setting it might be a little hard to digest having all 24 preludes. I used to play all of Iberia in one concert and I thought it was a marvelous idea, but some people told me it's a lot of Spanish music in one recital, and in a rather long recital too, because I also used to add Navarra. I think there is a case to be made that there will be never enough Rachmaninoff recordings, because he's such a vital presence and continues to be, and I think his presence in our lives is really growing, and it's especially amusing to consider past critical opinions of his music. If you look at the 1954 Grove, there was an article, the entry on Rachmaninoff, written by Eric Blum, who was the editor, said that on the whole the music doesn't have much future, if you can imagine that. But at the time Rachmaninoff really wasn't to us what he is now. He's become a necessity. So do you think there are differences perhaps between America, Europe and Asia with respect to Rachmaninoff's reputation or to the popularity of his works? I think Rachmaninoff's reputation is growing everywhere. I think he's really essential for all of us. The immediacy, the wonderful melodiousness of the music, and the way he just plunges directly into our hearts and all of that, we finally realized what a great musician he was. And as I said, one is what an essential ingredient he is to our lives. You've also played in Russia, in Moscow. Do you think there's a special feeling about it? To play maybe in the same venues as Rachmaninoff did in front of a Russian public? Oh, I think definitely. And I remember one of the last concerts I gave there was... I did the second Sonata, the 1931 version, also with a couple of preludes before. And I have to say that for one reason or another, there was a special warm feeling and perhaps an added sense of occasion when playing these for an audience who just lives, breathes and talks Rachmaninoff and eats Rachmaninoff. Apart from Rachmaninoff, you have recorded many pieces from the Russian repertoire. You have recorded the complete Scriabin Sonatas, the Sonatas by Nikolai Metner. You've recorded an album with music by Nikolai Roslavitz. Is there something special that is appealing to you in Russian music that you wouldn't find in a different repertoire, even if you have recorded many other pieces from French or American composers? Well, I think I've always been attracted to the richness of it. I mean, that's the word that really comes to my mind the most, is that there is an incredible richness and there's an unbelievable melding of craft and true inspiration. Of course you could say that in Bach and Beethoven, but there is something special in Russian music that I find that separates it from the rest, but I'm still really trying to identify exactly what it is. Of course, even Russian music varies in interest, of course, but the best is among the very greatest that I think there is, and sometimes in very many different ways. And there's quite a few Russian composers which are, while they clearly deserve more of our attention, I'm thinking of Lyapunov and his transcendental etudes, which are really masterpieces of their kind, marvelously conceived for the piano with some wonderful ideas, and a composer named Georgy Katoir, who was in really complete obscurity for most of the 20th century because he's mostly remembered as a composition teacher at the Moscow Conservatory. But his miniatures are really marvelous and I think surpass a lot of what, for example, Lyadov or Ruskiy Korsakov wrote. They really surpass him in interest. So, I mean, these are just examples, but the font of Russian literature is very vast and very worthy of further exploration. It's not always easy to get access to the printed music, of course, but at least now in this day and age, it's easier than ever. So you're not only a world-class pianist, but also a researcher or a musicologist in a way? Well, I wouldn't elevate myself to your position, of course, but let's say I'm a great, great, great enthusiast. In conclusion, it should be mentioned that Marc-André Amellin not only provided the fingerings, but also gave us valuable advice with regard to possible mistakes in the historical editions, especially missing accidentials. So, we are convinced that a lot of Urtext editions offer you the most reliable musical text there is today. And of course, we're looking forward to our upcoming joint projects that will be certainly more Rachmaninoff in the future. Marc-André Amellin, thank you very much for joining us today. It's my pleasure.


You know, one of the biggest frustrations that I hear from my patients is this very similar conversation that has manifested itself in hundreds of ways, but I've heard it so many times. Why is it that my doctor says they've run all the tests? Nothing is wrong, but I don't feel that well. There's a very, very, very important reason for it, and I wanted to talk about it in today's video because I think it will help you. Hey guys, Dr. Alex Hein, author of the health book Master of the Day and Doctor of Chinese Medicine. So before we jump in and answer this important question today, two very important links right below this video. The first is if you would like to become a patient of mine in Los Angeles or virtually a telemedicine, you can contact my private practice right below this video. There's the contact info to reach out, and we'll get back to you. The second is for a free download, which is four daily rituals that can potentially help you add years to your life with traditional Chinese medicine. So those are right below this video. So one of the most common frustrations I hear from my patients and I myself had experienced is this idea or this experience of not feeling quite right.  And you're very confused because you still don't feel well. But your doctor says there's nothing wrong with you. Just go home or more often they say, take an antidepressant or go to the psychiatrist or you're just stressed. And you know that this doesn't connect internally. You know that this does not resonate because you don't feel that well and you know what it's like to feel well and you know that this is something new for you. Now, on the sad side of the story, very often I see this in patients who then go on to be diagnosed with something later, six months, two years later. But for most cases, there is nothing really wrong from the traditional medical perspective or biomedically, nothing is showing up. But what's really going on here? That is really the million dollar question. And let's talk about this today from a Chinese medicine perspective because I have heard this many, many, many times. And it is in these early stages where you really have to nip things in the bud and recognize that something is wrong. But it may not be measurable from a traditional medical perspective yet. A couple examples that I see frequently are people who end up getting persistent or frequent indigestion. And maybe it's that last meal of the night where you're getting a lot of mucus or phlegm in your throat. Food doesn't quite feel like it's going down. Maybe you're getting that knot in your throat that Chinese medicine calls plum pit chi. And maybe even you go as far as getting an endoscopy or a colonoscopy due to other bowel issues. And of course, it's negative. Another one is maybe you feel really anxious or you're not sleeping well or you're feeling really depressed. And again, the same story. You know you're not yourself.  So what gives? So let's talk about three reasons why you do not feel well and yet all the conventional labs and traditional forms of diagnosis and even technological forms of diagnosis are not showing anything. Number one is that there's something going on with your nervous system. I call it nervous system level disease for lack of a better word. And many different parts of your body can be affected by your nervous system. It's the reason why you can think about an anxious experience and then you can get indigestion next meal you eat. It's why there may not be anything diagnosed and yet you're sleep messed up. You're still getting headaches. You're still getting digestive upset. You're getting menstrual cycle changes or you just don't feel right. But there is nothing measurable that can then be diagnosed or treated. Reason number two, Chinese medicine calls this one symptom plum pit chi.  So it is not something necessarily materially there. There's no tumor. There's no, in this case, there's no thyroid disease. There's nothing that is measurable, but the person feels like there's a lump in the throat when they swallow. Now, often this is linked to strong emotions, the most obvious being sadness. If you've ever gone to cry and for whatever reason you can't at this exact moment or you hold it in and you feel that not in your throat as if you're about to cry, you've experienced how emotions can cause a physical symptom very acutely. And then as time goes on or as you cry or as that emotion passes, that plum pit chi will go away. Plum pit chi, the way I think about it is that there's a chi level of illness that precedes material illness. And emotion is probably the most useful example because someone can experience the not in their throat, loss of appetite, sadness, but then it doesn't progress into anything else, right? Or it may, right? Chronic lump in the throat because I'm always feeling anxious or sad or depressed or whatever it is, may then progress to a structural illness later, or it may not. And the quote chi level illness can just be anxiety. The chi level illness can be an emotional upset that then affects a woman's menstrual cycle. It's well documented that women's menses are affected by emotions, but they can also be from low body fat and it can also be from all kinds of other issues. So when we're talking about this idea of chi level illness, the way I like to think of it is pre structural illness or pre measurable illness. It is not real. It is real, but it is not going to show up on any traditional diagnosis or any traditional labs, maybe not yet. Now one final example of pre material illness is let's say diabetes. Diabetes is a great one, right? Cardiovascular disease still the number one killer in the United States. And when we're talking about the predisposing factors, chi level pre material illness, maybe it is you're noticing a little bit of frequent urination or you're noticing some issues with your eyes or even more likely you're noticing getting really tired after meals. That's a key symptom of pre diabetes, right? So maybe at that point blood sugar is measurable, fasting glucose is not where it should be or maybe, you know, the urinary symptoms or maybe there's some hypertension creeping up or maybe A1C is showing up on some labs, moving in the wrong direction, right? But that will not show up right away either. That can be years in the making. And obviously there are probably millions of people running around with undiagnosed prediabetes or diabetes. But now let's say the person has full blown diabetes and now let's say 10 years have gone out and now a small percentage of those people have developed cancer and now a tumor is actually showing up, whether it's prostate cancer or whether it's colon cancer or whether it's some other kind of cancer. So 10 years ago there was nothing really measurable, right? Just a little bit of indigestion, a little bit of maybe gallbladder problems, a little bit of blood sugar is not looking very good or cholesterol is not looking great. But before that there was nothing even measurable, but maybe you had some low grade symptoms and now 15 years later there are tumors. So this idea of that I like the most is prematerial or pre structural illness that is moving in the wrong direction, but maybe cannot be quantified yet. So understanding that many illnesses maybe most start off from an immeasurable or immaterial level, maybe that immaterial level is purely physiological and it's not quite measurable yet. It's not quite structural, but eventually it will lead and progress to the structural, the measurable, the tangible over time. And I think this is often why many illnesses begin from the immaterial or let's just say let's call it nervous system level because it makes it a little bit more tangible. It may start off as a nervous system disorder or just symptoms of being in a sympathetic dominant state where we're in fight or flight, but then eventually may progress to something more material or more serious. And so it's important to catch things when they're in the let's call it nervous system sensitive state and we can prevent it from becoming something more serious further down the line. Alright guys, so I think that is very important to talk about because it is one of the most common things I hear probably from half my patients that basically stopped going to their traditional medical provider because they didn't feel like they were getting their needs met, ended up coming to see me and when they were clearly helped they were wondering why I was able to treat something that their doctor was not. And this is frankly the reason why that is the case. It's very common within my field as well. So just some food for thought. Again, before you guys go, link below this video. If you'd like to become a patient of mine locally in Los Angeles or virtually via telemedicine, you can contact my private practice right below this video. There's also a free download there for you for daily rituals that potentially help you add years to your life with traditional Chinese medicine. So check out these other related videos before you go and I'll catch you in the next video.


What's up everybody and welcome back to the channel. We are here today for SSR round four qualifying at homestead staring at my newly Modified and tuned 370 z v8 under the hood with a new livery on there. So the car now obviously has more Visual appeal it's got some chrome and some green, but it's also got a body kit higher up in the weight We are at a 500 horsepower max for SSR We're gonna run some correct practice laps here before our qualifying runs are actually gonna happen Then we're gonna hop in the party with probably valiant and I can't think a couple other people are qualifying today as well We do our qualifying runs. I'm feeling super confident in the car, and I'm fair feeling very comfortable in the track, so we're gonna go and basically Run some quick practice. We do have the full fan tech set up with our dashboard 900 degrees rotation Handbrake and everything all squared away in the new base so Definitely more of a solid Solid base for me, and it's making my you know transitions everything easier because it's not wobbling around like my other base was so like I said definitely been more comfortable in this 370 retune the tune was a combination of some other people and Definitely great to have these guys help me out get the tune dialed in Fortunately, I believe I'm the only member of to us as competing in this round So I gotta do my best and throw down So we're gonna run some practice real quick like we would be running our qualifying runs Just heat up the tires getting into a nice and warm temperature I have a little gauge on my dash that tells me when they are close So we're gonna run this like we would our two practice ones But we're gonna run them like it would be our qualifying run 50 roll both here machine in quick tap of the break a little bit Off of that rumble Then I wanted to be kind of dropped a little bit past it But nonetheless a still a very solid fair run Probably two up early on the bank and a little wall tap as we had a little nose edge So I believe I dropped the tire in the beginning, but still none less solid. I Believe that would be at least a scoreable run Is it a perfect run nope not by any means, but we are going to keep running this because We have qualifying and I will be bringing you guys all that once I happen to the lobby. So you guys will see that Got some notifications going on on my phone So SSR round four is actually going to be in the rain So qualifying is in this weather and then the actual event is to begin rain off the under store Which is gonna make the event very interesting the event is this weekend. So Let's run another one and see if we can't get a better Run for a second run if you roll in Transition quick tap the break kind of line the car up Getting right out to the edge wish I was a little bit closer at touch and go right on the grass nice angle transition up the bank Not as high on the bank, but we don't have to go all the way up We got to get as close as we can to the ball But we can do a wall tap at our own risk because if we change angle, we're gonna get docked a lot of points So we're just gonna probably play it a little bit safe on the first run as we always do a very Tentative calm get a get some qualifying runs on the board I'm not sure how many people are registered for this round of the pro drivers So I'm not sure if there is more than 24 So we want to make sure we at least to get one run in the books that way if there is less than 24 We will be in the show for tandems and we'll be able to compete When the time comes this weekend So we're gonna run another one my tires are a little bit more worn than they would be in qualifying But we can see how we can get this run done Try not tap in the brakes. Oh, that was way off That was definitely a two-tiered drop that would probably be a zero So don't want to do that on my qualifying run. Don't want to throw it too hard and zero out So I'm definitely more comfortable now than I have ever been in this car You know, thank you to itanum adi fated illusions for Helping me out with working some tunes to make me realize how the car needs to feel and They have different driving styles, which helped and I was able to Combine basically their tunes and how they felt to make the tune that I'm running now that I'm super comfortable And I will have to make some adjustments For the rain, but I'm more focused on just trying to get these qualifying runs down and then I will work in the next few days on fine tuning it for rain weather and Rain tandems That's better Not all the way out to the touch and go but we're still On a decent run too much Too much angle over there So I'm gonna get ready to get into the party and then go for my qualifying runs So hopefully we can do what we've been doing today and make our qualifying runs good The moment you're going over your notifications are off and then you go look and you're like, oh, hey look What's up, dude?  You do have a meant amount of following right so who would like to go first?    It's all good My escorting the lightest of the lot Minds I actually put some more weight in this 370 since the last round put a little bit more weight in it They had all the way Hey, well Scorpion Aussie, so I Think the best part about this is I'm recording all of this First run Who He's went ahead. I am inside it. Um, I saw that that should be decent enough