So, one more thing I want to make a distinction between a type of adversaries we are going to see. We said that the adversary cannot see what is the loss value predicted by the player in each round ok. He would have observed it in the fast, but in the current round he do not know what is the loss value predicted by the adversary. So, had he seen, had he is been able to see the loss value predicted by the adversary, he can always make the loss value incurred by that adversary very high right. If he predicts the adversary the loss to be 0, then the learner predicts it to be 0, then the adversary can assign one to it and he can make him suffer more losses. So, because of that we said that ok, we allow the learner to randomize his strategy ok. And because of that adversary and we did not allow the adversary to know what is the strategy that the player is going to I mean whatever the final action that the player is going to select in that round ok, because he is basically randomizing it. Now, he is not able to and see what because of this randomness what is the action that the learner will be selecting, but once the learner selects in that round he knows the adversary what is the action that the learner took ok. And because of that he cannot manipulate what and he is going to assign the losses before the learner selected an action in that particular round ok. So, suppose let us say the learner is going to randomize, but at the end of the randomization he picks a particular arm ok. So, what we said again revisiting that in in in each round learner picks distribution PT and picks loss vector LT. The adversary may know might have observed what is the actual action that has been selected by the learner, but in the and based on that he may have some information about how the learner is going to come up with this new strategy. But suppose the learner is using a deterministic strategy then the adversary can what he do he can see what is the next action that the player is going to play and give a very high loss to that. But given that in the in the teeth round we have made the learner to pick this actions according to some distribution the adversary is is no more having that capability. Because you are choosing this actions in according to some distribution he cannot particularly make some actions to have a very high loss and others low loss right because he apparently do not know which is the action you are going to select because you are randomizing. But once you select an action he knows that in that round you selected that action and maybe in the next round he may get some sense of what you are doing what is your strategy and accordingly he can come up with his losses.  So, because of this even adversary can update the way he is going to pick his losses in every round ok. Because adversary we are not assuming anything about the way he is putting losses right. So, we can consider a worst case and see that this adversary is choosing this losses in such a way that he will make you incur maximum penalty or maximum loss. So, based on this we are going to consider two types of adversaries called oblivious and non oblivious. So, we will come across these terms in the literature when you read about this adversary setting. What does oblivious says oblivious says that the adversary is not of adopting his losses by observing what the learner is doing ok. So, for example, what we can say the loss vectors for the T rounds before the game starts the learner can decide up very ok this is how them I am going to assign the losses in each round without knowing what the learner is doing. So, he will come up with his losses he fix that and you are going to play against that. If this is the case then we are going to say adversary is oblivious you still do not know the learner do not know what is the sequence it is just that the adversary has come with this sequence before the start of the game. But in the non of PS the adversary can in each round can decide what is the loss he is going to assign to the actions based on the past observations. So, I understand the difference between these two now oblivious and non oblivious adversary. So, which is the more difficult adversary non oblivious right because he can in each round he can see what you are doing and try to incur maximum damage to you. But the analysis we did so far does it hold for both the cases or on any of the specific cases. So, we did not assume whatever the strategy of the adversary we said this right like even he may be updating his losses based on the observations made so far ok. So, our analysis still holds because that is why we have two expectations right like one expectation who is over the randomness of the adversary. So, in each round based on this observation the adversary can come up with a new loss according to some he may be updating his distribution in every round ok. So, you adversary seeing that you are playing some strategy by to seeing what is the actions are going to select. Based on that he may be updating his strategy in every round may be one possibility he may have his own PT to say I am going to assign high values to this actions and low values to this action whatever and accordingly he can update his strategy in every round ok. So, whatever we have done the analysis can hold for the non oblivious adversary, but of course, this also holds for oblivious because oblivious is a simpler case I really. So, in that case if I take like this I really do not need to do the expectation on the strategy of the adversary right because adversary is already picked a sequence and I am facing that sequence whereas, here the adversary can keep on updating his strategy and there could be a randomness in the way he assigns the losses and that randomness can keep change from one round to another. The way we define regret of a policy pi to be this and we have also said I am interested in the expected value of this I said this is going to be the. Now, in this case what I am seeing is second case what we said that this is going to be with which we called it as pseudo regret ok. So, this is we are trying to guarantee the regret in expectation whereas, this is like a when you come through a sequence of losses this could be your true loss incurred. So, let us say that I want to give instead of bound on this expected regret I want to give a bound on this regret where you are going to not take the expectation over both randomness of the adversary and the randomness of the learner ok. See when you are going to run this algorithm for n round you are going to incur some regret based on the sequence of losses you have observed right, but when we gave this bound in expectation whatever the bound we get this need not hold on that particular realization because the expected bound can be different from the bound you are going to give on a particular realization right. So, because of this what happens it may happen that in expectation this bound could be smaller, but if you look into one particular realization this bound could be pretty large. For example, this is like if you have a random variable X and its expectation. So, this X let us say it takes 100 values when you draw one sample from this X that some value of that random variable could be much higher than this expected value right. So, in this says we may want to guarantee itself when you are going to look into when you draw one sample of this what is the probability that this is going to be actually small or that the value you have got from this sample it will have a bound that will have this that will be have the same bound that you gave on the expectation. So, what now basically I want to ask this question or whatever the bound you have here let me call that as regret value maybe I want to see that whatever the value of X you got it is going to be smaller than the expected value itself. Then if you have a bound on expectation that bound also holds on this X with that probability right. So, same thing you may want to do here it is basically saying that if you observe one sample how does it concentrate about its mean value ok can we say something about this things ok. Now, but when we do this we are now going to consider only the oblivious cases where we say that this sequence is fixed by the adversary apriori, but I am only now looking into the randomness of the learner. Can I say anything about what bound this regret has you may be interested in that right. So, now let see if we can give a bound for this quantity rather the expected value ok. So, quickly one thing is when you want to give a bound on the sample itself rather than the expected value you want to make sure that the estimates you are going to have there of course, they should be unbiased and what is the other quantity that I would like. So, what are the properties you look at when you are having an estimator one is it should be unbiased another one is its variance should be small right if its variance is too large then it may it fluctuates too much right. So, let us now quickly to see that what is the variance of the estimates we have in the exp3 ok. So, what is the we have estimates to be of this format right. We know that in expectation this is equals to LTI, but what about this variance you can verify that this variance is like again of the order like 1 by PTI because like this term gets squared and you will have PTI here, but you can compute this to be like of the order 1 by PTI. So, if PTI happens to be small in a particular round then you see that the variance can be very large right. So, which the variance is very large your estimates are not good enough and because of that you cannot expect like your values to start concentrating well I mean soon ok. So, because of that even though when we use this kind of estimator in the exp3 algorithm it gave us a good bound on the expected regret, but if you are going to look at the this quantity itself directly it may end we may end up getting a small a very bad regret because with some probability this quantity can be very high that is like this may not happen with some probability that every time we are going to draw a sample it need not be smaller than its expectation it may be larger than this also. So, at all I want to give a good bound in probability I need to make sure that my estimators have good variance ok. So, how to get a good variance do you see any easy way. So, when is the variance is going to be bad when when these guys are small when PTI is very close to 0 these guys are going to be very bad that is when some quantity PTI is very slow I am not picking it often right because the probability of selecting that term becomes small. So, I am not observing it enough times. One possibility is somehow if you can increase all of this by some factor gamma right because of this even if PTI is arbitrarily small this quantity will not be very large right. What is that in in that case it is going to be at least going to be greater than 1 by gamma right you are ensuring that this goes. So, one way to ensure this is kind of do some exploration let me write that now what this algorithm is called as pxp 3 dot p. So, again this algorithm has initialized pg then k then sorry this is input then initialize with l 0 i equals to 0 then for t equals to 1 2 3 you do the same thing PTI equals to what for all i now you are going to do now for all i you have the estimators. So, now, you are going to say gamma by k and for all i you do the same thing. So, what is the difference between the exp 3 and exp 3 algorithm which step we are differing PTI right. So, I should also adding 1 minus gamma here and also gamma is an input. So, now tell me what is what is the difference between exp 3 and exp 3 dot p here what is that I am changing. So, gamma is between 0 and 1. So, I am waiting this was there already right I am assigning a weight of 1 minus gamma to this and weight of gamma to this. What does this mean? I am going to choose an arm i which is a convex combination which is a convex combination of these two. So, this was my earlier probability and now this is my new what does 1 by k means here what are that a 1 by k implying it is basically saying that uniform weight. Now, what basically it is saying is I am taking uniform distribution with weight gamma and 1 by gamma weight the other distribution I have right alternatively what this thing is this is like P T is whatever like the new P T I am going to have 1 minus gamma of P T P T was the earlier one with gamma uniform over k you understand this. So, earlier I was only I am taking these probabilities with this now I am perturbing it by a uniform distribution, but I am weighing them accordingly. So, the earlier algorithm you had it was a kind of assigning the probabilities based on the losses you have observed. Even though there was some discounting factor here which control basically exploration and exploitation, but here you are deliberately bringing another term which is biasing it towards somewhat uniform exploration also. Suppose let us say you said gamma equals to 1, gamma equals to 1 means this term is not valid right no more affecting what affects is only 1 by k that means your uniform distribution you are selecting. If you are going to set this gamma equals to 0 it is exactly the exp3 algorithm we had earlier it was only looking into this exponential weights, but now we are giving taking linear combination of this uniform weights and the probability defined through this exponential weights. Now, with this kind of things you see that P t i there will be always one constant term we are adding right gamma by k because of that you see that this P t i here will be never 0 very close to 0 it will be at least gamma by k always right this quantity is going to be a gamma by k because I do like this I am controlling my variance right. So, because of this this P t i is not going to be arbitrarily 0 it will be at least gamma by k and because of that this will be at least lower bounded by some positive quantity it cannot be arbitrarily 0 close to 0 fine. Now, the question is what is the bound I am going to get for this ok I am just going to state this and we are not going to the proof you see already the proof of exp3 that was already pretty right. So, you can go through this proof yourself, but the steps are largely the same except to take into account the factor the additional factor gamma by k ok. I think I made one more thing I had to add not only this, but there is also a beta there we should go as an input to this algorithm ok there is another term beta there or any yeah it will not be it will not be anyway we are basically biasing it ok for any. So, we can come demonstrate this kind of bound for exp3, exp3. So, now, we are saying that like suppose if you give delta as an input factor another factor here is delta here. So, you see that we have so many input parameters here. So, if you are going to set beta like this ok. So, maybe what you should do is only these are inputs you can set beta in this whatever the way you want, but I am saying that this is enough based on that you set your beta like this and your eta to be a constant all these eta's to be like this and your gamma to be like this. If you can do this you can show that the regret is upper bounded by some 5.15 this is some constant times n k log k by delta and this bound holds with probability 1 minus delta. So, because we are giving on the sample regret right it is not an expected regret it is a sample regret. So, we can only say this holds with some probability and we are saying that this holds with probability 1 minus delta. Suppose, let us say you want this to hold with very arbitrary position that means, you want to set delta very small. If you set your delta very small this beta is has to be large right and you also see that if you set your delta to be very small this bound is also going to be larger this bound is like function of delta. So, if you want it with the arbitrary precision you can expect this bound to be also worse larger right because if you want it to be like very high precision this is going to be bounded by this maybe then the one can only guarantee that ok. In that case I will give a larger bound ok like this and similarly one can suppose like here I wanted you to give delta as input. Suppose, you do not give delta as input ok if this delta is not there then I will am going to set beta to be like this and suppose if I am going to stop after n rounds I am going to claim that my regret is going to be this and this is going to hold with probability again 1 minus delta. If I knew delta apriori I would have set like this and then I would have guaranteed this. If I do not know the delta I am going to give you guarantee with high probability guarantee with 1 minus delta, but this bound is I can only guarantee this much. You see that compared to this I have ended up with an extra factor here right. So, this is the penalty I am going to incur if I do not know this delta upgrade. Any doubts about do you understand difference between expected regret bound and high probability regret bound? Which one is desired? Expected regret bounds are desired or high probability regret bound. So, this is called high probability bounds because you are going to give the regret to hold with high probability and that is the with what position you want it is given through this delta parameter ok. So, any questions about or any confusion about difference between high probability bounds and expected bounds or ok which one you prefer for algorithm? Let us say you want somebody to give an algorithm for your problem. If he gives expected guarantee you would be happy or if he gives you high probability guarantee you would be happy. You would like high probability right why is that? So, the one you actually face not what would have happened if you kept on running it multiple times or in expectation ok. So, these are desired, but these are also very sensitive in the sense you want this whatever the regret sample regret you are going to observe to be bounded. It may happen that with remain this is true with probability 1 minute delta with another delta probability it may happen that this will not satisfy this property and that value could be very large and that is often the case ok. So, to control that with whatever probability you are giving this that is going to well behaved like this it requires bit more effort by tweaking your algorithm in certain fashion. So, that you control your variance ok. I will just take couple of two three more minutes to just introduce one more algorithm which you are going to see in the assignment. By the way if you have an high probability regret bounds like this one can always converted this to expected bounds you know how suppose let us say. So, this is just I am going to write this here. Suppose let us say x is the random variable is value is upper bounded as 0 to 1 1 by delta probability that x is going to be less than or equals to now 1 delta star using this relation. Suppose let us say if you can tell for some random variable x what is the probability that it is going to be larger than 1 by delta for a given delta. If you know this then you can translate that bound as a bound on your expected regret you understand this. So, let us quickly see how to use this result in in this case. So, here my random quantity is what this regret. I know that if I am going to rewrite my regret I know that if I am just manipulating this take it that side then this guy being greater than log k by n k this guy being greater than this log 1 by delta. So, I am saying that this bound holds with probability 1 minus delta that means, that the opposite inequality holds with probability delta right. If I am saying that this relation holds with 1 minus delta if I say that this this if I look into greater than this holds with probability delta right. So, suppose I know that this relation it holds probability delta. So, now, I if I am going to treat this quantity as x I know that this guy being larger than 1 minus delta that is log 1 minus delta this holds with probability delta. So, then this probability I know is at least delta this is with with probability at least or at most because this is at least here. So, if that is the case this is at most that means, this term I can write it as upper bounded by delta right not delta. So, I am saying that this holds with at least 1 minus delta. So, the negation of this should hold at most delta right. So, because of that if I am going to define this quantity as delta this to be x then I know that this relation holds by this proposition with probability delta. So, if I plug it in here I am going to get this to be delta by 1 by delta this happens to be 1 and now I know that this quantity in expectation is upper bounded by 1. So, that is expected value of R n dx p 3 p this quantity here minus 5.15 and k log k square root log k by n k is upper bounded by 1 then you can translate this to expected bound on this quantity which will turn out to be. So, you have through this and this relation you will end up with expected regret bound of exp 3 p.  So, one last remark I want to let us say there is one more algorithm that you have to implement in the book that we call as exp i x what that algorithm does is instead of getting alpha by k here it adds the gamma here explicitly in this that is the only difference. So, earlier what you are doing by adding gamma by k you are having an explicit exploration right you are forcing uniform exploration, but now by adding here you are not forcing that explicit information, but you are still enforcing that your p t i this denominator is at least gamma even this p t i is 0. By this you can see that I am not having an explicit exploration some kind of explicit exploration happens with this addition and when we will see in your assignment that the case we have specified this kind of algorithm actually performs better than your exp 3 p and exp 3 algorithm ok. So, that is what and I will you not mention any regret bound for this, but you understood what is the exp i x algorithm. So, for that you also need to give input gamma.


All right, how's everybody doing? All right, it's an honor to be here. In the next 10 minutes, Joe and I are gonna show you what the future of computing looks like. But first, I want everybody to just take a second and think about a computer and what comes to mind. I bet many of you were thinking of something like this, or maybe this, or maybe even this. Maybe some of the elder members of the audience were thinking of an abacus, or a TI-83 potentially. Either way, all of these computers are different, but they're similar in some ways. They all have the same basic components. The basic components of a computer are inputs, processing, storage, outputs, and the human. It's important for us to remember that the computer is worthless unless there's somebody to deliver the inputs and receive the outputs, right? And so we have to remember that the human is in the loop with the computer, and let's remember that for the rest of the presentation. Joe, over to you. Thanks. Yeah, so humans are already part of a closed loop with our devices. And today, the way the inputs and feedback come back to us are sort of limited by the technology that we have. We have a very conscious relationship with our computers, where through keyboards and mouse, we tell it exactly what we want, and it gives us back the information. More recently, there's a subconscious loop that's developed, where based on our habits and our dwell time and what we sort of interact with, the information is subtly changed, what's available through news feeds or other notifications. But still, what the computers today have access to is just the tip of the iceberg. The biosensing technology that OpenBCI has been developing for the last 10 years is going to fundamentally change what our computers have access to in order to optimize the loop that we're a part of. Connor's gonna talk about how that all started. Yeah, so back in around 2012, I became obsessed with this mission of decoding consciousness. I had suffered some concussions playing rugby with Joe in college. Members of my family and friends were suffering from severe mental health issues or spinal cord issues, and I felt that the way to solve these problems was to take the information from the brain, AKA brainwaves, and put that information into a computer. I thought that the brain was the seat of the soul, was the key to consciousness. And so we set on on this journey to build a wearable, to take brainwaves and cheaply put them into a computer so they could be expanded into other applications, robotics, art, entertainment, gaming. And this is what it turned out like. We ended up building the ultra cortex and the cytan, the biosensing amplifier. For the past 10 years, these have been OpenBCI's flagship products. They've been worked with in over 100 countries around the world. They've enabled low cost education, research and development, and even deep tech innovation in the laboratories of major consumer technology companies. But there's been one shortcoming, and we've learned this over the past 10 years, is that we built a one directional brain computer interface. We didn't build a practical brain computer interface because we didn't close the loop. We only provided the system with the ability to send information into the computer. What we learned is that to have a true brain computer interface, you need to close the loop, just like the computer. The brain needs both outputs and inputs. In addition, we learned that brain data by itself is actually quite boring. It needs context. In order to truly understand the mind, the brain is a very important part of the mind, but you have to listen to the body also. Things like your heart, your respiration, your movement, the sweat on your skin. Right now I'm sweating, and it's because I'm a little nervous. So all of these things matter, and they add context. Over the past 10 years, OpenBCI has been innovating nonstop. We've been working with members inside the company and outside the company, leveraging the power of the open source movement to maximize innovation and access to the technology. We used the knowledge that it needed to be a closed loop system and it needed to be multimodal, meaning lots of different types of sensors to work on a new type of product. It's called GALIA. So GALIA is a sensor fusion super tool. It's packed with sensors that can measure the user's heart, skin, muscles, eyes, and brain. And it couples that capability with audio and visual feedback or the ability to kind of close the loop by AR, VR, headsets, and high resolution audio. One really cool thing about GALIA is that it is not just a concept. We've actually been working with the system for the past few years. Our Alpha partners, there are only a few of them because these things are difficult to build, have been helping us do things like create hands-free control schemes, replacing the mouse and keyboard in the context of AR, VR, or even 2D screens. But on top of interaction, we're also interested in this more passive form of brain computer interfacing, which is looking at quantifying the qualitative. How do we take these squiggly lines coming out of a computer and turn them into things like emotions, intentions, your digital twin? And so with that, I'm really excited that we're about to unveil what we've been working on for the last five years. This is the product, the GALIA beta system that we're gonna be shipping to customers in Q2 of next year. So Joe, take it away. Yeah, here it is. So this is the latest form of our headset that we've been building. This is what's gonna go out to customers starting in Q2 2024. And we're very excited by what these early adopters are looking to accomplish with this system. These are enterprise teams focused in entertainment, gaming, and training situations that are looking to build adaptive experiences that can change based on the real-time reactions of the user's brain and body. Product development and human factors research teams in the automotive and aviation industry that are looking to do product research on products that haven't even been built yet. They're using VR and they want to augment their surveys with quantitative data from sensors. And it's also, in the healthcare space, there are people looking to develop new biomarkers for disease and analyze the effectiveness of treatments. Inside of OpenBCI, we've been using GALIA for our own assistive technology projects that Connor can talk a little more about. In 2019, a legendary neurohacker by the name of Christian Byerlane reached out to me and he asked if we could help him realize a vision of flying a drone. This is something he'd never been able to do. And at first, I was very skeptical. I was, you know, I didn't know if we'd be able to do it, but we started listening to his body and we tapped him into his body and we realized that he had residual intention. These kind of little buttons riddled around his body that he didn't even know he had access to. So we connected electrodes to them. We amplified them. We built a control scheme for him that allowed him to learn how to use his muscles for the first time. We then translated that into some square bar graphs and kind of circle visualizers and then mapped that system into a two-dimensional joystick. At that point, we multiplexed it and essentially built a joystick system, two joysticks that he was able to use to fly a drone on the TED stage earlier this year. This was one of the most meaningful things that I've ever been a part of in my entire career. But it took $100,000 of equipment, six months of focused R&D and system integration, and it doesn't need to cost that much. And that's really our goal for the next 10 years is to take everything that we did with Christian and everything that we're building with Gallia and bring it into one system. This is our other announcement, is that we are going to be working on Gallia Unlimited for the next however long it takes to make it. So Gallia is everything that you see there put onto the body. Still gives me goosebumps, and I've watched that video about 200 times. So Gallia Unlimited, let's tear it down. This was one of the first drawings that we did to try and kind of concept it. I'm going to start with layer seven. Layer seven is what we are dubbing the neck tech at this point, which is where a lot of the hot and heavy parts of the PC are going to be moving onto the body. The top layers are an exploded version of the headset starting with the layer in the front, which is an aesthetics visor layer. Then there's a modular optics layer where you can swap in different optical systems for different scenarios. Layer three is a kind of inside out tracking and eye tracking system for both environmental and eye information, and layer four physiosensors for the face. So yeah, this is a cool ghost shell wire frame of the concept system at this point. And now I'll just jump through these guys real, wait, let's go back to this one. This one's cool. Everybody loves this one of these, right? All right, jumping through. So these are those layers that I was describing, but in higher resolution. So I'm just going to click through these for time. Some ear sensors and here's an exploded. So Joe, what does this help? What does this all accomplish though? Like I said, let's go back to that loop. We know from our customers today that the latency and the synchronization of all of these different sensors is a major challenge. By bringing this all into one system and putting it on the body, we are reducing the latency and speeding up this feedback loop. When that loop reaches the point where it's happening faster than our ability to perceive it, that we can't necessarily keep track of the ways that all of these sensors and inputs are adjusting in real time, it's going to unlock an entirely new form of human-computer interaction that feels like a natural extension of our bodies. And this is gonna have a lot of unforeseen potential, but it's also gonna have a lot of risks. In order to realize the immense positive potential of neuro technology, we need to change the current unhealthy status quo that we have with our personal data and our personal devices. We're not in control of that today. We believe that users need to be firmly in control of all of their data and given the keys to a mental vault. OpenBCI is committed to prioritizing users as the number one stakeholder above all others, including ourselves as the manufacturers. We think this is a key design constraint for any neuro technology company trying to put these devices into the world in a positive way. And it's something that, in order to make sure that our devices are really our trusted confidants, instead of digital saboteurs, we need to change the status quo. At OpenBCI, we have had a vision that has not changed, but only become clear to design the next great technology, turning point in human evolution, and finally merge with our greatest creation. I don't believe that the 21st century will be remembered as the century of artificial intelligence, but rather I believe it's going to be immortalized as the golden era of human intelligence. At OpenBCI, we are building the first computer that leverages all of the vast and ever expanding capabilities of AI with a contained and controlled objective to put you in control of your mental vault, and protect your mental health, safety, and freedom to flourish.  And in every way, this computer will behave like it's part of your body, brain, and mind. So with a final announcement, as of today, December 1st, we are launching our series A, and so if you are interested in helping us accomplish this mission to build the operating system of mine managed by you and your mental vault, please come find us after the talk, and we would love to chat with you. Thank you, thank you.


Hello and welcome to the session. I am Asha and I am going to help you with the following question that says, find equation of the line passing through the point two two and cutting off intercepts on the axis whose sum is nine. So let's begin with the solution, the intercept form of a line upon A plus Y upon B is equal to one.  So we are given that A plus B is equal to nine. Let this be equation number one. Now the line passes through the point two two therefore on substituting the values of X and Y in the intercept form of the line we have two upon A plus two upon B is equal to one or we have two B plus two A is equal to AB. So this is the sign equation. Now we will solve equation one and two to get the values of A and B. Now from equation one and two have two can be written as taking two common from the left hand side here A plus B is equal to AB and A plus B is equal to nine. So we have two into nine is equal to AB. So this implies AB is equal to 18. And also A plus B is equal to nine. So substituting the value of A which is 18 upon B in this equation it can further be written as 18 upon B plus B is equal to nine or we have B square minus nine P plus 18 is equal to zero. Now splitting the middle term it can be written as B square minus six P minus three B plus 18 is equal to zero. Now taking B common from the first two terms and minus three common from the last two terms it can further be written as B into B minus six minus three times of B minus six is equal to zero or we have B minus six into B minus three is equal to zero. Now as we know if the product of two numbers is equal to zero then at least one of them is zero. So this implies either B minus six is equal to zero or B is equal to three. So this implies B is equal to six or three. And substituting the values of B that is six and three in this equation we will get the values of A three or six. So this implies if B is equal to six then A is equal to three and if B is equal to three then A is equal to six. Now intercept form upon A plus Y upon B is equal to one. So first let us consider the case when A is equal to three and B is equal to six. So we have X upon three plus Y upon six is equal to one or we have taking this x-axis we have two X plus Y is equal to one or two X plus Y is equal to six. So this is the first equation and now let us consider A to be six and B is equal to three. An equation of the line is X upon six plus Y upon three is equal to one or we have six LCM X plus two Y is equal to one or we have X plus two Y is equal to six. So this is the second equation of the line and thus our answer is the equation of the lines are two X plus Y minus six is equal to zero and X plus two Y minus six is equal to zero. So this completes the session take care and have a good day.


This video will awaken you to the truth of the narcissist When you first met the narcissist They seemed so interested in you They wanted to learn more about you. You felt as though you were developing a relationship with them You felt as though you were going to build something significant or meaningful with them And you were willing to invest whatever it took To ensure that the relationship would have a stable foundation One that could not be destroyed The problem is While you thought that you were building something together You were actually building something on your own and the amazing person That you thought you had met in the beginning Was nothing more than a fabrication A false appearance or impression Which was designed to lure you into their world When the narcissist first met you They were grooming you They were preparing or training you for the purpose of being their source of supply Once they began to establish that you held something of value or significance That is when they knew that you were a suitable target To lock you into the relationship They knew that they had to give you a mirage of what you might like to see Of what you might desire or expect from a relationship partner But it was nothing more than an illusion It was nothing more than an unrealistic hope or wish that cannot be achieved The narcissist was not being truthful about who they were or what they were about The qualities traits likes and interests that they displayed to you Were nothing more than a fabrication A false appearance or impression That they created Because they knew that was what you wanted to see They created a fake world full of lies Full of false appearances or impressions Which they could then use to manipulate you and extract whatever they needed from you in that moment When the narcissist first met you They saw a gold mine They saw a source of wealth valuable information or resources They saw something that produces a lot of what they desire When they try to lure you into their fake world They are setting up a campsite They begin by studying you They begin by devoting their time and attention to gain in knowledge about you They conduct a detailed investigation and analysis and Then they set up their campsite a place where they can excavate a Place where they can reveal and then extract all of the valuable things that you have to offer and This is the only reason why they got involved with you.  The reason is because they have no other choice They are trying to survive And they are deficient They don't have enough They are also inadequate They are insufficient for the purpose of surviving They cannot survive on their own Which is why from the moment they meet you And recognise your value They will try to set up their campsites around you Where they can then extract the resources that they need to survive They act as though they are powerful And they have an exaggerated sense of their own importance or abilities When all of their power and resources comes from you They trick you into giving it to them And then act as though they are superior to you It makes no sense from a logical standpoint But narcissists are very emotional creatures They consistently feel emotions like shame, fear and guilt Which you will also feel if you are around them Because they don't want to deal with reality They don't want to deal with the truth So they project these emotions onto you If you are involved with a narcissist And you feel a negative emotion Whatever you are feeling It's because that is what the narcissist wants you to feel It is not because of any negativity that you have produced Rather it is the negativity that has been transferred from them You feel negative because they have taken something from you Your happiness and contentment Your wealth, informational resources And when they take this from you It begins to make them feel a little more positive It's all energy But regardless of what or how much they take from you They will never be satisfied Narcissists are overwhelmingly negative They can never be happy no matter what they have And that is why they always have to trick people into giving something to them Negative people have a negative amount They are deficient in something While people who are positive have an abundance They have plenty to give When the narcissist is acting negative towards you It is because they feel as though they are inadequate or deficient in something The narcissist recognises your value But they know that they don't have anything to offer you That is why they created the false self That is why they have to lure you into their fake world They see you as a gold mine And from the moment they meet you They spend all of their time and effort doing everything they can To extract this gold from you They don't want to live a reality They don't want to accept the truth of what they are Or what they are doing to you And that is why they use tactics like denial, projection, blame shifting and gaslighting They are negative because they are inadequate or deficient in something They only acted positive in the beginning Because they were trying to trick you into giving something of value to them Narcissists are empty, soulless beings That have nothing to give or offer to you It's all a lie It's all a fabrication They have nothing more to display than an illusion A false appearance or impression And as long as you are willing to be entertained by them They will put on a good show But it isn't real It isn't grounded in reality And they are only doing it to take something from you Thank you for watching I hope this video resonated with you Please like, comment, share and subscribe Click the bell icon to receive notifications for my future videos If you are lighter than me My paypal link is in the video description Coaching and inquiries you can email me at www.coaching.com Thank you for watching and I'll talk to you soon


The Colgate Palm Olive Peat Company makers of luster cream shampoo and Colgate dental cream bring you our Miss Brooks starring Eve Arden And we should like to open our show with greetings and best wishes from Colgate Palm Olive Peat for a gloriously merry Christmas And now our Miss Brooks It's time once again for another comedy episode of Our Miss Brooks under the direction of Al Lewis Well, many of us are spending this Christmas Eve with our families and friends But our Miss Brooks who teaches English at Madison High School isn't quite so fortunate No, my family was too far away to visit and it seems my friends had other plans But I made up my mind not to brood about it and I was trimming a rather tiny tree in our living room When Mrs. Davis, my landlady, joined me That's quite a nice Christmas tree, Connie It isn't really a Christmas tree, Mrs. Davis, it's called a friendship tree You see, I trim it by putting all my greeting cards on the branches with strips of cellophane tape Looks nice, doesn't it? Yes, it does. You certainly received some pretty cards this year And the sentiments are so lovely Look at this one I got from my principal Mr. Conklin, what does it say, dear? It's very heartwarming, Mrs. Davis It says, to Miss Brooks, may the coming year bring you much more efficiency in your work Signed, oh Conklin Oh, I can hardly believe it's Christmas time again What happy memories I have of the earlier Christmases There was one I'll never forget I was just eight years old and when I tiptoed into the living room There was my father standing with a tree The minute he saw me, his eyes crinkled up and he started to laugh So that his big white beard and its huge punch just shook with glee Your father was made up of Santa Claus? No, he always looked that way But you get back to the present, Connie I'd love to stay here and celebrate Christmas Eve with you But I promised my sister Angela I'd come over to her place You remember, Angela, the absent-minded one Oh, certainly, Mrs. Davis She always got a big thrill out of the holidays too Even when we were girls Of course, the poor dear could never remember when it was actually Christmas And one Christmas day she did the funniest thing What was that, Mrs. Davis? What's what, dear? What did Angela do? Angela Your sister My sister The absent-minded one What did she do? Well, I haven't spoken to Angela in some time What has she been up to? I wish I knew Maybe I can refresh your memory Christmas morning, Angela did the funniest thing Christmas morning isn't until tomorrow, Connie You must be confused Well, don't worry about it I only get these spells once in a while Well, you shouldn't let it go, Connie If you don't mind my offering a little advice I'd like to suggest that you train your mind to concentrate more I'll do it, Mrs. Davis Now then, I've developed a little scheme Which works wonders for me Supposing you have trouble remembering Where you put things around the house Well, you just keep repeating the location to yourself For the sort of rhythm For example, I just chant to myself The mustard's in the closet The bread is in the box The mustard's in the closet The bread is in the box Now isn't that simple? Mustard's in the closet Bread That's wonderful, Mrs. Davis If anybody wants a mustard sandwich, you're really ready Yes Now, before I do anything else I want to invite you to join me tonight Join you? Yes, dear I'm going over to... Angela's house Oh, yes, that's right Oh, she's so cute with that little absent mind of hers Why, sometimes she forgets what she was talking about Right in the middle of a... Oh, dear me, I hope there's enough milk for the cat Well, I'm sure if we... But then maybe someday Or if it doesn't seem to And that's why I can't join you tonight But thanks anyway, Mrs. Davis I'll just spend a quiet evening at home here But how about Mr. Boynton? Don't tell me he was too shy To ask you for a date on Christmas Eve Why do you think there's mistletoe on all four walls? No, Mr. Boynton asked me all right But then he canceled yesterday Said he's going upstate to visit his folks for a couple of days But don't worry about me, Mrs. Davis I'll have a gay time I'll listen to the radio, read And from this window I can see our neighbor's television antenna But what about the little gifts you've got for Walter Denton And Mr. and Mrs. Conklin and Harriet When are you going to deliver them? They told me not to bother They said we'd exchange on the 26th The 26th? But I don't think the day after Christmas Is the time to exchange gifts You don't You should see the department stores What's that, Mrs. Davis? Oh, it's Minerva Where are you, dear? Oh, she's over by the tree Here over, I'm Minerva Isn't it the strangest thing How she bites at the pine needles? I guess the rosin in them appeals to her I swear she likes the taste of it I guess to her it's like a Tom and Jerry Or rather a Minnie and a Mickey Come here, Minerva We might as well get friendly We're going to spend the evening together Well, I'll be running along now, dear I hope you won't feel too lonely I'll be fine, Mrs. Davis After all, I do have an imagination I'll hang up my stocking in a little while Then when I'm pretending I'm asleep I'll sneak in and fill it Before you know it, it'll be midnight Midnight of Christmas Eve I can just picture it A short, thin man in a black suit Come sliding down the chimney with an empty bag St. Penelus, the schoolteacher, Santa Claus Well, at least you're not bitter Now, Connie, about my sister... Angela Oh, thank you, dear About my sister Angela Yes? Good night, Dorothy Good night, Bernice Oh, stop drinking those pine needles, Minerva Come over here That's a good kitty Now, I'll just settle down and Mrs. Davis is rocker And we'll have ourselves a nice, quiet rock I've got to exercise more My bones are rusting Oh, it's the rocker It's kind of soothing at that You seem contented enough, Minerva Because the night before Christmas And all through the house Not a creature was stirring Not even a mouse Sorry, Minerva I didn't mean to catch you Gosh, I'm sleepy Now, who can that be? Expecting anyone, Minerva? That's funny, nobody's here I'm here Where? Oh, leaning on my knee What can I do for you? I'm a salesman But I don't believe in giving any sales talk or sob stories All I do is tell you what I'm selling And if you want to buy, okay If not, okay Okay, what are you selling? Well, it's Christmas Eve I'm just a small urchin A little on the underprivileged side I'm trying to make a few dollars to get some wood To heat our tiny apartment So while she's singing to my three sick sisters My mother's lips don't turn blue That's what I like No sob stories They're selling handkerchiefs I'll take six No, ma'am I'm selling Christmas trees They're only a dollar a piece Oh, I've already got a tree It'll make it 50 cents But I don't need to be... How about a quarter? Look, little boy I can arrange payments Please take one, ma'am These aren't ordinary trees, you know They're magic Magic? Yes, ma'am You'd be surprised what miracles will happen Well, a quarter isn't too much to pay for a miracle It's 50 cents I thought you said 25 That's when you saw her tupper to sell Oh, well, before I melt down to my coal buttons And the stovepipe hat, here's 50 cents You won't be sorry, ma'am Here's a little tree Say, it's kind of cute at that Would you like to come in and help me set it up? No, I can't I gotta get right home My sitter's been alone long enough Sitter? What about your mother and the firewood? That's just a routine My folks are attending a dinner The other bank presidents are giving for father With a pitch you've got You'll have your own bank by the time you're 12 Thanks a lot Good night, lady Merry Christmas Same to you, you little underprivileged millionaire I'll put this tree over here Maybe we can find some extra trimmings for it in the morning Minerva, will you stop gnawing on those pine needles? I wish I knew what made them so appetizing to her Meow Now you come here and let those things alone There we are Well, I guess I'm not the only one that's spending Christmas Eve alone Without family or friends But who can tell? Maybe Santa Claus has something up his big red sleeve That I don't even know about yet Of course, I do have a squeaky rocker and Minerva Jingle bells, jingle bells And merry stuff like that Oh, what fun it is to rock with a big fat drunken cat I had in the living room Christmas Eve With Minerva the cat on my lap I couldn't help noticing that the tree Which I'd bought from that wealthy urchin Had a rather peculiar luminosity Although there wasn't any artificial illumination It seemed to glow from deep down in its branches As I rocked back and forth I started to get very drowsy The little boy said this tree was magic, Minerva Meow I don't believe it either Still, it is Christmas Eve So very strange things have happened on Christmas Eve What's that? Oh, I must have been dozing Coming Well, it's Walter Denton Come in, Walter No, use no way Gracias Into the living room, Walter Thanks, Miss Brooks Here, I brought you this little gift to put under your tree Oh, that was very thoughtful, Walter Put it under this tree over here Okay Say, you got two trees, haven't you? Yes, one for Minerva and one for me Meow Don't pay any attention to her She's pine needle happy Well, Miss Brooks, as you know I was supposed to spend the evening Nestled snugly in the tight little confines Of my own small immediate family circle For heaven's sakes come out of there You're giving me claustrophobia But I went to my father and mother And crowed their permission Wait a minute, Walter You crowed their permission? Yeah Crave, craven, crow, isn't it? Of course not Crave, crave Let's see Crave, craven After you crowed their permission My presents for a long enough while For me to deliver to you, Miss Brooks The little token of my esteem and affection Which is now ensconcing under the tree Walter, are you still in my English class? Sure, Miss Brooks I'd better bone up a little One of us is going to flunk this term What I'd like to say, Miss Brooks Is something that I've wanted to say for a long time Yes, Walter It's a little on the sentimental side Perhaps for a so-called Hep high school boy to be telling the teacher But it's sincere, Miss Brooks I'm sure it is It's something I feel deep down inside of me, Miss Brooks From whence so many of one's Warmer emotion stem That's whence they stem from, all right Of course, even if it does seem Over sentimental or even downright sticky Christmas Eve seems to be the time You can say things like this And not sound over sentimental or sticky Christmas Eve is the time to say them I just hope I hear them by New Year's Eve What I want you to know, Miss Brooks Is that I'm grateful For what? For my association with you During the past semester at Madison High School Well, thank you, Walter I've tried to be a capable teacher Oh, your teaching was nothing I don't mean scholastically As a teacher, you were very adequate I mean personally The interest you took in me and my problems For that I could never thank you If I lived to be a hundred Of course, you'd be gone a long time by then I owe Noel to you too You don't know what it's meant to me To have your ear whenever I needed it It was nothing really, I have another one Especially about girls Gosh, remember how silly I used to act about girls Every time when I've looked at me I giggled like a kid And then overnight I matured I met the one woman who mattered Harriet Conklin She certainly made something out of you, Walter I don't know what, but something And you saw me through the difficult Transition period of thatimour as well While Harriet and I were adjusting to one another It was wonderful to be able to come to you For advice, Miss Brooks It isn't every boy who has such an interest Taken in him by some intelligent, elderly person Give me back my ear, I can't hear you Not that you're ancient or anything Gosh, I've seen girls who don't look as good as you do Girls? What do you think I am?  Yes, Walter, I was We were going for a wheelchair ride together But he had to visit his folks upstate His folks?  Under the tree on your right It isn't much, just a remembrance Gee, I almost forgot I can't open it yet Why not? Oh, you mean you want to put it under your tree at home And open it with your family Not exactly, but I'll get it later, Miss Brooks There they are now, I'll answer it There, who are now? Come on in We should have stayed home Christmas Eve Besides, it's freezing out Now, Osgood, don't be so grouchy Hello, Miss Brooks, Merry Christmas Why, it's Mr. and Mrs. Conklin and Harriet How are you all? I'm cold It's too bad Come here, Minerva Rub up against Mr. Conklin Meow What's that?  She's not that hungry I don't like cats Why doesn't she go chase a mouse or something? You forget, Mr. Conklin This is Christmas Eve There isn't one stirring Say, Harriet, yes, Walter? There's a lot of mistletoe around this room I know, it's real pretty Osgood, notice all the mistletoe in this room What? Oh, that green stuff More often than not, it makes me sneeze Oh, come on, Osgood Let's see if it does Oh, now Martha, don't embarrass me I don't like that It doesn't make you sneeze Does it, Harriet? I'm willing to find out Here's a nice wreath of it on this wall Yeah Well, here we are If it's all right with Harriet, it's all right with us Come on, Walter We're getting our shoes to lead Harriet Isn't that cute, Osgood? Oh, come here, dear How about one for your faithful old wife?  Frankly, Mr. Conklin, I haven't had much chance to work on anything Haven't had much of a chance, but you've been away from school all week Your vacation started last Monday I know, Mr. Conklin, and that's what I took the week as I mean, a vacation is something you go on when you get the opportunity to You don't work on it or during it unless, even though I didn't actually go anywhere when my vacation came along, I went on it or was on one, usually And you wanted to be the head of the English department These are as good as this is no time to talk of school affairs We're here to spend part of our holiday with Miss Brooks It was very nice of you to think about me, Mrs. Conklin It was nice of all of you I want to wear a Walter and Harriet Denton, get my daughter away from that mistletoe at once But Mr. Conklin, Harriet isn't allergic to mistletoe No, but I'm allergic to you Harriet's almost irresistible sometimes especially alongside older women like Mrs. Conklin and Miss Brooks Sounds like the bell, I'll get it Boynton, come in Thanks, Miss Brooks But I thought you were going upstate to see your folks I was, but they sent me a wire that they wanted to come here for about a week or so they'll arrive in the morning so I thought I'd drop this little gift off for you tonight Oh, but you shouldn't have, where is it? Let's just put it under the tree in the living room Look who's here, everybody Well, it's Mr. Boynton Hi there, Mr. B This is nice Hello, Boynton Pretty cold out, isn't it? Hello, folks This is beginning to get more like Christmas Eve every minute Sit down, Mr. Boynton I'm certainly glad your folks decided to visit you instead of vice versa So am I There's a particularly good reason why I'm glad There is? Yes, it gives me a chance to see how my guinea pigs are affected by this cold snap So far they haven't reacted at all What do you expect them to do? Blow on their paws? Miss Brooks, have you pointed out the mistletoe to Mr. Boynton? Why don't you stop that nonsense, Martha? It isn't nonsense Mr. Boynton, look at the mistletoe Mistletoe? Oh, oh yes, a very interesting example of the flora found in various areas throughout the globe An evergreen parasitic shrub It is indigenous to the regions where apple trees and oaks are bound Now that the lecture is over, may we ask questions? Certainly, Miss Brooks Wanna stand under it? Stand under it? Well, you see, because of certain characteristics in its makeup An allergy is sometimes aggravated by its presence I'll take a chance if you will Come on, Mr. Boynton Yeah, come on, Mr. Boynton Just bring him over to this wall here Well, I'll get under it if you like Well, don't just stand there Can't you see Miss Brooks is cooking? Well, don't fuss for me, I couldn't eat a thing Not standing under the mistletoe signifies? Well, I know what it signifies to most people But to me, it's just... Adjum! Well, there goes 85 cents worth of mistletoe I know what let's do Let's open up the presents right now A splendid suggestion, Walter Shouldn't we wait until just before we leave Might be less embarrassing that way Well, if you want to open them now Gally, this one tree is pretty crowded I'll put some of these packages under this little one over here Look out, Walter, you're bumping into one of the branches Look out! I'm just feeling when I touch that branch What kind of a feeling, Walter? Well, you're Harriet Conklin, aren't you? Well, sure I'm Harriet Conklin Walter, what's the matter with you?  If you want me to stay interested in you You've got to be more alluring, youthful, glamorous Feminine in that real feline Brooks way Walter, have you been drinking pine needles, too? Look at that tree, it seems to be glowing What do you mean, glowing? It's just the reflection from the street lights This party's giving me the me-me Holidays, indeed Here, I'll just move the tree where it won't glisten in our eyes Here we go Ho, ho, ho! Merry Christmas Ho, ho! Merry Christmas Of course I'm Mr. Conklin Happy-go-lucky, fun-loving, gag-a-minute Osgood Gag-a-minute Osgood? Sometimes I've wanted to Miss Brooks, is that really you standing there? I think so, Mr. Conklin, why do you ask?  What are you going to do, Mr. Boynton? Just call me Phil, Connie And this is what I'm going to do Wonderful, beautiful dream Mr. Boynton, where are you? That's real enough, I'll be right there Oh, sorry, Minerva, I didn't mean to drop you Mr. Boynton, but you all just left I mean, come in We thought it would be nice if we spent our Christmas Eve together, Miss Brooks Yes, and we brought a few little gifts over for you I'll just put them under this tree here Yes, do that, Walter Aren't you going to ask me why I didn't go upstate, Miss Brooks? I know why, Mr. Boynton, your folks are coming down to see you How did you know that? I just got the telegram Don't let's get too carried away with the holidays We've got to prepare for a hard school season ahead, Miss Brooks Oh, let's not talk about school affairs now, Osgood Walter, look at the mistletoe Yeah, look at it Now, just a minute, before we go through all that again Would you please touch the tree, Mr. Boynton? The one on the left with the... My, it's gone There's only one tree Miss Brooks, are you all right? Of course I'm all right Could I have dreamt that part, too? Mr. Boynton, would you do me a favor, please? Of course, Miss Brooks, what is it? Would you touch the Christmas tree? Touch it, but I... Please, it's important Well, all right There Nothing happened What did you expect would happen? A miracle Excuse me, I'll be right back I had a lurchin' and I'm selling magic Christmas trees But you just came here... Please buy one, lady, they only cost 50 cents a piece 50 cents? That's right Here's two dollars, give me four of them This is Eve Arden From the bottom of my heart To you in the audience To you in every home, on every road In every city and town In the busy places and in the lonely places Oh, a very merry Christmas to each of you With our sponsor, the Colgate Palm Olive Pete Company Who make luster cream shampoo And Colgate dental cream All of us here in the studio Have gathered to wish all of you Throughout our beautiful and bountiful land The most joyous of Christmases And may these words ring round the world And sink deep in the heart of everyone Peace on earth, goodwill towards men Merry, merry Christmas, everyone Our Mystery Liberally's Trinket of Laughs Listen to Mystery Mrs. Norrie Tune in Tuesday evening Over most of these same stations And be with us again next week At the same time for another comedy episode Of Our Miss Brooks, Bob LeMond Speaking Stay tuned now for Jack Benny This is CBS, the Columbia Broadcasting System


The two's complement format is the method that we currently use for representing integers in computers. It's harder to read and write than the sign-in magnitude format, but it actually makes our arithmetic work out nicely. We won't have to worry about special cases between positive numbers and negative numbers. We can actually just do our arithmetic exactly the way we would expect, and things just happen to work out. But it does end up being a lot harder to read and write than we might like. Our positive numbers are still really easy. You just write down the positive number using however many bits you've got. Again, it will have lots of zeroes on the left-hand side, and we'll use the most significant bit as an implicit sign bit. Again, we won't specifically set this to be a sign bit, but it will be zero if we have a positive number and one if we have a negative number. So if we do want to represent a negative number, we would start by converting the number to binary, write that in binary using however many bits we've got, say 32, and then we would apply the two's complement operation to that number. The two's complement operation will allow us to convert a number between positive and negative representations, and what it will have us do is flip all of the bits in our number, so we'll change all of our zeroes to ones, all of our ones to zeros, and then go back and add one more to this number. Again, it's a little odd and convoluted, but it does make the arithmetic work out. And when our focus in the hardware is on processing the numbers, that's what we're really interested in. This method allows us to do our computation much faster than we otherwise could.


There's a couple more people filtering in. We'll just let them come in. I quite cunningly only have about 30 minutes of content, so we've got a bit of space for slippage. So my talks on securing the public cloud. OpenStack is an amazing tool, an amazing framework for building up cloud infrastructure. There's a lot of problems in terms of trying to leverage that for a public cloud, because a lot of the different assumptions that have been made when OpenStack was built and the initial designs. So I talk to a lot of that and go through. So my name's Rob Clark. I'm a security architect for HP Cloud. I've been with HP Cloud for about two years, so right up from the decision we started to take on OpenStack and build that up into a proper product. My background is in secure design, architecture, and cryptography. I was one of the founding members, along with Brian from Nebula and the OpenStack security group, and also one of the founding members of the OpenStack vulnerability management team. If you find a vulnerability in OpenStack, blog about it if you really want to, but what would be nice is if you sent it to VMT so we could all patch our stuff before it becomes live. So say come for the security, stay for the shiny. Today we're gonna give away a HP Envy super thin, super awesome laptop. I can't win it, unfortunately, because I'm an HP employee, other HP employees here can't take part, unfortunately. But yeah, we have it here. So those of you that can manage another 28 minutes of me will get the chance to be rewarded. Okay, so how many people here are responsible in some measure for the security of their OpenStack involvement? Cool. So that's about two thirds, maybe three quarters. So you should have some interesting stuff here. The rest of you are probably interested in security or in the wrong room. Some of this stuff will probably scare you a little bit. Right, so here's an amazing graph that tells you nothing, but what it actually describes, going from the left side is where your private clouds are. As you move across to the right, the threat and attack surface of your cloud deployment increases. So somewhere in the middle, you have clouds that are set up to do web-facing operations, clouds that have interactions with different other clouds or different interfaces. And then on the right, you have public cloud, which is an interesting place to work right now. This is about where the controls in OpenStack get you too. OpenStack gives you a certain level of preparedness, but it assumes a lot of other controls are in place. It assumes a deployment in a reasonably safe and non-hostile place. There are a lot of assumptions and a lot of bits of the design that need to be changed or augmented. So what do you have in the private cloud? In the private cloud, you know who your users are.   You can give them frameworks. They understand who they're working for and what they're doing. Very, very different to having customers. Networks in which clouds are typically deployed are already secured. There are well-understood ways of doing this. Clouds are normally deployed by large companies with global real estates. They have policies, enforcement. They have appliances, application, gateways, they have all this stuff. They have all this stuff that protects all of their other network assets. And in that situation, it's not so much of a headache to just pop up OpenStack and a few wraps inside of this nice secure area. You can't do so much of that in the public cloud and I'll go through why in a moment. You have policies. Your company understands what they want this cloud to be used for. Some places will have multiple clouds to service different business needs. These are easily enforced and checked. Private clouds can inspect their own data. One of the biggest concerns people have with a public cloud is how safe their data is. They don't want rack space. They don't want HP going through and trawling through all of their files, inspecting them, understanding them syntactically. The reason is because they like to have a measure of security and privacy, but what do malware detection systems do? What do antiviruses do? They go through and do all this stuff. You can do that in the private cloud with no problem. You can snoop, manage, use a traffic. You have these well-defined border controls that we've already spoken about. You can have them throughout your data center to detect and control stranger anomalous traffic. You have very simple ways and very stringent rules about what can and can't go across your network. You understand and protect for your business needs. So in the private cloud, you really have a lot of control. Not all this control is necessarily built into OpenStack, but you have the ability to apply other compensating and preventative controls because of the nature of the business you're doing. You can, by default, restrict what people do. Okay, if they don't like it, then it will get bubbled up through your management chain and a policy decision will be made. But that's the way it works. So we've just been over. Users are accountable. There are established routes for responsibility and attribution of actions. Define network access controls and corporate policies constrain usage. Users can be held to specific use cases. If you fill out a use case or something for spinning up 10 instances on the cloud, it may say this is being used as an FTP server. The security networking guys will bring up your FTP server policy and apply it for that group of nodes. If that starts spitting out SMTP or something else, you know you've got a problem. There are many options for user control and discipline. So this comes from everything, from training, understanding, awareness to discipline. So making people realize that they are being constrained in what they can do. This isn't a free resource to your company. You're still having people consume resources that others could, and you need to make sure they're used correctly. IP reputation protected by clearly defined border policies. So you have an IP block given to your company. Things like mailability of email, spam filters, and a few other things, take this into consideration when making the decision about what to do about data that's come from your network. You need to be worried about that. And you have established abuse handling mechanisms, both internal and external. And the public cloud, we can't make many assertions about what people are gonna do with our cloud. In fact, it's a really bad idea to do that. We don't know what the next innovation, web 5.6 or whatever the next web innovation is gonna be. We don't know how this data's gonna flow. We can't detect anomalous stuff in the way you would like. We operate at a huge scale. We have big pipes. We're constantly expanding in terms of capacity and network support. This makes it very difficult to take normal static boundary controls, either boundaries of internal parts of your network or right out on your edge and apply them to a public cloud. We have a very robust set of fraud business logic components. But there's really no way of escaping the fact that new identities are cheap and easily obtained. And the best fraud systems in the world still have to be told or have mechanisms for detecting malicious use or the fact that credentials have been lost. So if we have certain malicious actors who may want to come onto our users, come onto our service, use it for six hours to do whatever dastardly deed they want and then leave. And if they pick up the right set of credentials and things, that's really difficult stuff to control. We have a global user base across any and every service. We see very, very different packet shapes go across our networks. We have no idea what the next big thing will be. And detecting abuse is really, really hard. So I'll go into that a little bit more later. In the private cloud, you have clearly defined policies. I'm highlighting this again because it's really important. You have clearly defined policies. You can spot very easily when something steps outside of that when it breaches the norm. When you have only a vague idea of what's going down your pipes, working out which one of them is the right one and which one is the wrong is tricky. So in the public cloud, we can't make very many assertions. Our users are largely unaccountable.  You can ask them to politely leave your service, but they'll just go and use another one. That's not a preventative control where the public are concerned. You have open network requirements. We cannot set and arbitrarily make decisions about what data users can put across our network. Users have complete control of what they use their instances for almost over all behavior types and profiles are presented. Identities are cheap. Few data controls we can realistically apply at the edge. A constant battle to identify and control abuse of users. So here we go on to some specific use cases. In a private cloud, you know what data is gonna be stored. You have the ability, if you choose to, to apply analysis to that data to detect malware, to detect. If you have a multi-classification hierarchy in your data system, you can use that to pick up documents that are tagged and in the wrong stores.  And they're okay with it because they work for you. They share the data with you. You all have the same level of privilege. We have a whole bunch of terms of service, but they're largely permissive in terms of what you can do because they have to be because we can't predict what our service is gonna be used for. Privacy is a major concern for customers so we can't go sneaking around. We can't go looking in their files. Inspecting data is very difficult. There's very good cases and legitimate uses for encryption of files and we see this. One of our big partners, Panzora, they work with Dreamhost and they have an appliance that you have at multiple sites and it presents you with a sort of a global file store. And that encrypts everything before it puts it on the cloud and our cloud backs up the Panzora appliance. But everything that's stored in our cloud from them is encrypted and we as HP can't go in and look at it. Nova has a whole bunch of similar problems. There's a whole bunch of interesting things you can do to try and control what people do with Nova. So uses controlled by policy. Internal deployment options mean that you can configure who can deploy what sorts of image. But one of the really interesting things here is that you can force your users to deploy certain images of certain types with certain controls. So all of your endpoint security. So these can have encryption on them. Perhaps they can have IDS, they can have antivirus, they can have all the things that your IT company tells you you need to have in terms of endpoint security. And you can have this all on their VMs and it'll make them slower, but the corpora has made a decision that they accept the cost of that to bring it out. We can't do any of that. We have people spinning up all sorts of stuff, installing all sorts of stuff because they see it as a disposable resource. It's out there, it's on the public cloud. Most of the time they're spinning up things can be transient in nature just to test something. So we get insecure VMs popping up all the time. And some of them do get abused and get into problems. We have constantly expanding capacity, especially in networking and other areas, which makes it very difficult to use common sort of static controls. The cloud is designed there to deal with anomalous behavior. So we can't sit in a room and say, well we are going to have exactly this much usage over this much period of time. We have to plan big, we have to plan and do things at scale. So here's some abuse that we see people trying to do with HP Cloud. So we have to get people storing things that our terms of service say we don't want. Okay, might not necessarily be illegal, but take it somewhere else. We have copyright stuff, sometimes people try and pipe copyright stuff on the cloud. Okay, that's not new, that happens everywhere. We need ways of dealing it, dealing with it and detecting it. Exploit payloads are a really interesting thing to have. So if your browser gets an exploit, normally that exploit is a shim exploit, it's very small, it's slipped past an antivirus, could do things. The first thing that does is it goes and downloads a big lump of data to explain what it should do, whether it's an executable or the rest of it. If you were to combine Swift with CDN for doing exploit delivery, then you would have a lightning fast delivery coming from very different network points around the world, distributing your exploits for you. That's cool. And of course these guys can encrypt it on desks, they can just use basic symmetric encryption. So even if you have antivirus, you won't be able to get it. File dumps, sometimes we can see this sort of behavior where a compromised machine will just be used, the cloud will be used for exfiltration of data for storage and later retrieval from a different place. It kind of makes sense. Nova can have all of these problems, plus a whole bunch more. The reason it can have all of those is because you can use Nova for storing files. You can spin up a VM, spin up some persistent storage, run NFS, FTP, whatever you want, and now you've got a file store. But we see a lot of malicious use going out from VMs, or we see a lot of attempted malicious use going out from VMs, putting port scans, SSH, brute force, SQL injection, denial of service stuff, and spam. And that's, you know, a lot of people don't have to deal with this or at least it gets caught with their borders. Private controls, you can have a rack. You can make a decision that at the top of that rack, you're gonna have IDS, you're gonna have an application firewall because you know that that rack is a cloud, but it's a cloud-serving SAP or serving something out. You know what sort of data's going in and out, you can build stuff for it. And that's a one-time cost because you're building something out for a purpose. If we were to do that in that way, there's a really big scale impact of that because we end up paying for the IDS twice. These IDS need to be fast and very performant because we don't get in the way of our users. So they're expensive. Now we have HP properties like Tipping Point and ArcSight and other technologies we'll talk about later, but they still have revenue representation that they need to have within the company and so it's not like we can just go and raid their warehouse and steal all their stuff. And even if we did, we'd avoid the first cost but not the second, which is that we have very high-density racks. If we have to take three or four of you out of that to put a security appliance in, that's cost us a whole bunch in compute or in storage that could be used to generate revenue for the company. We have some ways of dealing with some of this stuff. The reason that we're not releasing it right now, as is, is because it's very tactical. Some of it is not code that's ready for consumption by the outside world. Some of it isn't necessarily an appropriate way of doing this in OpenStack. These security initiatives have been running for a while and they work, but they were built against older versions of OpenStack that were doing older stuff. The first thing we did in the quantum was a glint in someone's eye when we started doing this and now it's an amazing thing with people talking about having firewall as a service. Some really cool stuff there, but what we can bring to that party is what we've learned in the last year in terms of how we can protect this and the sort of abuse profiles we actually see. Yes, for tracking. So most of the people we use for the IP reputation is just for spam stuff. I can't call them out individually because somebody else actually deals with a lot of that stuff. But if you're interested, drop me an email and we can talk more about it because we've got a whole bunch of information on this sort of stuff. So we have controls that are very tactical in nature. They're at places in the stack that you might not necessarily want them to be because hindsight's a wonderful thing. But what we wanna do is work with people to understand and build these controls into OpenStack. So the firewall as a service stuff that some guys are working on is really cool. Other stuff like just securing internals which I'll speak a little bit more in a little while we can do right now and are doing with people like the OpenStack Security Group with the Nova hardening project that started maybe a year ago. And I think it's fizzled out a bit now but actually bought some good security innovation for a short period of time. So what I'm gonna talk about here is just a little bit on how we deal with malicious virtual machines. So we have a whole bunch of things we're worried about coming out and going across our border because at the end of the day that packet leaves your network with HP's name on it. Okay, it's got an IP address that IP address says HP. We don't want HP packets landing on SSH brute forcing undoing all this other stuff. We just don't want it, it makes us look bad. So we have a mechanism that scales out with Nova and it scales out because it sits on the compute host and it messes around with IP tables. There's a few other things to look at traffic as it leaves. We don't do deep inspection. At the moment we made a very deliberate decision, not to, one it's computationally expensive and IP tables isn't the tool to do that. And two, we have this general ethos that we don't want to go snooping on people's data. So what we do is we look at the sign packets, we look at all the number of different new connections that are going out. We found with the little bits of profiling we can understand when all these things go out. Now one of the obvious problems with this is that you have a localized knowledge base. So you have your IP tables and your decision engine or whatever running behind that. But that only knows what's going on this host. So if I was a smart hacker and wanted to do some bad things with the cloud, I might write something that uses the APIs to spin up 30 or so VMs in a premium layer, ultra small, they send out small bits of data. Soon as they start getting rate limited, they crash out, you keep the floating VMs so they don't get reassigned to you from your pool, spin up a whole bunch more, do it again. That's hard to detect with this and we're looking at kind of interesting ways of leveraging bits of HP's property like ArcSight to start doing correlation across the cloud and saying, well, this tenant's doing kind of slow traffic over here but they're doing slow traffic from 30 other places over here and it's all going to the same place, okay? This is what we wanna avoid. We wanna avoid our services getting compromised. And the reason I bring this up is because I'm now shifting to looking at individual services rather than border controls. OpenStack inside is very, very vulnerable, okay? On the outside, it's reasonably hard to get in. There are reasonably well understood interfaces but on the inside, if you were to have somebody gain a point of presence within your network, then you've got a really big, painful problem for a number of reasons. Architecturally, most things inside OpenStack trust the other things inside OpenStack. What that means is that somebody on the side, somebody in your network can start representing themselves as other parts of your system and there is at the moment no way of verifying it and even in the places where OpenStack allows you to turn on SSL point to point, most of the time it's not doing any sort of endpoint verification and where it does a lot of the time, well, there is no R back inside of OpenStack at all. There's no way for OpenStack to understand conceptually that say a network node shouldn't send a certain type of message to your billing system or something like that. It's just not there. So these are a few things I wanted to call out specifically that we've been working on and other people have been looking at. One of the things I wanna mention in a minute is how well security is improved. So just keep these in mind, crunchy, squishy, loads of stuff that breaks. We've been talking about this for a while and internally I have a few different tactical things that I'll deploy to try and make the pain a little bit less. This is just finger in the air interpretation of how I've seen security and the discussions I've had with people. I now go into a room at a design summit and I don't have to put my hand in the air and say, well, there's no security there because people are already talking about it. They might be talking about it in slightly naive ways and that's kind of where the OpenStack Security Group comes in as a function to allow people to consult on security stuff to say, is this a good idea of dealing with this? What's the best way of securing this type of message? But I just want, you know, this room is full pretty much. It wouldn't have been a year ago. Okay, people care now. This is good. Cloud scaling, I've been fixing the message signing. Eric's doing a talk right after this one that I recommend you all go and see because he's gonna highlight exactly how bad some of that stuff is and what he's done to try and fix it. It needs a little bit of development to get to be production ready, but it's good. Nova messaging with RBAC, this is a really big thing. Nova is so big and so complex, the idea that one component doesn't know who's talking to it and whether or not it should be asking for something is terrible. Now, Nova's got a lot of good things going for it, but the security side isn't one and we're gonna work and change that. Swift Stack, in the last couple of days, we've been talking to them about doing the message authentication between the different components of Swift, which is a lot easier because Swift, pretty much everything has ultimate level of privilege and what you're protecting against is someone on the side injecting something on your network. At Memcash Deep Protection, asking for integrity, there are a whole bunch of configuration things in the different parts that we have deployed that can just be turned on. There's a whole bunch of stuff. So how many people here would like to see an open stack hardening guide come out of the security group? How many people would like to see a document on best practices for setting up and configuring SSL across all the different components in open stack? Cool. This is where normally someone goes, yeah, but it'll make it all really slow. No? Cool, cool. It will, by the way, but there you have to make a cost managed decision and you can put other compensating controls in place in areas where you don't feel the SSL's appropriate. And again, we'd encourage you to, if you've got ideas, come join the open stack security group and come talk to us about this stuff. So that's basically it. I don't wanna scare too many people with the public cloud. I do have a laptop to give out to someone. There's a sticker, an HP Cloud services sticker under one of your chairs. Someone finds a sticker, they'll get a really shiny thing. If you wanna help, please consider joining the open stack security group. If you wanna help more, come work for us. I'm sure there's a sticker somewhere, I know roughly where it is. No, it says HP Cloud on the sticker, sorry. Good try though. I think we've got a winner. There we go, congratulations. You got better applause than I did. Cool, there you go. That's why we all put conference stickers over the webcam, right? Cool, yeah, questions. So there's a few options. It depends what you're defining as privacy there. If you're defining their privacy from other users, their privacy from you, privacy from us as the cloud operator, you're absolutely right, you can. But if you are genuinely concerned about a service provider abusing you in that way, then the public cloud just isn't what you're looking for, right? You always have a hostile process of problem. You are captive within our system and to a certain extent we can do what we want. You can do, there are various things you can try and put in place like encryption and other stuff, but at the end of the day, everything's running in memory, everything is accessible. So if you're genuinely worried about that, then to use a compute example, public cloud probably isn't what you want. For the object storage example, there are absolutely a whole bunch of interesting ways you can work around that. I mentioned Panzerra earlier because they're doing this at a really big scale with us. They're taking data from companies that have massive corporate IP concerns. They're encrypting it and they're storing it in our cloud encrypted. And they do some cool stuff with PGP or some cool asymmetric encryption to make it work. But yeah, and even people who do, well, that's because it doesn't work. No, it's a very valid concern and there are even potentials around there's some interesting stuff going on in terms of trusted computing, but that actually bubbling up to something you can deploy in the cloud on a production hypervisor is a long way away. We have a ArcSight deployment at the moment that we use for a number of the things that you would use ArcSight for. We're still learning really what the best way to use it is. I mean, ArcSight is incredibly powerful and gives you so many different options.  So yeah. There was a question over there? What we do at the moment is use them internally. We have various properties that interact with customers externally. Fortify is a good example of a company that interacts with customers externally. And there would be good reasons for them to come and look at the cloud. And we have talked with them about that sort of thing. But really, as a deliverer of services like that, unless you were gonna put it kind of into our password framework or something else, that wouldn't be something we'd drive directly from HP Cloud so much as we are a service provider and we would provide that service to various properties within HP and otherwise they'll wanna come and use it and deploy it. But if you wanna talk more about that, if you grab me at the end and we can run through it all because there's stuff I can't present, so yeah. Cool, anyone else? Great, well thank you very much. Good work. Thank you.


It's a perfect lead-in. What's the there? Where are we taking laser tag fitness over the next 12 months 24 months 5 years? What's what's the plan for world domination? Yeah, nice. So I'm following the kind of standard startup entrepreneurial model, right? First thing I did was an MVP. I just wanted to see if this would even work I got some equipment. We went out to I made a deal with the city of Las Vegas use their outdoor football fields and Just proved that it's a workout right measured heart rate We counted 12 calories per minute, which is you know right up there with rowing and some of the most intense workouts that you can Do so the MVP was a success then I went for the minimally marketable product So people just to prove people are willing to pay and yeah people are wanting throw money at me Yeah, right all their friends. Yeah, I'll pay for this guy and I want to stay for two like I said So that's where we're at today. We just finished the MMP