Yes, I will just show you one study wherein we have applied ANN and GP and some very interesting conclusions probably can also be seen out of that. The study pertains to application of ANN and GP to estimate the coastal sediment transport. Now as some of you may be aware that the waves generated by the wind which is a continuously occurring phenomenon in the sea, they break when they come to shore because they cannot sustain their motion in shallow waters. Because of that a current is produced which has a component parallel to the coastline. Now this current carries lot of sediment in it. Now when such sediment movement which is parallel to the coast crosses a deep channel which is used for the ships to navigate inside and outside the harbour, they deposit that sediment load, lot of material gets deposited and ports and harbours they spend tremendous amount of time every year in dredging out that material. In fact in India we spend I do not know maybe more than couple of thousands of crores of rupees per year in all these ports and harbours to dredge out that material. So the estimation of that sediment that gets deposited is indeed necessary so that in port budgets you can keep that much money for dredging in the next year and so on. So accurate estimation of siltation is indeed necessary and but this is very difficult because the phenomena involved are indeed very complex. Now currently what is done there are only empirical formulae which are popularly used to estimate that sediment transport and therefore we try to see whether we can get good results by GP and ANN. But as I mentioned ANN cannot be just applied like that because it suffers from some problems like lack of guarantee of success in a new problem, new application. Accuracy levels obtained are arbitrary and you have to go on perfecting it. There are also a difficult choice of training schemes, architecture, the learning algorithms, very control parameters etc. And therefore any new application of ANN must address this issue and then present the results to the scientific community. Now therefore in this project our objective was to develop a suitable neural network to obtain the longshore sediment transport rate LSTR, Longshore Sediment Transport Rate. We also wanted to understand the processing of the input done by ANN and done by regression and also physical consistency. We also wanted to develop estimation procedures on other soft tools like GP and if necessary we wanted to explore possibility of developing hybrid models. Now as I mentioned traditionally there are certain formulae which the design codes recommend. One is such regression formula given by coastal engineering research manual, another one is Walter and Bruno equation, third one is energy plus method. They all relate the outcome to the causative variables in an empirical manner. Now we have collected data, one of the co-authors of this paper collected data along the coast of Karwar here, this is that Arge beach, there is a 4 km long coast and in that coast in the field for about 4 months they collected, he collected the data from February 90 to May 90 of significant wave heights, average wave period, breaking wave height, breaking wave angle, width of surf zone, mean sediment diameter, long shore current and so on. And of course the sediment was also collected in order to know its rate Q per unit time. This is a typical mesh trap to collect this sediment. Now we had to discard a large amount of data because all these values were not simultaneously available at many times and ultimately we ended up with only 81 data examples. Now note that these 81 examples are looked short but in field it is very, very difficult to collect all these variables by means of instruments which are indeed very costly and very difficult to operate simultaneously. Now to begin with we developed a simple network wherein the input was the causative parameters, the output was the rate of sediment transport. It gave us fairly good measure, good kind of performance during testing that means with respect to those data sets which were not seen by the network in training. This is the predicted rate of sediment transport, this is the observed rate of sediment transport. In general the correlation coefficient and mean absolute error and root mean square error were quite fair. Then we all based on the data set that we newly obtained, we also fitted some regression equations like this. And when we compared all these results we found that by manipulating with the networks properly we can get a good network having fairly good amount of performance criteria. Correlation coefficient root mean square error and mean absolute error compared to the multiple linear regression and non-linear regression of different types. But of course within the neural network itself certain training schemes can give you much better results. Now again it is not, there is no guarantee that use of some particular network is going to give, always give you a better kind of result. You have to try out all these training schemes in network architecture. But the point that is to be noted is something like this that when we compared the values of rate of sediment transport predicted by formally advocated by design codes and the actual rate of sediment transport we got this picture where we expected all values to fall on this along this line of exact fit. But if we use one formula RCE, RC formula this is the picture that emerges, if we use another formula this is the picture that emerges in fact certain negative values are also predicted meaning that the drift is in the different direction, negative direction. So like that first of all we ensured that the existing formulae at the given location of that car var are definitely not good. You have to go by the new formulations, new formulations could be neural network because neural network is substantially high level of accuracy compared to these existing ones. Then so accordingly we recommended the network then we also ensured as I mentioned that the neural networks behaves in a consistent manner with the physics of the phenomenon as the wave height increases the rates of this sediment transport also the increases. Now yes now then another study that we did is like this that we did a parametric variation with respect to traditional regression and also parametric variation with respect to neural network and that gave us some insight as to why regressions fail and why neural networks excel. As you can see here in this particular figure wherein we have plotted these sediment transport rate with significant wave height both process by ANM and by regression and in this next figure we are we have plotted the rate of sediment transport against the increasing breaking wave height and using the ANM and regression and in both cases we are finding that when it comes to regression you know the regression tries to do some kind of very rigid approximation to the input whereas here there is a lot of flexibility in modeling. So neural networks tries to I mean the traditional regression tries to pass the data through some very constricted path whereas lot of degrees of freedom are available when it comes to the neural network. So neural networks invariably enjoy what we call a high degrees of freedom in processing and that is why they perform better. So similar conclusions were drawn by other variables yes then another thing that we did is like this neural networks gave better results than regression but even then it is still possible to go at a higher level. Then what we did we developed a basic network using the training set of data then we repeated the training by attaching another network in series found to it. So the idea was that this network will do the basic function approximation and fine tuning can be done by another network later because by doing by giving a network like this you bring an additional you know flexibility to the data modeling and that work again very nice the correlation coefficient again substantially improved compared to the single stage neural network. Then many times you know these are these things are used by field engineers if you talk about neural networks etc they may not be very receptive. So what we did considering the fact that some this non-linear regression results may also be acceptable to some level we try to give a coupled equation that combines the input of the regression and then computes the output with the help of neural network and such an equation based on a coupled form is given over here and that also works fine but not as fine as the pure neural network or two stage neural network. Then we applied the genetic programming and we found that it gives results similar to a good well trained neural network this is the graph of predicted sediment transport rate with the observed rate predicted was calculated using the genetic programming. Then again we did so many things to see if we end up with some better results we trained the model using ANN and results of that trained model were used as input to develop a genetic programming and obtain the output of the rate of sediment transport accordingly and these are the results first we did training using GP primary training and fine-tuning using ANN here we did find primary training using ANN and fine-tuning by GP and we found that all these methods also give results which are definitely I mean they are not an order of magnitude big than greater than the ANN but consistently they were found to be better than a single ANN. So this is what we found so if somebody wants to take a cue from it and applies to and wants to apply the same combined or hybrid modeling in his own case he will find some good elements of his I mean some good hints out of this study. Now this is a locality learning actually they belong to a class of models which are called local models. Now so far this ANN and others we have seen that they are global models in that you know you take the you develop a model with the help of trained data and continuously use the same model here these are local models in the sense that whenever any new input is given they will find out which are the they will pick up the related data from the input database and using some criterion and apply a local model to it and then use it to obtain the output from that new input. So these local learning belongs to that class of models called local models which are different than global models in that there is no single model that fits to the all data. Then the local models fit data into a region which is called around the location of the new input or query point as it is called these are there are certain terminologies which are traditionally used by those mathematicians or you know control theory people. Now this locality learning is a memory based learning in that it does not discard the training data like ANN but you make use of every data or part of data every time in making a new learning. So learning is rather incremental here it is non-parametric that means from the data you do not work out the parameters once for all and use these parameters but every time you do some kind of incremental learning over and above what you have done so far and locally linear models are selected and fitted. Now so basically what it is done is like this see suppose this is the new input x then in locally weighted regression we using some kernel function like the Gaussian function as you can see here is a Gaussian kernel function this x is input variable and this e k and d k are the two parameter centers and distance metric distance metric could be typically a Euclidean distance metric roots square root of x equal plus y square. So like that using this kernel functions you this is a typical kernel function shape this is a plan you can say so for a new query point or new input you identify the training patterns which are closed then to those identified local points you fit a regression and use it to obtain the output this is I mean conceptually it is like this then you have a class of locally weighted regression models called locally weighted projection models in which the input data are mathematically projected into these orthogonal or perpendicular directions and along each direction a linear model is fitted after identifying the required points with the help of these kernels and average of all this is ultimately used to obtain the output. So the things that here are indeed extremely complicated and the mathematics involved is quite involved is quite complex to explain but conceptually the things involved are like this. Now so far two of our students have used this technique again to solve similar problems estimation coastal sediment transport rate from the causative parameters and estimation of score depth of a schism okay. So this is the same problem which I was mentioning the data near Karwar was well taken the input in this case was significant wave height period width of surf zone breaking wave height and the output parameter was rate of sediment transport and as you can see this is the predicted versus the observed sediment transport rate this is the exact fit line that means had the data been perfectly predicted all points would lie along this line we got a good correlation coefficient which is 0.88 comparable to usual Nn but again you know we had to go on refine this technique and see whether we it can give results which are more acceptable than Nn or not then of course they work much better than this traditional techniques recommended by design code that is the definitely the advantage. So we found that the locally weighted regression technique they produce more accurate estimation of the rates of sediment coastal sediment transport than the traditional formulae. Another application of this LWPR technique is the estimation of score downstream of a spillway again the same kind of a data observed in the field and models was used the this is the maximum score depth it is to be related to this head then this discharge radius of bucket lip angle etc and as regards field data were concerned there were only measurements of discharge and head used to obtain the depth of score in fact the that US our Indian standard code recommend only use of this Q and H1 to find DS for generalization purpose when we use these two parameters we found that LWPR resourcing about 0.9 correlation coefficient during testing and it works better than the traditional formulae if we use the model data where apart from discharge and head radius mean sediment diameter then lip angle and then the other tell water depth DW where use that input and that significantly you know improved the relationship we got a correlation coefficient of 0.97. So it means that the practice that is followed in design code of using only discharge and head to obtain the score depth is no good you must include other parameters also in order to get a better estimation of the score depth. So this shows the relative comparison between the results of a locally weighted projection regression then the best trend ANN and the formulae used by different investigators in field like Martin Sveroni's who in see a new statistical regression also fitted that also didn't that didn't work much better. So right now we can say that LWPR results are comparable to that of artificial neural networks maybe if we are able to refine this technique further we can they can go one step beyond ANN and also but right now we have to keep the fingers crossed. So we are only saying that this core prediction could substantially improve if the LWPR regulation technique is used in place of the traditional formulae. So like that so many studies have been made with respect to this GP MT and so on.


drdweud, mae gallwn i chi'n ceisio yw'r gy官llun. Purwyr sydd eisiau, fe wnes o'r drosweithio, felly rydyn ni'n mynd i'w ddweud yma yn y cymuned.  Mae'n amser yn eistedd o'r cw practice, felly rwy'n rhaid i gael i'w gwiswch, mae'n gyhoes o danau, a yna arweithio'r cyfrinig? Rwyf yn oes meddwl am ddigonio, a rydw i gael cael cyfrinig ar gyfer y gwirionedd. Ond i gael bod weithio'r cyfrinig, ac mae wedi gael eu bod yn cyfrinig, mae weithio'n cyfrinig. Rydw i'n gweithio'n cyfrinig, rydw i'n credu peomôn yw bod Ar스�engenau Paul eyddwni'n cyfrinig. Dyna, byddwn ni'n cyfrifiadau gyda gwyrdd Caerdydd. Rwy'n gwirio gyd yna bod ni wedi ei ddisgrifio panwn ni â cyfrifiadau cyぉ, fel y dd lakeshwyr Civataid. Ieithio gan hynny. Byddwn ni'n gwirio'n gwirio yr oedlawer dros yr aelod ar yr aelod yn aggariannol, iddynt yn yn cyfrifiadau y mae â'r cyfrifiadau post amgylwyr, ac mae'n gwirio'r gallu cyfrifiadau cyfrifiadau ein bod ni'n gwirio, ac mae'n cymdeithasio cyfionol gan dechrau'r unrhyw ar ôl. Yn ymwysig, yw y cwrdd yma oddi'r cyfnod y ffordd mewn cyfrannu cynllun gyda'r cyllidau gyda sredig o'r cyfrannu cynllun gyda'r cyfrannu cynllun cyfrannu. Ac rwyf wedi'u cyfrannu cyfrannu cyfrannu cynllun cysylltiadol. Gwyddo i ddweud y gallwn gwneud mewn ddechrau'r cyfrannu cyfrannu. Cym Carrgeon we face, and I think this is driving a lot of the things we are seeing at the moment like the vote for Trump for example in America, is the disappearance, really, the gradual erosion in the putron Abeirans of what we might call traditional jobs, the kind of jobs that my parents had and possibly my grandparents and maybe yours too. The routine jobs in factories riding jobs in factories, on production lines that weren't inspiring jobs in their own right necessarily it was a lot of armies of people all essentially doing the same thing but which partly as a result of unionisation and you know the pressure to increase wages to a decent level meant there for a lot of people it gave them the comfortable lifestyle that they wanted and it is that comfortable lifestyle that explained me a part... a dyma'r cyffstylau y gallwn i'r bwysig ydy'r cyffstyl o'r plwythau i'r cyffstyl o'r rwtyn cyflawnol o'r panhau a'r cyflawnol. I'r ffordd o'r ysgol yn gwybod lle'r ffath ar y cyd-rwyng. Rwy'n yn i'n meddwl, ac rwy'n gwybod am y peth wahanol, ac yna rwy'n gweld i'n gwybod ar gyfer y cyflawnol, ac ydych chi'n gwybod ar y dyfodol. Rwy'n gwybod ar gyfer, ond rwy'n gwybod ar gyfer y cyflawnol, As a contractor, I'm occasionally as an employee, I was not a great deal more secure. And then in 2002 I gave it all up thinking I wanted to sing really. So I then spent 10 years or so in exceeding the insecure job being a singer and a teacher. And then in the financial crisis, as Paul said, I popped up doing some writing just because I was cross about a lot of things and found that I got red and now I do a lot of writing. I've lived in what you might call the gig economy for 30 years, I think. And I see what's happening now with the rise of self-employment and an increasing number of people living in this very insecure and unstable lifestyle. And I look at that and say, yeah, we've, you know, performers have been living like that for hundreds of years, probably. So in a way, I understand the uncertainty and I understand what it does to the mind and what it does to the health of people who are, who dreamt of stability and security of maybe a job for life. Something, yeah, it didn't inspire them. They went to work to do a job and then they came home to do whatever it was they wanted to do. You know, people are often very much more productive in their spare time than they are at work. And then finding that the reality is living from job to job, a succession of part-time temporary zero-hours jobs, low wages of spells of unemployment, being forced into taking any job just to get them off the unemployment statistics, sanctioned if they don't, and increasingly dependent on benefits because work just does not provide them with the income that they need. The difficulty of managing an uncertain income and certain outgoings. How do you pay your rent or your mortgage on a defined date every month when you have no idea when you're going to get paid? Or if you're going to get paid because your work might have dried up that month. The government at the moment has a push towards enrolling people into pensions. Anybody who works, it works in the uncertain economy, the precariatus guy standing calls it, really safe for pensions because they can't take the risk that comes with having to commit to a pension plan, which means they've got to pay out a certain amount into a pension plan on a certain date every month and they can't do that, so they don't. This has nothing to do with how much they earn. They might earn quite a lot, but they can't take, but the mismatch between the uncertainty of their jobs and the certainty of their outgoings creates huge, huge stress. That is where I think our employment is going. Interestingly, there is nothing new about this. In fact, the existence of stable jobs with wages was very much a 19th century and sort of first half of the 20th century phenomenon that directly arose from the big industrial complexes. As those are eroded and replaced with something much more fluid and transient, we're returning much more to the kind of seasonal and peace work type of economy that we've seen in the past. We're seeing a lot of resistance to this at the moment. We're seeing people wanting to bring back traditional jobs. The Luddites of the 19th century are back with us in force. Let's bring back these kind of stable traditional jobs. I don't think those jobs are coming back. We have people who want to have job guarantees. I don't have a problem with job guarantees, but where government tells people what to do, that could ease some of the pressures. Should we really be looking for that kind of command economy where people are still told what to do? You will do this job. For me, I think there's another way, and I think we can work with the way in which work is going, which is to do towards something much more fluid, much more dynamic, and ultimately, for many people, I think, much more creative. By creating, shall we say, a place of safety, a haven, a rock, an anchor, to which they can anchor their lives, that removes the existential threat of saying, if I don't work, I don't eat, which in many respects is a denial of their basic right to life, which they are asked to compromise by, in effect, giving up their liberty, their freedom to choose what it is they do with their time. And the price they pay for that, in many cases, is serious unhappiness. What are we doing to ourselves? These are the rights of man, the rights of humans. So I think there's another way. I think that we can create a basic income which will relieve people of that stress. It will give them the basic means to live irrespective of their circumstances. And we can say that they can have that income whether or not they're working and however they choose to work. Because the problem with benefits systems, like we have at the moment, where people have unemployment benefits and then it's abruptly withdrawn when they start work, is that it creates a conflict between those who are not working, who are seen as getting something for nothing, and those who are working damned hard for not very much more. If we could remove that and say, actually everybody is entitled to that basic income and it is theirs by rights and nobody can take it away from them, then we have removed much of the stress that eats away at the mind, that destroys happiness, that wrecks health, and that ultimately creates far more cost for society because unhappy people are less productive, they're less creative, and ultimately they are their mental health is wrecked and we spend huge amounts of money in trying to keep them unhappy. So why can't we be more creative? Why can't we give people this kind of anchor which will enable them to choose for themselves what they do, to discover for themselves what they value? Because one of the things about a crisis of work as we have now is it creates a crisis of our values. What is it that we really value? In the past, we have valued making stuff. Yeah, real jobs are making stuff. In the future, and it's already happening, making stuff is something that robots can do better than us. These are the jobs that are disappearing, are the making stuff type jobs. Even some of the caring type jobs are disappearing as well, but they tend to be the more routine ones. The things at which humans excel, we think we're beginning to discover as a non-routine, the things that require human interaction, the things that require creativity, and all of those, the ability to interact with each other, the ability to empathize and the ability to create are our birthright as humans is what we do. And I don't just say that as an artist myself, but I strongly believe that actually all humans have the ability to be empathic and creative and to collaborate. So, if we could create a basic income which would support people so that they can do things that make the best use of their creative ability, their empathic ability, their ability to work together to collaborate, then I believe we could have actually a much more productive and a much happier society. One of the criticisms that's usually levelled at basic income is, well, people will simply stop working. And I think the essence of this is basic. If you set it too high, then probably people will stop working. But if you could actually simply relieve the basic stress, then I think that most people would want to do something productive. And as we face, as we go into this crisis of work, we know that the forms of work in the future, the businesses of the future, the industries of the future will be things that we can't imagine right now. And they will be created by the entrepreneurs among us now and particularly among our young people now who will invent things that we can't imagine. If we can support them to invent those new forms of work, produce those new industries, those new businesses, then in the future we can expect them to return to us the support that they've received. I'm rounding a little bit here, but it seems to me that one of the problems with universal basic income, as I said, it tends to be thought of as welfare and I don't see it like that. I see it as a support for work. One of the changes, technological changes we have at the moment is the growth of online and internet-type businesses, which enable people to work very much more from home from where they are. And that opens employment, or not employment, but work, productive enterprise, let's call it that, because even work has connotations about doing something unpleasant and I don't think it is. I think work should be fundamentally enjoyable. To people who currently see themselves as not able to work. So it's about empowering people to do creative, productive and interesting things that benefit all of us and in the end return more to us in terms of productivity, prosperity and happiness than we pay out in terms of supporting those who are trying to work with the new forms of work and develop the new forms of work that we will see in the future. So universal basic income. Let's abandon our fears that we won't be able to afford it and say actually we can't afford not to afford it because at the moment our piecemeal welfare system is expensive. It's divisive and it is disempowering people. It is forcing people into any job, however unproductive, however drudge-like just in order to live and it is impeding or shall we say disincentivising companies to automate, to innovate and to design work in a way that makes the best use both of human beings and of our robot colleagues. And I use that term carefully because my last point to you would be that one of the things I think that is dominating everything is this terrible fear of automation and the way in which it's going and we see ourselves as being superseded by the machines. But actually we can work with these machines. We can collaborate with them to do things that we can't imagine now working alongside them and collaborating with them in a funny sort of way. Even if they are artificial intelligence, if they're intelligence machines, even more can we collaborate with them. Surely in creating new forms of intelligence we're just increasing the capability of humans.  Do we fear our children? So let's support each other, let's have the support for humans as we move into this new era so that we can have a truly happy and productive collaboration with our robot children in the future.


Live from Las Vegas, it's theCUBE. Covering Discover 2016 Las Vegas. Brought to you by Hewlett Packard Enterprise. Now here's your host, Dave Vellante. Hi buddy, we're back. This is day two of theCUBE coverage at HPE Discover 2016 in Las Vegas. I'm here with Ray Wong, who is the chairman of Constellation Research, Principal Analyst. Ray, thanks for coming in. Hey, thanks for having me. For a real quick fly by. I know you're headed to the keynotes. Couple things, big news today. GE and HPE getting together. Big computer company and GE, industrial internet giant. Really the first time that GE has got together with a big player like this. I know they've done some things with Pivotal, but what's your take on that? No, this is huge, right? GE being the digital industrial, HPE jumping into this market. They've had a long history of working with each other, but here they're putting together the predict software and the HPE capabilities. That's one of the big things that's important in the internet. If you think about what's happening with IoT, we've gone from sensors to stacks to platforms, and we're about to get into networks. And as we make that transition, I need security. I need to make sure all these devices are at computational power, and I've got the network speed. Yeah, so HPE could be an arms dealer for that deal. Now, Meg Whitman yesterday talked about HPE as a digital transformation factory. What does it take to be a digital transformation factory? You know, a lot of what has to happen is you've got to bring together the pieces around business models, what's happening with insight and the insight streams, and the ability to actually take all this stuff and make it easy for people to use. People want to be able to consume this on demand and be able to put the parts together. Right now, it's a mess, right? People are piecing things together all over the place. There's a lot of app dev that's happening, and I think HPE is trying to industrialize that. All right, last question is, HPE as a company in total, and specifically their software business, what does HPE have to do to shore up its software business and really drive growth there? You know, I think they're starting to do the focus around the analytics piece. That's core, getting the big data around it. Then the rest of it's really on partners and ecosystems, and you're seeing them do that right now. HPE's partnership strategy, that's going to be the key to actually bringing the ecosystem back to getting back into the global 2000 accounts and then going into the verticals that they've been strong with. So leveraging that sort of vertical crown jewel and everything around it. Vertical crown jewel, and the partnerships, and the partnerships that are out there. Excellent. All right, hey, thanks for stopping by. It's great to see you. Thanks for having me. All right, keep it right there. We're back with our preview of day two right after this word.


All right, welcome everyone to the talk Beyond Namespaces. Virtual clusters are the future of multi-tenancy. I'm Lukas, and I'm the CEO of Loft Labs. And I'm based in San Francisco, but originally from Germany. So, you know, excuse the funny accent. Together with my team, we're working on some really exciting things in the Kubernetes space. Our commercial product Loft essentially enables large companies, you know, to provide self-service, isolated namespaces to a large number of engineers, really like an internal provisioning platform for Kubernetes. So, we really care a lot about multi-tenancy, about user experience, developer experience, and about self-service. And because we care so much about these topics, we're also heavily involved in open source. We're working on four different open source projects. Our oldest project is called Dev Space. It's a developer tool for Kubernetes, and it's essentially a replacement for Docker Compose that is designed to be, you know, for Kubernetes, that you can streamline your workflow with Kubernetes the same way as you can do with Docker Compose with your local Docker daemon. But now you can also do that with a remote Kubernetes cluster. We're also working on Kiosk, which is a multi-tenancy extension for Kubernetes. And on JS Policy, which is a policy engine that allows you to write policies in JavaScript or TypeScript, making it much easier to write these policies and maintain them over a long period of time, even where someone in the company leaves that was the re-go expert writing policies beforehand. And one of the projects that we're working on is VCluster. And that's what we're actually gonna talk about today. It's a really, really exciting project around virtual Kubernetes clusters. So let's dive in. Beyond namespaces, virtual clusters are the future of multi-tenancy. Gosh, that's a pretty heavyweight title, right? I don't even know why you're attending this session. The future of multi-tenancy. Ooh, wow. What was that, right? Virtual clusters, never heard of that. You're probably all here because of first part, right? Beyond namespaces, right? You know, namespaces, yeah, I got this, right?   If we actually ask Google, what is a Kubernetes namespace? I mean, Google came up with Kubernetes after all, right? So let's just take a look. And if we go to the Kubernetes documentation, it reads there Kubernetes supports multiple virtual clusters backed by the same physical cluster. These virtual clusters are called namespaces. So namespaces are virtual clusters. Dang, we don't even need this talk, right? It's built in in Kubernetes, you all know about it. I guess we're done here, right? If you ask me, this is pretty outdated. Namespaces are not clusters. So they are not virtual clusters. Namespaces, and that's also part of the documentation, provide a scope for names in Kubernetes, right? For your policy, et cetera. Names of resources need to be unique within a namespace, but not unique across namespaces, right? So I can have two deployments called database and they live in two different namespaces and I don't have any naming collisions, right? That's great. That's what namespaces do and that's about it, right? They don't do a lot more. But as we all know, a Kubernetes cluster is much more than just naming objects. So what is a cluster? Not all objects are in a namespace. There are a lot of cluster-wide resources. They include nodes, persistent volumes, and even namespaces themselves, right? Namespace is a cluster-wide resource. If you actually want to check out which resources are cluster-wide and which ones are namespaced, you can actually ask kubectl, right? You can run kubectl API resources and you can either use the flag namespace true or namespace false to get the respective resources and Kubernetes will tell you all the resources in your cluster that are available.  There's a couple, yeah, a couple more. So this slide is not for you because we heard earlier Stephen Augustus in his keynote was talking about we need help with documentation in Kubernetes. That docs page that I was showing earlier in particular, that sentence about virtual clusters is over five years old. It hasn't been touched pretty much since the inception of Kubernetes, right? And really a lot of people need to get involved to actually maintain this vast set of knowledge that we're building in the Kubernetes documentation. So after this talk, everyone should know the differences between namespaces and virtual clusters and should be able to fix this. And whoever is a first-time contributor to the documentation fixes this will get some kind of a little surprise present from me. So pay close attention to this talk and hopefully there's an edit page button directly on the docs page, right? Just Google Kubernetes namespace to the docs, open that pull request on GitHub. Well, let's get back to the topic. Multi-tenancy, why are you even here? Why should you care? Well, in my opinion, spinning up thousands of single-tenant Kubernetes clusters is a really terrible idea because it's very, very costly and it's very, very hard to manage. Just imagine you're spinning up a Kubernetes cluster for a thousand engineers, right? And they're spread across like 200 teams. You're gonna end up with 200 clusters per team or even a thousand clusters if you provision one for each individual user. And none of these clusters really is gonna scale down to zero. And then you gotta maintain things like ingress control or CERC manager, Prometheus, metrics, all of these things, right? In all of these clusters, that's a lot of work and it's really, really hard to keep in sync. And what happens if someone breaks a cluster, throwing away a cluster, recreating that? Typically, the user, the actual engineer wants to just connect this Kubernetes cluster to the CI-CD pipeline or just do some pre-production development work there. Doesn't have the permission to destroy a cluster and recreate it. It's pretty tough. So what about namespaces? Can't we use multi-tenancy, create shared clusters and essentially separate things by namespaces, right? That's the alternative. And a lot of people are doing that today. If we're comparing those two approaches, we see that namespaces have a lot of advantages. They're much cheaper. It is much easier to share resources, like for example, shared ingress controller for all of our tenants in this shared cluster. But a lot of other things are really problematic, like isolation of tenants, right? As we saw earlier, a virtual cluster is essentially just a naming strategy, right? The scope for our names. That's about the isolation level that a namespace provides. So we need to add a lot of things like network policies, our bag, right? We need to really lock these namespaces down so our tenants can't get out of there and actually bring the cluster down or harm another tenant, et cetera. And that's a lot of work. And if we're doing it well, then we're restricting that very same tenant that now cannot do certain things, right? So let's say there's a team in the organization that needs five namespaces and needs to do things across five namespaces, but you set up network policies in each namespace to lock the traffic down to that particular namespace. Now you've got to make exceptions for that team and who's going to clean up these exceptions later on, right? It's a pretty big mess when you're using namespace-based multi-tenancy. So if we're comparing those two approaches, separate clusters for each tenant versus multi-tenant clusters and separate namespaces for each tenant inside these multi-tenancy clusters, then we see that the benefits and the downsides are kind of like opposite on both sides, right? A lot of times we see problems like that. Can't we just get the best of both worlds? That's what we're trying with virtual cluster and with our implementation vcluster. vcluster is an open source project. You can access it on vcluster.com. You can find it on GitHub. And it tries to be multi-tenancy solution for Kubernetes that is beyond namespaces. It is more extensive than what a namespace offers, but at the same time, it is as lightweight as a namespace. So let's take a look at what that means. What do I mean when I talk about virtual clusters? For me, a virtual cluster is a control plane that runs inside another Kubernetes cluster. What is a control plane? Well, it is an API server, a Kubernetes API server. There's a data store where our namespaces, pods, et cetera, are stored in. That's typically at CD. Then we have a controller manager, which controls our replica numbers. If I create a deployment with five replicas, someone's gonna create these five pods. That's what the controller manager does. And then there's a scheduler, which then takes these pods and assigns them to nodes to actually where the keyboard starts these containers for us. And then we have the workloads on top of these control planes. And typically, we wanna create a namespace, we wanna create some pods in there, we wanna create a couple of other namespaces. And then what we always do is we talk to this API server. That's our gateway to Kubernetes. That's our single source of proof in a way. So, for thinking about virtual clusters that run on top of another cluster, and we have the capability to spin up workloads inside namespaces, then why not create a control plane that runs as a pod inside a namespace of our cluster? That's what a virtual cluster is. That means we have an API server and potentially a couple of other components. And it really depends on your attitude towards virtual clusters and how you technically wanna implement this, but you're certainly gonna need some kind of entry point that you talk to. So now we're not talking to that API server of our real cluster anymore, we're talking to this API server up here. So when I run a kubectl command, I talk to a pod, right? That runs a separate API server. So let's take a look at how this actually works. I recorded this demo and we'll create a namespace in a local, let's say, mini-cube cluster. We call it host namespace because it's supposed to host our virtual cluster. And then we're using the cluster CLI, which is a very lightweight binary to create a virtual cluster. We call it VC1 and we tell it, create it in host namespace, right? That's our namespace. We see that the cluster under the hood executes a health command, but you don't even need that. You could just run kubectl apply or create a customization out of it, right? But for ease of use, just running helm under the hood pulls a chart, deploys it to your cluster. And then we run recluster connect VC1 and specify our namespace again. And what this does, and you see that here in the output, it actually starts kubectl port forward to now connect to this API server, right? And the second thing that it does, and that's why the CLI is pretty handy to get started with virtual clusters over just using kubectl, it also creates a kubectl config file in our current working directory. So we're split the terminal here and I'm exporting the kubectl config environment variable so that all my kubectl commands now point to that virtual API server and not to my real clusters API server. So any kubectl command I'm running now is inside the virtual cluster. So let's just list all namespaces and we'll see there's a couple of namespaces in there like kubesystem and default and they've been created 51 seconds ago when we started that virtual cluster. We can also list pods in the kubesystem namespace and we may not even have the permission to do that in the underlying cluster. We're not admin in the underlying cluster, we just have access to a namespace and now we're admin in this virtual cluster. That means we can also create namespaces in that virtual cluster, solving our problem with network policies. I can now do things across 10 namespaces although I just have access to one namespace in the underlying cluster and of course I can schedule workloads and that's actually the tricky part, right? Creating a namespace is just an entry at CD or a data store but what happens if I create a deployment nginx in this case, I set the replica number to two and I schedule that in our newly created virtual namespace NS1. If we list the pods for these deployments a second later, we see that they actually get scheduled. The first pod is still creating and the second one is already running but where is it running, right? That's a question and I'm gonna dive a little bit into this, we'll see both of them are running now. Our virtual cluster seems to function like a regular Kubernetes cluster and that's really the goal with virtual clusters. So let's recap of what happened here from an architecture perspective. We created this host namespace in our regular Kubernetes cluster and then we deployed a virtual cluster with the vcluster CLI for ease of use, right? A virtual cluster has mainly two components. It has a stateful set, we call that VC1 just like the virtual cluster we created and it has a service. The stateful set essentially creates a pod. It has replica number one in this case and inside this pod is really where our virtual cluster lives now. We have two containers in this virtual cluster. The first container is a control plane. It has an API server as we talked about earlier that's definitely what we need to do any kind of Qtcl interaction and it has a separate controller manager and it has a separate data store as well so it has a separate state from the underlying cluster to store our pods, namespaces and everything we do inside the virtual cluster and then the third component is the so-called sinker and that is what is replacing the scheduler. You may have noticed our control plane is incomplete. The scheduler is missing. Instead we're gonna have the sinker and we're gonna talk about this in a second. Next part of the demo was essentially running Vcluster Connect which establishes this port forwarding connection through this Vcluster service so that we can now talk to our Vcluster API server. And this API server is, Vcluster is a certified Kubernetes distribution. It just recently became a certified distro. It's a very new project. We just launched it in Q1 this year and very recently became certified. That means this API server that we're talking to is 100% compliant with all the conformance tests that we have in Kubernetes and it behaves one-to-one like a regular Kubernetes cluster. You won't be able to tell the difference except I guess after this talk you should be able to know some tricks on how to find out if it's actually a virtual cluster. So let's get rid of our underlying cluster and just focus on the virtual cluster for a second. Let's get rid of this underlying control plane. The first thing I ran in this demo was creating a namespace. All right, that's an entry in our data store. By default, Vcluster is using SQLite because it's a very, very lightweight data store and by default we're using K3S's API server which supports SQLite as a storage backend but you can also use Postgres or even at CD if you need full-blown virtual cluster and we're currently working with K3S but we're also working on making real Kubernetes API server work with Vcluster as well as one of our next steps. So we're creating a namespace so that creates an entry in our data store and then the next thing we saw in the demo was creating a deployment with replica number two, right? So we have another entry in our data store, that's it. That's all we're doing with the API server and then the controller manager, part of our virtual control plane sees that new entry, right? It gets notified, it's listening on these objects and sees, okay, replica number was two, I create two pods. What does that mean? Well, it just writes two more objects into our data store. So we have four objects in our separate virtual cluster state now. We have a namespace, we have a deployment and we have two pods that are owned by this deployment. And in the beginning, these pods are just, they're waiting to be scheduled, right? They're nothing more than just an entry in a data store and now that's part of the scheduler to actually schedule these pods to nodes. But in a virtual cluster, instead of the scheduler with the sinker and that's actually what makes it really, truly virtual, what the sinker does is it copies the pods from within that data store that we have inside the virtual cluster to the underlying host namespace so that the host clusters scheduler can now schedule these pods, right? That means all the restrictions we have in terms of network policies, what we have in terms of our bag, anything we have in terms of service accounts being mounted into these pods and all these things can be restricted by the underlying cluster. You can have regular admission control, right? Everything is still enforced, but only at the pod level. The deployment doesn't exist inside the underlying cluster, only the pods. And because we can obviously create multiple namespaces in our virtual cluster, what about naming conflicts, right? We were just talking about that earlier, namespace, being the scope for names, how do we solve that? Well, what the sinker does when it sinks from multiple namespaces down to a single namespace in the host cluster, it actually renames these pods and it adds a suffix with the virtual namespace in this case and has one for both of these pods and even with the name of the virtual cluster because we could have just like three stateful sets with a virtual cluster inside the same host namespace, right? So we need those two suffixes. And it's really important to understand that sinker only sinks the minority of things, right? Very, very few things, mainly pods. So sinker sinks only low-level resources. That includes pods plus everything that pods need to start, right? So we typically take a look at that pod in the sinking process and we see it has a config map that is mounted. So we'll sync that config map as well, but the other 5,000 config maps don't need to be mounted. Same for secrets, of course, and same for persistent volumes. We also sink services to make service-based communication possible. And there's two optional sync resources which are also really basic resources in Kubernetes and that's ingresses. We added that because there's a lot of need for like shared ingress control or across different virtual clusters, right? So this is actually by default on NV cluster but you can disable it with a flag pretty easily. And then the question is, yeah, what are the nodes inside virtual cluster, right? What if I run kubectl get nodes? That's actually up to you as configurable because sinker sinks in both directions. It doesn't just sink pods down, it also sinks the status up. That's why we saw earlier, one of these pods was container creating and the other pod was already running, right? And we saw that inside the virtual cluster, although that state actually lives in the underlying cluster because that's where these pods are being scheduled. And it's really important to understand that those are only very, very, very few resources in our Kubernetes cluster. All higher level objects are not being synchronized. Only very basic resources are being synchronized. And high level resources include everything that is replica controlled, right? Deployments, stateful sets, steam insets, all these secrets and config maps which have nothing to do with pods where we just store some kind of state service accounts, jobs, a lot of these things are not synced. And most importantly, CRDs and the custom resources that we create from them. And that actually creates a really interesting possibility. If you want to install HelmChart today, you know, any kind of machine learning framework, there's a very high probability that you will need to add CRDs to your cluster. But if you're not cluster admin, you can't do that because CRDs are cluster-wide resources. But in your V cluster, you can do that. And the great thing is we're shifting left, right? We're shifting this permission and also the responsibility for these CRDs to the application-specific teams that actually care to work with these custom resources. And that's really great for IT teams because the underlying clusters can be pretty dumb. You know, they don't need any CRDs, right? They may need to add an ingress controller there and some basic monitoring for these pods that we're scheduling and obviously some network policies, right? But we don't need anything specific to applications. We are not going to run into any conflicts of CRDs either, right? Two teams can have two versions of CRDs and run side-by-side in the same host cluster but within two virtual clusters, very, very interesting. So the vast majority of resources exists only in the scope of our virtual cluster. So what about pod networking and DNS? Well, pod-to-pod communication is a given, right? Pods are actually running in the underlying cluster so they can communicate VIP just as they can in a normal cluster. Pod-to-service communication, as we heard earlier, we, by default, sync services and we do wire them up to the actual write pods, right? So that works out of the box as well because the sinker takes care of this. And then what about cluster or V cluster internal DNS? Well, as you may have seen earlier, when we listed the CUBE system, the pods in the CUBE system namespace within our V cluster, there was one pod already running and that was core DNS. So V cluster, by default, has in its CUBE system namespace a core DNS deployment and that one creates a pod, that pod is being synced down to the host cluster, right? That means we have a pod and also a service for DNS down there in our host namespace which now is managing our DNS. That means when the sinker synchronizes down to the host cluster, the only thing we need to do is modify the pod spec and point it to that DNS service instead of the regular cluster-wide DNS service and then DNS-based communication and name resolution works as well. And then, as I mentioned earlier, ingress as sync is pretty interesting as well to even get more capabilities out of this. So now let's get to a very interesting question. What happens when I run CUBE CTR get nodes inside a virtual cluster? Well, it's like always an IT, right? It depends, right? There are multiple options here. The first option, that's the default option, is fake nodes and they're dynamic. That means what we do is we let the schedule of the underlying cluster schedule our pods and then we see which nodes do they end up on and those nodes we add in our data store because a node is just an entry in our data store, right? Inside the virtual cluster and we tell this virtual cluster this node exists and then we fake it, right? In a way that we rewrite the name, we rewrite certain things in this node specification to make it obscure for the user what this node is about but the node for the user virtually exists. There's also the option to not do that obfuscation and just have the plain node being synchronized into the cluster. We can also enable a flag that will synchronize all nodes from the underlying cluster if we wanna see our tenants, I have our tenants see all nodes in the host cluster or we can add a label selector for our nodes and essentially enforce our pods during the sync process, right? To automatically get that node selector so that a certain V cluster can only use certain nodes and only can see certain nodes inside the cluster and all of this is configurable. We are pretty straightforward flags that you can pass to the sync container. What else is possible with virtual clusters? It's very, very exciting because there's a lot of things that you can do with it. One thing you can do is also run kubectl inside these pods which is very exciting because when you're thinking about it, this is a pod that actually runs in the host cluster, right? So if I run kubectl there but I started this pod from within the virtual cluster so if I run kubectl and I talk to, with a service account being mounted, I talk to the host cluster. So that's why we actually changed this environment variable in Kubernetes so that when you use the in cluster config for kubectl, it talks to the virtual clusters API server instead of to the real underlying host API server. So we get the true cluster experience even when running kubectl inside a pod. We can expose virtual cluster API servers. It's just a service in Kubernetes, right? So we can add a load balancer to it, type load balancer or we can put an ingress control in front of it and make it available to outside of the cluster, not just via port forwarding. There's a couple of things upcoming which are really exciting as well, making network policies work. If you're creating a network policy inside of your virtual namespaces and that has a namespace selector, that's a little tricky, right? Because you may not have the same namespace in the underlying cluster but we can also do that with changing things during the sync process and we're actually working on that right now a couple of weeks away from making this work. Pot disruption budgets is another hot topic that we're working on and non-rude vclusters. Right now, K3S runs as rude and they have the option, I think they recently released the option to run K3S as non-rude and that will be possible with vcluster as well. It's one of the most important steps in making vcluster very, very resilient and isolated and unless the virtual cluster is there is something very interesting, right? You could now talk to this virtual API server and run vcluster create again, right? Create a stateful set there, create a service and connect to this virtual cluster, right? You can see it, you can go pretty crazy about this and Rich Bowers, which works with me at Loft Labs, he's also attending this talk if you wanna chat with him later. He made a pretty great video about, it's called vcluster inception, nesting virtual clusters. You should definitely check it out. There are a lot of use cases for virtual clusters. You can create them for ephemeral CICD environments, any kind of integration end-to-end acceptance tests. You can spin up preview environments per pull requests and get an entire Kubernetes cluster. You can even have different versions of Kubernetes being tested in your CICD now on the same Kubernetes cluster, right? Because that API server you can enable alpha and beta flex is independent of your underlying cluster. The only thing your underlying cluster needs to do is creating pods, creating services, right? Very basic things, right? I guess if the pod spec changes with a future version, right? There may be some incompatibilities, but that the pod spec is having a breaking change in the future that probably we, very more problematic on other edges than virtual clusters. You can spin up these remote development environments that your engineers directly work with Kubernetes. So instead of having them maintain their pet mini cube clusters or Docker desktop, have them just spin up virtual clusters, right? Their throw way, they can create one, they create another one for a different project, right? That's actually what we do with our commercial project. So with loft, engineers are exactly doing that, right? They're spinning up these virtual clusters and namespaces. Before we open sourced V cluster, virtual cluster was for about six months already part of our commercial offering. So we already have companies working with this technology and essentially providing these deaf environments to the engineers and propping the local host environment entirely. And what we do as well is we put those environments to sleep when engineers are not working with them, right? So automatically pausing these virtual clusters, purging all the workloads and automatically spinning them up again when new cube CTL requests come in so that when your engineers leave the office at 8 p.m., everything turns off 30 minutes later because they're not working again or they're shifting between their virtual clusters, but they're only really working with one at a time and we really wanna make virtual clusters cattle in a way and make them disposable, right? And you want the engineer not to have to treat their pet local host cluster as they do it today. We see a lot of experimentation where you really need a lot of compute workload, MLAI workloads, we see cluster simulations as well. It's a very interesting concept, adding fake nodes to the cluster and things like that, right? There are so many things that you can do, like have like 10 virtual nodes mapped to the same underlying physical node, right? All of these things are possible, even virtual cluster spanning across different Kubernetes clusters, right? There's so many creative ideas of what you can do with this and you can really make multi-tenancy more resilient. Wing-Wing, that's kind of the name of the conference and you can do things like sales demos and higher level things as well with these virtual clusters. So how to get started? I hope you all got excited about virtual clusters and we try to make it as easy as possible to get started with them. You can essentially just download the VCluster CLI and run VCluster create and VCluster connect in any, pretty much any Kubernetes cluster. You can head to the documentation for more detailed getting started guide. Source code is available on GitHub if you wanna dive a little deeper, if you wanna open issues. We also have a VCluster website with some information. You can follow Loft Labs on Twitter. We regularly post blog posts about virtual cluster and shoot them out on Twitter. And definitely if you have any questions, reach out, right? That's why we're all going to a conference. We want this interaction and I'm so glad that we have this personal hybrid format again, right? Where we can really connect to each other. So if you have any questions, I don't ask now or join us on Slack, reach out via Twitter, come by the booth. I'm gonna be at the booth right after this talk. We're, when you're entering the exhibit hall to the right, close to the project maintainer area. Booth number is SU-49. We have a couple of pretty nice swag and I especially wanna point out, we have KubeCon postcards. They look like this and that really meant to be sent out to your colleagues who cannot be here in person. So feel free to grab one and just send it out to whoever cannot be here in person. And since we're a startup and we're working on really exciting technology in a lot of different open source projects as you've seen on the first slide, we're so hiring. So if you wanna work with my really brilliant CTO, definitely check out our careers page or approach any member of our team, reach out to us and see if we can work together. And I think we have about two minutes left for questions. So if you have any questions right now, just raise your hand, happy to answer them. Thank you.


physics channel for physics please subscribe my channel hello everyone before the video watch it first come on man no need to be scared with this it is simple a thermal scanner same like a thermometer and other devices which are used to measure temperature so what is a thermometer a thermometer the device that measures temperature the degree of hotness and coldness of substance there are three temperature scales in use today Fahrenheit Celsius and Kelvin this is a liquid in thermometer there is a mercury inside and you can see the red color if you look at the reading it is 23 I guess the length of this thermometer is called the stem of thermometer and you can see the range is after 100 there is 10 more places if you come back to the thermometer you can find before 0 also there is 10 more it means the range of this thermometer is minus 10 degree Celsius to 110 degree Celsius let's talk about two important terms here to fixing our temperature scale one is called lower fixed point and one is called upper fixed point we need to make two standard points here the lower fixed point as you can see on the screen is 0 degree Celsius whereas the upper fixed point is 100 degree Celsius let's talk about some more terms related to thermometers for example sensitivity thermometer whose liquid expands more due to a slight change in temperature are more sensitive the narrower that you the higher the sensitivity of the thermometer range range means the minimum and the maximum measure by the thermometer if you remember the last slide we studied that the minimum was minus 10 degree Celsius and the maximum was 110 degree Celsius responsiveness a thermometer with a larger ball takes longer to response to temperature changes similarly what is linearity a thermometer should respond to temperature change uniformly it means the thickness of the thermometer where the mercury is there should remain same let's talk about the structure of thermometer this is a liquid in glass thermometer with long narrow tube there is a bulb here and mercury inside and it's contained a same thickness so what do you think what is a normal temperature of body it is 37 degree Celsius it means this normal temperature in between 35 degree Celsius to 42 degree Celsius so the normal temperature of human body is 37 which started from 35 till 42 okay so let's talk about the unit of temperature the unit of temperature here is degree Celsius this is the unit of temperature here let's have a look closely this is a capillary tube and the if you provide some heat to the thermometer the mercury start moving from left to right quickly while there is a bend here the bend is to prevent the flow of mercury back towards its original and you get time to read the temperature on the thermometer so you can see here closely there are 10 divisions between 36 and 37 so these 10 divisions shows that each one is 0.1 it means 36.1234 so the reading is 36.4 but in some thermometers there are five divisions also one over five means 0.2 degree Celsius


What's going on everyone? Sam here with Layton Sportsguards. We're ripping 21-22. Canadian Contenders, Optic Basketball, Hobby 10 Box, Half Case Break number 11, Random Team Style. Here's a look again at your random results. As always, you can find these on the website on the results tab as well as the link in chat. Good luck everybody. Let's do it. Now to four to go on number 13. That's breaking relatively soon. Number 12 is sold out. This is obviously number 11. So good luck. I'm going to go live. Why not? I've got like 30 new followers in my last shoot. Make sure you're doing your job over there. All right. Good luck everybody. Here we go. We already cut these. That's good. That's good. No talk for you, Roy. Yeah, Sean is warming up. The banner is bright. All but two came out on that one. All right. First look here, guys. Good look. It's moderate or rip and fire right there. Joining. Lock here, everybody. Contenders, Optic Base. Yolkich Red to not numbered. Well, Mellow Ball Refractor. There's Hakeem Elijahwan. Nice first auto legendary contenders for the Rockets. They're 23 out of 49. Grats on that. We've got Hoop Dreams, Herbert Jones, and Franz Wagner on the Red Ice Lottery Ticket. Practiced Lottery Ticket. Again, is not numbered. Nice ice. Yeah, these are what, 50s probably? Yeah. Cats. Trey Murphy, Rookie. Not numbered. Kawaii Red. Number 299. Nice one there. Got Alexey Pokeshevsky. That is 134 out of 149. Nice poku. Hey, you got it. No problem, Brennan. Hoop Dreams, Jeremiah Robinson, and Zach Levine, all-star on the Red Ice. Let's go, Brennan. Brennan's in. Brennan's all in on it, dude. What a great pool in the shop today. Gold giddy. Gold vinyl giddy. Gold something out. Yeah, one guy came in and broke three cases of this in the shop today and just went on an absolute pair.  Cole Anthony. Tobias Harris, not numbered. Got Jimmy Butler, that's numbered 299. What up, Brady? What's up, Brady? Oh, by a Usman Garuba Rookie Auto, not numbered for the rockets. Playing the numbers game is Nikolay Jokic, and Uniformity is a Jalen Green on the color match. Nice one there. That sucks, dude. 11. Hey, gotta find a good one, man. That's really what it is. Gotta find a good community of it. Yeah, Facebook. Yeah, right here, late in sports cars. Pretty good community in general. Yeah, it was a fantastic community. Randall, whoops, whoops, whoops. Sorry, Devin Booker. Orange, not numbered. That's nice. Black Pandora, Pascal Siakam. That's pretty sick. We've got a one-of-one printing play. That's gonna be Jason Preston. And there we go, Clippers on the combo spot. Jason H. Congrats, man. Nice one there, buddy. One of one. There you guys go. That's a magenta right there. Nice Preston. Go, dude. Got Willis Reid. And playing the numbers game Red Ice is gonna be a Nikolay Jokic. 11, go check our website out. Yeah, man. We got all kinds of stuff on there for sale. Yeah, honestly. Really good prices. Sam, if you like hanging out too, we're live over on YouTube and Twitch seven days a week. Join the Discord. Yeah, I got a Discord. Yeah, it's a lot of stuff. Got a Facebook page, all collectors and stuff. Join the club. Oh, yeah. Absolutely. Tyree. Deontay Murray, Black Pandora. Black Pandora is not numbered. They are just a short print, though. That is random teams. 28 spots in the break.  Got Jaden Springer on the orange auto. That's gonna be 15 out of 25. Yes, no, five out of 25. That's going to be sixers. Go to latensportsfarts.com. Go check the breaks schedule under LSC main. Trayman and Nikolay Jokic. Contender's Optic. 33 out of 75. Nice one there. Okay, everybody on TikTok, I apologize when we get a Josh game. I apologize in advance. Yep. Good lord, help us. Steph Curry. Joshua Primo. This is Karis Levert on the blue. That's gonna be numbered 78 out of 99. Nice one here. Going to the Rockets. We've got Alfred Shengun, 21 out of 49. Turkish Tim Duncan. Nice one there for Houston. Congrats, each town. They got a nice Shengun. Sweet shots. RJ Barrett. Brian, we have spots available. And at Jalen Bridge. Two breaks from now and the same kind of break. Yes. And another one after that as well. Go to the website latensportsfarts.com. Hello. Yes, sir. Yes, sir. Yes, only one auto and back. I think they've almost always been one auto and basketball football. It's two. But I think basketball is pretty much always been one. Appreciate your Stephen. Stephen. Lanzo ball. What up, Stephen? Colin Sexton, not numbered on the red. Stephen McCool. Got a Tray Murphy. The third. Nice one there on the refractor auto for the Pelicans. Congrats, New Orleans. There's lottery tickets. Scotty Barnes. Smackdown. I know he's awesome. It's just Sam. Tray Young. Giddy is not. It's on there on the red ice. Oh, that shtick is so funny, dude. I love my Aussies. That shtick is so nice. Damn. And this dude starts trotting around the office. Nope. Taking it right back. I used to pick Dylan up at daycare. The Black Pandoras, I would say, are the insert you're hunting. They're a little bit shorter printed. And then anything numbered, like the cracked ice, the gold, Seth Curry. Say a red, Nicolay Okich. Not numbered. We've got Tray Mann on the refractor rookie auto. Nice one there for the thunder. Congrats, OKC. I really like that they have thicker stock, dude. Yeah, no, I agree. Scotty Barnes playing the numbers game. Let's go into the Raptors. Another one right there. And cracked ice. Kevin Durant on the blue. That is 44 out of 75. Blue ice. Brian, I would say right now, if you order, have the expectation that most, there's a 75% chance it'll go tomorrow. We have a full case of, full case of Bowman Chrome hobby is our first personal. And I mean, that's going to take at least an hour. Figuring that we finish on time and everything. Thanks, everybody, for joining up on TikTok as well. Tyler Hero. Joshua Karimo. There's a Scotty Barnes refractor rookie. Nice one there. No problem, Brian. We've got Isaiah Livers rookie auto going to the pistons. That is the refractor not numbered. Congrats, pistons. All by a plan. The numbers game is Carl Anthony Towns on the insert and blue ice playing the numbers game. Evan Mobley, numbered 42 out of 75. Nice rookie there for the Cavaliers. Thanks to the basketballs there. Quack Kings. Quack Kings. Some roses too. Good kid. Appreciate you. Nice one there on the Evan Mobley. Beautiful card. Let's go Dolphins. Let's go Dolphins. I'm coming back. I'm getting over it a little bit. Every minute, every second, we're getting better. All right. When we hit a nasty banger, I don't want to use, we'll be going crazy. I feel that for sure. Oh, Gene, not to be Fred Van Vleet. There's an orange Christian Wood. Another one. Wow, Sean. That's a banger. Wow.  I hope so. I think it is. Yeah, I hope so. I get the hair. Holy cow, man. Holy cow. We've got one of one printing play job, Merritt. Oh. Bang. Let's go, Gris. Brandon A. Holy moly. That is a monster. Monster. It's a live job as well, man. Let's go. Let's go. How's that taste? That's awesome. There you go, TikTok. Take a look at that. Take a look at that right there.  Love pulling job, man. I know everybody's saying I just clicked the live as you guys pulled it. Monster, monster card. Congrats again, Grisly's. That's Brandon A. with Memphis. Let's go. All right, first band of the day. Nice. Later, bud. Take that negativity right to the exit. Sweet shots. Donovan Mitchell. Oh, that's my favorite thing to do. Blue ice, LeBron James. I'm back to being fired. Not numbered. Or red ice, I should say. Red ice, sweet shots. We got one down. One down. I know. We're almost there. All right, guys. Do a quick recap here. Such a fire break, man. Isaiah Livers, that's going to the Pistons. Trey Man Thunder. Trey Murphy. Pelicans. Alfred Shengun Rockets. Jaden Springer going to the Sixers. Uzman Garuba Rockets. Alexi Pokhachevsky for the Thunder. And we've got a Hakim Elijah one for the Rockets. We also had a Jason Preston on the one-of-one Clippers.  One-of-one. That will do it for the Break, guys. Thanks again for the fill. Next up, we've got another one of these coming right on.


Hello and welcome to the session. In this session first we will discuss sections of a cone. Let this L be a fixed vertical line. Let this M be another line intersecting the fixed line L at a fixed point V and inclined to it at an angle alpha. Suppose that we rotate the line M around the line L in such a way that the angle alpha remains constant then the surface generated is a double-naped right circular hollow cone which is referred as cone and extending indefinitely far in both directions. So this is the cone. This point V is called the vertex. This line L is called the axis of the cone and the rotating line M is called the generator of the cone. This vertex separates the cone into two parts called the nape. This is the upper nape and this is the lower nape. If we take the intersection of a plane with the cone the sections are obtained is called the conic section. So we say basically conic sections are the curves obtained by intersecting a right circular cone by a plane. We obtain different kinds of conic sections depending on the position of the intersecting plane with respect to the cone and by the angle made by it with the vertical axis of the cone. Let this beta be the angle made by the intersecting plane with the vertical axis of the cone. Now the intersection of the plane with the cone can take place either at the vertex of the cone that is at this point or at any other part of the nape either below or above the vertex. Then we have when the plane cuts the nape other than the vertex of the cone. Then we have the falling situations like when the angle beta is 90 degrees then the section is a circle then when we have the angle beta is greater than alpha and less than 90 degrees then we say the section is an ellipse. Next situation is when we have angle alpha is equal to the angle beta then the section is a parabola. In three of these situations the plane cuts entirely across one nape of the cone. The next situation which can arises when the angle beta is greater than equal to zero and less than alpha then the plane cuts through both the nape and the curves of intersection is a hyperbola. Next we discuss degenerated conic sections when the plane cuts at the vertex of the cone. We have different cases like the following. The first case is when angle beta is greater than alpha and less than equal to 90 degrees then the section is a point. In the next case we have when angle beta is equal to angle alpha the plane contains a generator of the cone and the section is a straight line. This is the degenerated case of a parabola. Then we have one more case in which the angle beta is greater than equal to zero and less than alpha. The section is a pair of intersecting straight lines and this is a degenerated case of hyperbola. Now we discuss the conic section circle. Basically a circle is the set of all points in a plane that are equidistant from a fixed point in the plane. This fixed point O of the circle is called the center of the circle. Let's consider any point P on the circle then the distance from the center to any point on the circle is called the radius of the circle. So here we have OP is the radius of the circle. Let's consider the center has coordinates HK and a point P has coordinates XY and let OP be equal to R then we have equation of a circle with center at HK and radius R is given by X minus HD whole square plus Y minus K the whole square is equal to R square. Let's find the equation of the circle with center 3 minus 2 and radius equal to 5. Now from here we have H is equal to 3 and K is equal to minus 2 and the radius R is equal to 5. So the required equation of the circle is given by X minus H the whole square plus Y minus K the whole square is equal to R square that is X minus 3 the whole square plus Y plus 2 the whole square is equal to 25. So from here we get the equation of the circle is X square plus Y square minus 6X plus 4Y minus 12 is equal to 0. This is the final equation of the circle with center 3 minus 2 and radius 5. This completes the session hope you have understood what are the sections of a cone and the conic section circle.


So as you can see look at the breadth of the market. It's moving to the very bullish side That's because it's it's coming down from I mean, it's coming up from a lower level So we do have some candidates that are on the bullish side.  Oh Baidu is up too and and so is Alibaba So let's see if the bullish momentum continues in that case. Let's come back to Alphabet here and And as you can see Alphabet is at 1115 1116. It's already too high. I mean, it's gone up $17 So I'm not sure how good of a trade that might be Facebook and Alibaba might actually be better Let's look at Alibaba is up to Alibaba is up to but markets are still a little Soft on the ES so 2680 is a resistance. Yeah, okay On the ES right? Yeah, so 2680. It's right there right now So let's look at okay Google is also coming down. So Google is now up only $8. Okay, so it was up 17 It is now up only $8 Okay, so we have a 31 Delta at 1120 not bad. So 30 Delta If you have five contracts, we can go in for that But I want to see if if the SMP is going to cooperate or is it going to go down? If that's the case then Google won't be the trade 1109 that's very good. Let's go take a look at our position quickly Alright, so this is up about 344 already. So what kind of a trade is it? This is a $2,200 trade. Okay, so we got in at 450 and Five contracts. So it's a $2,200 trade. Let's go back to market watch and watch this Okay, I want to see what we have here Okay, we have a profit of 750. Okay, you have a profit of 750 1113 so it should go even higher actually But I'm going to be ready with taking off two contracts on this because this is a great profit All right, let me take two contracts off because you know, you have a profit and so We got to take that off. Let's see what happened over here. It's at 1113 point nine four All right, so we have a profit of about 800 out of which we have booked about 300. Okay, so open is still 518 and The PNL for the day is 818. So exactly we have booked 300 and as we know these things can change Anytime so I'll keep one contract ready. I want to take one card We took it off previously at six. So here we are at 650. I'll take one contract off Okay, so a little selling pressure coming into the ES over there. I don't want to take a risk We've got a great profit. So I am closing it. So this bar is going to end in about 15 seconds. I think 10 seconds. I'm of the opinion. Let's try to just close this Okay, sold it at 710. That was a good trade. Let's see. What did we do one zero? Something here one zero one zero two zero. So I mean almost close to 50% on that rate. So that was very very good Okay, it started the recording again The it wasn't recording. So we're down about 270 on Netflix Yeah, I'm definitely going to do that Because it's going down further At least let's get a debit spread going That would be the issue there. So let's just watch and wait and see Okay, so just close the short call now. We have a chance for Netflix to move up again looks like it wants to do that I'll tell you what let's go as a credit spread here and I'm going to try to get a credit spread and get a better recovery 1.69 Send okay 1.69 So now if you see we have a credit spread and It is 347.5. I believe And this one is 350 the long call and so let's see if we can Turn this into an iron condor Of sorts let it go down first a little bit and then we can put in the iron condor Right now itself if both of them expire worthless you can see that we would be up by four cents okay, so From 1.69 and 1.65 But looks like even the es is a little tired. So decided to go in for the for the credit spread And what we'll do is We'll keep it ready for In case you need to turn it into an iron condor at an equidistant level. So This is about 300 and so it's about five dollars away from the money And so that would be somewhere near 335 337 So let's see if it can go down further that way we can increase the The body of the condor Okay, looks like some volume is coming into Netflix right there. So I would tend to put the The Cell vertical at the 332.5 that would be sort of mid-price there And so let's go ahead and create this and so for 10 You want to 10 we got 40? All right, I'm going to go in for it. So 400 bucks Okay, so We have an iron condor Let me take this off and if you look at the risk profile, that's exactly what it is. It'll be right in the middle


Welcome back to our lecture series, Math 1220, Calculus II for students at Southern Utah University. As usual, I'm your professor today, Dr. Andrew Misseldine. In the last several lectures in this series, we've talked about various convergence test. We started off with very simple ones like geometric series and telescoping series. We moved on to the integral test with the p-test as a special case of that, very important special case. In lecture 39, we introduced the comparison test and the limit comparison test. In lecture 40, we're going to introduce one more convergence test for series. This is known as the alternating series test. Some of our examples here will have been derived from examples found from section 11.5 in James Stewart's Calculus textbook. So what do we mean by an alternating series? So an alternating series is a series whose terms alternate between positive or negative values. So what I mean is you're looking for a series that looks something like the following, n equals one to infinity. You can have this negative one to the n times some other sequence. Let's take one over n, for example. What you see right here is that these alternating series is going to have this power of negative one that sits in front of it. Because as you take different powers of negative one, you can alternate between plus, minus, plus, minus, plus, minus. You might see negative one to the n. Probably more likely you're going to see negative one to the n plus one. Or sometimes you might see negative one to the n minus one. The distinction here is do we want to start with a positive or a negative? If n starts at one and we take the nth power, this will start off as a negative. And so if you take a plus one, then one plus one is two. You start with an even power of negative one. That's going to give you a positive one. So if you take this series, for example, the sum equals n equals one to infinity of negative one to the n plus one times one over n. If you take away the negative sign, this is just the harmonic series. But now it has this alternating factor, plus, minus, plus, minus, plus, minus. And so this right here turns out to be the alternating harmonic series. And so while we've seen the harmonic series before, it's a p-series that is divergent. It turns out that the alternating harmonic series is actually a convergent series. And because you have some plus, minus, plus, minus, plus, minus, there's some cancellation. Some of the negative gobbles up the plus. And it does it at such a rate that actually the series will be convergent. And we're going to talk about that in a general idea. And this is the idea behind the alternating series test. So suppose we have an alternating series where n equals one to infinity the sum of the sequence a sub n. And we want the following conditions here. If we look at the absolute sequence, so this is a little bit of vocabulary I want to point out here. So if you have a sequence, a sequence a sub n, then its absolute sequence, the absolute sequence is when we take the absolute value of said sequence. And so what this does is the absolute sequence will guarantee there are no negative numbers in this sequence. Everything we pause for negative. And why that's sort of important is that when we do things like the comparison test or the integral test that we talked about before, those required as part of the assumptions that all the terms in the sequence have to be non-negative.  And so sometimes we want things to be absolute here so that we don't have to worry about some issues that come up with negatives. And so that's also sort of something that comes up in this discussion with the alternating series test. So let's consider the absolute series the absolute sequence involved here. So we want that the absolute value of a n plus one will be less than or equal to the absolute value of a sub n. So we're requiring that the absolute sequence be decreasing. It needs to be decreasing. And we also want that the limit as in approaches infinity of the absolute sequence a sub n is equal to zero. So we want that the absolute sequence converges it converges to zero. Now, if these two conditions are satisfied, if the absolute sequence that is if you ignore this alternating factor of negative one, in that situation, the absolute sequence would be this guy right here would be the harmonic sequence. In that situation, ignoring the negative signs does that sequence decrease towards zero? And if so, that tells us that the alternating sequence will be convergent. And so those are some very nice conditions to look out for. And so let's see some arguments. Let's see some evidence. Why does this alternate series work? Why does the alternate series test work? So just for the sake of simplicity, let's start off with the assumption that a one is positive. We're going to assume that the first term of the sequence is positive. Now, if that's the case, if the first term is positive, that means our sequence has to look something like this. That is a sub n has to equal negative one to the n plus one times bn, where here bn is the absolute sequence, right? Now, because it's all channels switch negative or plus negative, plus negative, plus negative, the first term is positive and needs to start off positive. So we have an n plus one right here. This would happen if a one is positive. Now, the other option is maybe a n actually starts off as negative. We allow that as a possibility. A one could be a negative number. Now, if it is, that would actually mean that a n is going to look like negative one to the n times bn, where again, bn is just the absolute sequence right there. So the only difference between the starting term and being positive or negative really comes down to, should we have an n plus one or an n as our power of the negative one there? Now, the good news is, clean this up a little bit, the good news is that these two options, right? If you have negative one to the n plus one bn versus negative one to the n times bn, these only differ by a factor of negative one. They only differ by a factor of negative one, right? And as such, when it comes to the series in play, you have the series a sub n versus the series negative a sub n. And times in a series by negative one doesn't change the convergence or divergence of that series. So if one converges like this one, then so does that one. And if this one converges, then so does that one. So we are actually safe to assume that the first term is positive. And therefore, our sequence has the form a sub n equals negative one to the n plus one times bn, where b is this positive sequence. So we're gonna use that assumption for the rest of this proof right here. So the series, if the series is convergent, it's the limit of the partial sums. So the partial sums are gonna come into consideration here. Let s sub n equal the sum, the partial sum k equals one to n of the sequence a sub, that should be a k right there, typo, sorry about that. So let's consider this partial sum. And let's actually look at the first couple terms here. You're gonna like this. So looking at the first even partial sum, we're gonna take s sub two. This is gonna look like b one minus b two. Now, because of the original assumption that absolute sequence is decreasing, if this sequence is decreasing, that means b one is bigger than b two. And if b one is bigger than b two, that means their difference is gonna be positive. So this right here is a positive term. Well, I guess it could be zero because b one could equal b two, that's perfectly fine. So s two is gonna be positive. Now let's look at s four. S four is gonna involve s two, which is positive. Plus it's gonna take b three minus b four. But again, the sequence of b's is decreasing. So b three is bigger than b four, which means that the difference of these b three minus b four will likewise be positive. So you have a non-negative number, s two plus a non-negative number, b three minus b four. This tells you that collectively, s four is gonna be a non-negative number as well. And this keeps on happening. If we do s six, you're gonna get s four, which is positive, plus b five minus b six. Now, since b five is bigger than b six, their difference is positive.  And this is gonna happen over and over and over again. If we apply induction here, we could eventually get up to the term s two sub n. This will be s two times n minus one plus, we're gonna get b two n minus one minus b two n. So why do I keep on getting plus minus, plus minus, plus minus? That's because of the alternating factors, right? So this first term has a positive sign in front, then a negative sign, right? And then we're gonna have a positive sign, then a negative sign. A positive sign and negative sign, a positive sign and negative sign. That's the alternating bit right there. We're always getting plus minus, plus minus, plus minus. And so b two n minus one is bigger than b two n. So their difference will be a positive number by our inductive hypothesis. We know that s two n minus one is positive. So this thing will add up to be something non-negative. You get right there. And so what we see here is that s two n by induction will always be positive. It's always gonna be positive. But we actually say something a little bit better than that, right? We actually see that the sequence is in fact increasing, right? Because notice that s four is s two plus something. So it's bigger than s two. And s six is s four plus something positive. So it's bigger than s four.  I mean, you might be adding zeros that might have not got bigger at all, but that's okay. Our inequalities have less than or equal to. So this tells us that our sequence is increasing. We have an increasing sequence. I mean, it's a monotonic sequence. It's an increasing sequence, but it's also bounded, right? Because it's increasing, it's gonna be bounded below by wherever it started from. All of these things are positive. So we're gonna be greater than zero. Who's an upper bound? Who's an upper bound for this thing? It turns out with a slightly change of perspective, if you take any number in this sequence, we're gonna start off with s two n again. Well, actually you can see it right here. If you take s two n, if you list all the numbers b one, b two, b three, b four, b five, all the way up to b two n. In that case, you're gonna get plus minus plus, sorry, plus minus plus minus plus all the way up, right?  Notice if you distribute this negative sign through, you're gonna end up with negative b two and plus b three. The next negative sign, if you distribute it onto b four, that'll be negative. If you distribute it onto b five, that'll be positive. So this does have the alternating plus minus plus minus plus pattern that an all-terrain series is supposed to have. Now, what do you see here? You have b one minus something.  So you have a positive number minus something. Again, b four is bigger than b five, so their difference is positive.   Those things are always positive numbers.  These things are getting smaller, smaller, smaller, smaller. And so what we see here is in fact, that S2n is bounded above by B1. And so we see that all terms here are bounded below by zero and bounded above by B1. So in summary here, S2n, it's bounded above by B1, it's bounded below by zero. And so this tells us that our sequence is bounded. We have a bounded sequence and we also have an increasing sequence. So the monotone convergence theorems applies and tells us that the sequence of even partial sums converges and thus it has to converge to some value which we will call S. That gets us halfway there, right? We know that the sum of the even partial sums will converge towards S. But what about all of the partial sums? What about the odd ones? Now, if you look at the odd ones, where I take the limit as n approaches infinity of two Sn plus one. Well, if you have a partial sum of S2n plus one, well, that can be broken up as you take the partial sum of Sn, that should be an S2n. Sorry, there's a couple of typos in this lecture here today. So if you break up S2n plus one, this breaks up as S2n plus the next term in the sequence which will be B2n plus one, which you can see right here, right? Now, separate these things. This then becomes a sequence as in approaches, the sequence of evens, S2n as in approaches infinity right here, that sequence will go off towards S as we determined over here with the monotone convergence theorem. And then the other sequence is the limit as n goes to infinity of B sub n. By assumption, since B sub n is the absolute sequence, this will actually converge towards zero. So we end up with S plus zero, which is equal to S right here. So this tells us that the odd partial sums, they converge towards S. We've already determined that the even partial sums converge towards S. So when we merge these two odd and even partial sums together, we see that the entire sequence of partial sums converges towards S. And this, and as the series is the limit of the partial sum sequence, we see that our series is convergent. And so this gives us, this shows us that the alternate series test does guarantee convergence here. And what were the assumptions that we needed? Remember, we needed that the absolute, the absolute sequence is decreasing. We needed those decreasing to make all of the inequality statements we use throughout the thing. We needed this to be decreasing to employ the monotone convergence theorem. But we also needed that this limit goes to zero so that we could merge together the odd sequence with the even sequence of partial sums and get that it's all convergent right there. It's a pretty nice argument. And it turns out that this proof doesn't just prove the validity of this test here. Also, when we talk about remainder estimates for alternating series, these inequalities we derived and the proof will be useful there as well. So put a pin in those ones. We'll come back to it in just a minute.