Okay, so welcome back everyone. We start with the afternoon sessions. The first speaker is Valerio Vitale here who will show you the how you can sort of fix this problem of coming up with good projections to Vania Ryan's system. And so his talk will be about Vania 90 and the SDM method. And it will be a mixed lecture with some hands-on tutorials there. And so please Valerio, thank you for coming and the floor is yours. Thank you, Antimo. Thank you for inviting me. Yeah, so today's tutorial is about SDM and how this can be used in conjunction with Vania 90. My talk is going to be the first part more of recap of what Lillin told you yesterday. And then we'll have a hands-on part of about roughly an hour. And after this talk, which is just a way of seeing how SDM can work in conjunction with Vania 90, June Fang will show you how to optimize everything with Aida. Right, so this is just a brief recap of yesterday and these days you should now be familiar with all these equations. But basically if you have isolated bands and you want to visualize isolated bands, you have to find a gauge. And if you want to maximally localize Vania function, this gauge is fixed by minimizing this spread function. And in a simple case where you have isolated bands like a semiconductor or an insulator, and there's more number of bands, these is achieved quite simply.  And you can create this localized function in this way. You'll do a loading of normalization and this is basically your initial guess for your new matrix. And as you can see, this works quite robustly. So for a simple system and a few number of bands, isolated bands you don't really need to know the initial projections. And of course, more complicated cases, but basically if you start from four s orbitals in the middle of the bond here for silicon, for example, which start with four s like random functions in a unit cell, eventually you still get to the minimum of this spread function. So that means the spread function is quite, the minimum is quite shallow, you have a large basin, and you can start from a different initial guesses and you will end up in a lower minimum. Things are quite different if you want to disentangle bands. The idea is similar, but now you have a larger space. You don't have a specific number of bands, but these bands are entangled with others, you have a larger space, but the procedure is quite similar. So you start with a localized number of functions, which is a number of bands that you want to visualize at the entangle. Can everybody hear me at home online? Can people hear me online? Okay. Can people hear me over at the end of the room? Okay. And yeah, so the procedure for entangled bands is not too much different, but then what you want to do is to find these states that in this energy window that you want to disentangle that maximize the smoothness of your manifold, the smoothness in the k space relative to k. And this is what's called a disentanglement, and this is a multi-objective optimization problem. So what happens here is that if you start from forest like random projections, or if you start from forest in three on silicon, which is what chemically your intuition suggests, you find two different minima, right? So you try to vanu your eyes at disentangle this band, and you end up in two different minima. So here initial projections come out. And entangled band is usually the most difficult case, and is also one of the most interesting case that you can encounter. So the algorithm that maximizes this smoothness of the manifold is the Suza-Marzari Vanderbilt, and is a multi-objective non-combat optimization. So it's highly dependent on the initial guesses. But there's an alternative method that we mentioned yesterday, which is based on the density matrix of information that you find in the density matrix, and in particular is based on the QR, the composition with column pivoting of the density matrix, which doesn't have this issue, doesn't suffer from this issue, and is a one-shot algorithm, and it's not an iterative algorithm. And it works by looking at information that you already have in your density matrix. So physically, the idea, as Linin said yesterday, is basically to find what's are the most representative columns of the density matrix, which in a sense are the columns that overlap less and are the most localized in your density matrix. And in general, if you have a gap or a semiconductor or an insulator, then your density matrix decays exponentially with the distance between electrons. But for metals, it's only decayed algebraically. So the idea is basically that you find, you use density matrix, which is for isolated bands, density matrix is basically a protracted to the space of the balance state, and it's gaping balance. And you can represent the density matrix, both in terms of your conscious states and your vanu function. And as I said, it is exponentially localized for isolated bands if you have non-topological systems. And you can think about columns of the density matrix in the real space representation as some sort of projection of the density matrix on two very localized over the delta like functions. So you can create a function phi centered on R0, which is basically the result of projecting the density matrix to a very localized function, a delta function for example. And this would give me a column of the density matrix. I think you've seen this picture before, but it's just to show you how this is done in a computer basically.  And this is basically what you get if you have a simple phi like orbitals. And as you can see, if I choose a column of this density matrix, this is usually a well localized function, and this goes from zero distances which are large here, for example. And apart from a phase, basically I have a quite well localized function which would be some more my feeling like orbital. So you can see that basically if I can extract this column by just doing a matrix multiplication of these density matrix times a very localized vector, which basically has a whole zero here and just one at some point. So that's the original idea. It's more physical intuitive. Basically you have this density matrix and the columns are well localized functions. And you want to select the columns that are the most represented in the way of this density matrix. And I could choose n random column, but this might not be, in a sense, linearly independent, also linearly independent. So you want to choose the ones that are as linearly independent as possible that means less overall, basically. And the idea is to use this qr with column pivoting, which is exactly what it does. So the qr method is exactly factorizing the density matrix into two matrices, q which is unitary and r which is top triangular. And it also speeds out a matrix which tells you which are how to order the columns, such as the first are the more linearly independent ones. For generalization to move the bands is very easy. It's not really complicated. So for isolated bands you can basically use the SCDM without any parameterization. So if it's a number of bands that you want to vanuize, it's the same, it's just a number of vanu functions that you want to obtain, then basically there are no parameters. You can still use this idea of a cosy density matrix where you use this profile function as I explained yesterday, but this would be just a cutoff basically, he decided function, for example, which sets your energy window in the middle of the gap. So this is really parameter free. And we have tested this idea on many systems, many iterating systems in this particular paper, we study 81 iterating systems. And we found, so these basically are on the y-axis is the difference, the main error I would say, the main error and the max error of your bands that are vanuized with the SCDM method and the DFT bands. And here you can see that basically we use the SCDM in isolation, so without further doing an iterative step where we also maximally localize the vanu function. And then in this light pink here, we also use the SCDM as initial guess to the maximally localize vanu function. And there is a little difference in reality to the SCDM only and the SCDM. So the SCDM works already without the extra step of the maximally localization. But maximally localization does help in some cases. So here the raw K is the different fineness of the grid in reciprocal space. So this basically tells you the number of points that you have in your K grid. So small raw K means high density. And you can see that the results improved. So basically we have the error, for example here we have basically 93% of all the systems, so 75, 81, the main error between the vanuized function, the vanuator interpolated function DFT is below the 2 MVP. But things are slightly more complicated if you want to decent tango bands and then in this case basically you have two parameters. In reality you have three parameters you want to choose. So basically in your calculation one parameter is the number of bands, which is not 6. And then you have these two other parameters, mu and sigma, which define your profile function F. And there are different ways of decent tango bands. For example in this case you want to vanuize the valence, manifold valence bands plus some conduction bands. And then you can use this complementary error function here, which basically tells set to 0 all the elements in the density matrix are above some certain region. But you could also choose something different. You want to basically decent tango bands, like for example only the conduction bands or just B bands in copper for example. And you can use a different profile function. In this case you can use a Gaussian function for example. And you still have to define these only two parameters mu and sigma, which define the center of your Gaussian and spread the energy region that you're interested in. So how does it work and how do we set these parameters mu and sigma? So the idea is that you can do it the way I want. You can use your chemical intuition and your physical intuition in a sense. You can set mu, if you want to for example vanuize bands up to this line here. You can set mu around this value and then a sigma, which is basically like bandwidth of your bands of interest. You can do that and that doesn't really work well. So if you choose these two parameters intuitively as you would, so basically mu around your upper bound of the energy window as sigma, which that contains the bandwidth of the bands you're interested in, doesn't really work. So we had to come up with a different idea and the idea to choose mu and sigma in a more reliable way is to use this concept of projectability. So what are the projectability? I think these are quite important because Jungtang also is going to talk about these. And it's basically the idea of projecting your conscious states onto the pseudo-atomic orbitals in your pseudo-potentials. So these five functions in general is on localized functions. But in particular, in our case, is to use the information in the pseudo-potential to make everything automatic. So basically you don't have to choose these five functions, but you extract them from your pseudo-potentials. And you compute this projection of your conscious states onto these pseudo-atomic orbitals. The square is sum over them and you get something which is between zero and one. It's bounded. And these basically give you an information on how different bands project onto these states. So you have example bands that have a high projectability and mostly on the core states. So this will have high projectability on the, if you have S or P orbitals in your system. And usually these have a high projectability because these bands are pretty flat. So in projective conscious states, these will look like very localized orbitals. And then you have other bands up here where your projectability decrease because this will become more and more delocalized and eventually you have the continuum bands. And so the projectability goes down to zero. So this is just a way to extract this information from something you already have which is the function of your pseudo-potential. And what you do, you do, you basically fit an error function. If you want to study, if you want to, for example, minimize bands with your error function, you basically fit an error function to the projectability and you find a nu and a sigma. And the algorithm that works for most of the materials is to use these recipes. So basically once you fit the projectabilities, which is what we're going to do in the tutorial as well, the optical, the optimal mu that you find is actually the mu from the fit minus three times the sigma from the fit, whereas the sigma optimum is the sigma from the fit. So the reason why this works, it's so many materials, it's not super intuitive, but the reason basically is that you have to find a sweet spot between your spread function of, I think my microphone was annoying. So basically you have to find a sweet spot where your spread functional is small, but the error in your interpolated bands is small as well. And here, for example, we plotted these on the left here is the spread functional as a function of mu and sigma. And here is the mean error of your interpolated bands as a function of mu sigma. And you can see that basically I could use very large mu and large value of mu and sigma. So introduce more and more bands in my optimization. These, of course, will result in a smaller spread function. I have more freedom now, including more bands that are higher in energy have more freedom to rotate them in a way that I find very localized orbitals. But at the same time, my binary interpolated bands error will become very large. Right here on the right. So basically you have to find a way of choosing mu and sigma such that your spread function is small, but also your error is small. And as you can see here, this is the line where we set mu minus three sigma for this particular system, which I think is the tungsten. But we tested on many, many systems. This line here where you set mu minus three sigma is actually always in this sweet spot of having a small spread functional and a small error. So it's just an heuristic. Okay, so an example of why this is cool and useful and can save many hours is, for example, in the carbon magnitude with projection. So if you want to do, if you want to project vanu-rise these bands from a carbon magnitude, you need all these projections. If you want to have such a nice vanearization disentanglement, you need all these projections are all S orbitals in the middle of bonds, right here. And all PZ orbitals, which need to be properly oriented according to the curvature of your carbon magnitude. So otherwise you don't get this very nice interpolation from vanu-1990. And nice disentanglement. So basically, if you think about it, you have to spend many hours to have this projection right. Whereas in using SCDN, you basically need two blocks, one in the PW to vanu-1990X where you tell that you want to use SCDN projections and what kind of disentanglement procedure you want to do. And just this line in the vanu-1990 input. And you get the same result, right. So you can play with mu and sigma. So that's much faster than actually playing with so many projections. So you have only two parameters. But if you don't want to play with mu and sigma, you can use the projectabilities. The projectabilities according to recipe, either these two values, right. And you're done. And we try this for metals and other systems, so over 200 3D materials, spanning quite a lot of the table. And we found that this works pretty well also for disentanglement. So it's not as good as the isolated bands of course. But we found that basically you can get for all the systems, well, for 97% of the system, you can get an error that is below 20 mb if you choose this density of k points. So this is usually what we suggest to use. But with these, basically you can have an error which is below 20 mb. And usually the error is mostly in the upper bound of your bands. So this is then being automated thanks to Antimo and Giovanni and Junfeng as well. So we put everything together, quantum espresso of 90 databases into AIDA. AIDA, it's a Python materials for multi-platform, which Junfeng will show you how to use in the next tutorial. And you can create this wonderful automated graph where you only think that you need to give to AIDA, I think the structure, right, of a material. And most of the parameters are already set up through the heuristics. Of course, you can choose them, you can select different k point mesh if you want, but basically you can feed AIDA with the structure and ask to get a vanearization of bands and then everything is automated through this procedure. And that nice thing about AIDA is also that it gives you this provenance graph automatically generated. So basically every time you can know exactly what kind of calculation you've done, you can redo it. And basically it's very useful for people that want for fair computational methods. So if you want to know more about it, you should really attend Junfeng Chao tutorial next. Right, so summary is that we all know that maximum localize a vanear function or vanear function in general are very useful that there is this issue with initial projections, especially for entangled bands. And the SCDM overcomes this issue in a very simple way. You only need to set up two, to define two parameters, three if the number of bands or if you include the number of bands as well. And these two parameters can be actually specified for you through an algorithm, through an arithmetic algorithm. And it works very well, both for isolated bands and for entangled bands. And we have tested, I think Junfeng is done other tests as well. And these methods also being then extended to speeders as well. So it's not just a block way function, but also a system with a spin orbit coupling. And as I said, it works quite well. It works particularly well for isolated bands, but it's also very, very useful for entangled bands. Right, so this is an algorithm. Most of the people I work with in this project, I think with Giovanni and Antimo, who set up all the AIDA framework, and these are the funding. Okay, so that's it for the recap of the SCDM. I think we can start directly with the tutorial, with the hands-on tutorial. So maybe I do a separate record for that.


Hello, and welcome to this episode of the Security Angle. I'm Shelly Kramer, Managing Director and Principal Analyst here at theCUBE Research, and I'm joined in this webcast by my co-host and partner in crime, Joe Peterson, a fellow analyst and a member of our CUBE Collective community of analysts. And today we are going to talk about the evolution of the AI threat and three stages that we think it's important to be on the lookout for in 2024. So AI, the evolution of AI, who's not thinking about, who's not talking about this, right? We feel like we spent some time talking in the last couple of weeks about what we think people need to be thinking about for 2024. This is gonna be a multi-part series. And today we're gonna talk about three stages of the evolution of the AI threat. So to set the stage here a little bit, it is not hyperbole in any way to say that AI changes everything and it's going to change everything. And I think that what we're experiencing now and what we've got ahead is as much of a revolution as it is an evolution. And we expect that revolution to take, to have as much of an impact on society, both through a personal standpoint and a business standpoint, as really the evolution of the internet. And when you think about it, for those of us who have been around a while, the internet changed everything. And I think that many of us can characterize our lives, right? And pre-internet days and post-internet days. And so the internet did change everything and AI is also changing everything and will continue to change everything. And that's why it's so important to think about it from a cybersecurity standpoint. So we have identified three stages that we think will see the AI threat unfold in. And what sort of the top of the list is that we know that human threat actors are going to be increasingly augmented by AI capabilities. And these capabilities, of course, will act as a force multiplier and they'll extend the reach and the technical capabilities that hackers have and can use. And so that's a little more than a little scary. We've already witnessed the leveraging of AI capabilities to generate ransomware and malware, but we haven't yet really been tested really on how Gen AI can be used or AI can be used as a cyber threat. And I think that generative AI, things like chat, TPT and others have already paved the way for what is coming next. And one of these threats is something that is called weak AI, also called narrow AI. And this kind of AI threat focuses on narrow tasks. And we think that weak AI is gonna thrive in 2024 and it'll provide an edge for threat actors in specific areas, things like discovering vulnerabilities and evading detection, pretty important things. So let's, weak AI, it is pretty simple. It performs one specific task. It is programmed for a specific purpose. It learns how to perform tasks faster and there's no self-awareness. So weak AI and narrow AI are synonymously used terms when they refer to AI of less than human intelligence. And this is often described in terms of scope, in terms of how many problems can this solve. So on the other hand, the other part of the equation from weak AI is strong AI. Joe, tell us about strong AI. Yeah, well, so one of the things that I love about doing these podcasts with you is, we're learning this whole new vocabulary as it relates to AI security, we kind of are. And I'm gonna take a minute and talk first about weak AI. Somehow we think that weak AI is harmless because it's name, right? But it's not harmless, it is targeted. It's laser focused, right? It knows exactly what it wants to do. So weak is kind of a strange name to give it based upon its real capabilities, right? So don't be fooled, guys. Don't be fooled when you hear weak AI and go, it's harmless, it's not. I think that how I think about it is that, we have been using automation, artificial intelligence powered things to do back of house tasks, routine automation, quick and dirty things, blah, blah, blah, to increase productivity, efficiency, all of that sort of thing. So I think to me, I kind of think of weak AI sort of maybe a little bit like robotic process operation or it just does one thing and it does it really well. And it is designed to learn to go faster. And those are all of the things that some of the automation that we're already using in our lives and our daily lives do. So when you think about this, it doesn't mean it's not dangerous. Just like you said, it just means that it has a specific, one specific task slash focus that it lasers in on. Right, like a little dog with strong teeth and then a big dog with strong teeth, which we'll talk about in a minute, which is strong AI, you know the scary thing about strong AI is it's got human-like intelligence and it goes by a couple of different names. Just like Shelley was saying, that weak AI is also called narrow AI, so you may hear it term that way. Well, strong AI is also known as artificial general intelligence or AGI because we love our acronyms intact, which is true. But then artificial super intelligence, which is ASI. And the scary thing about it is, and I think about it this way, Shelley, I don't know what you think, I think about a nation-state actor, a number of people doing the same things, right? So it's not just one small task, it's sort of an end-to-end approach by a number of people to take down the target, whatever that target is, right? And the scary thing about strong AI is because it's AI, it learns as it goes and it's really meant to supplant technical skills. Yeah, I think it's smarter and smarter and quicker and quicker and exponentially more dangerous. Yeah, right, so that's the scary thing about it. And while we don't have hard stats yet, we, you know, you and I were chatting off-camera about the rise in some of my percentages in the number of attacks that we're seeing, ransomware for sure. And I pulled this step from Harvard Business Review, I wanna read it because it was astounding to me. Cyber crime cost businesses more than 10 billion with a B in the U.S. last year. And a figure that is expected to reach 10.5 trillion globally by 2025. By the way, that's one year. Yeah, yeah, right? So you were telling me something about a ransomware stat that you saw. Can you share that? Well, I think that, you know, so ransomware is incredibly common. Ransomware will cost victims around 265 billion annually by 2031. That is a crazy 815 times more than the 325 millions that organizations spent on ransomware in 2015. Now, I know 2015 seems like 1,000 lifetimes ago, right? And in many instances it was, but think about it, 325 million in 2015, 265 billion annually by 2031. I mean, that's crazy. And, you know, as we were talking about this, you know, and really the different threat vectors and things like that, phishing, email are always very, very hot targets. 80 to 95% of cyber attacks begin with phishing, 92% of malware was delivered by way of email. And, you know, we can talk all day long about how email is dead and blah, blah, blah, but the reality of it is in the business world today, the vast majority of us get up every day and we check our email. We live in our email. That's how we communicate. And the reality of it is, you know, it's these attacks are increasingly becoming more and more sophisticated. It's so easy to be taken advantage of. It's so easy to be tricked. If you're moving quickly, you're not really paying attention. And yes, employees, they're your greatest asset. I hate to talk about employees as an asset of an organization, but employees are the lifeblood of any organization. But the reality of it is, they're also your weakest end points. And I thought one thing that was particularly interesting here, you know, there are industries that are more attractive targets for cyber criminals than others. The finance industry happens to be one of them that's at the top of the list as of course is healthcare. But the finance industry alone accounts for almost 24% of all phishing attacks. So think about that for a minute and think about the ramifications. In the US, a data breach on average costs $9.44 million and a cyber crime like a ransomware attack costs about $8 million. So think put that in perspective for a minute and think about the fact that here you are, maybe you're an enterprise, maybe you're in the mid-market range of businesses and you're focusing on growing and scaling your business and reaching your profitability goals and all this sort of thing. And you get hit with a ransomware attack. And you have to figure out how you're gonna pay $8 million to remediate from this ransomware attack. And oh, by the way, not only is it, you know, the financial consideration, there is a hit to your reputation. There's your customers that are impacted that impacts their perception of your company and all that sort of thing. So that's a very big deal. Another thing that I think is important to mention is that it was an average of 49 days in terms of the time it takes to find and identify a ransomware attack. So think about that. You are living your life, running your businesses, your IT team is great, blah, blah, blah and something happens, there's some kind of way that a threat actor gets in and languishes in your systems, in your network, digging around in your data, all different kinds of things for 49 days before they're discovered. That's a really long time. And by the way, the other thing about these threat actors, I think that it's really important to note is that they are so patient. And in some of the biggest attacks that we've seen, it's been identified that they have been waiting, lying in wait inside networks, inside systems for a very long time, just watching and waiting for the right opportunity. So that's kind of creepy. 4.1 million websites have malware at any given time, 4.1 million websites.  And no surprise, cloud security is the fastest growing cybersecurity market segment and that market is only going to continue to grow. So I think that those are some, if you aren't already thinking about, holy moly, what's the impact of AI on my security operations? I hope some of these data points will help you realize it needs to move to the top of the list. Yeah, we actually guys, you may or may not believe this, but we actually talk about this stuff off camera. We do, sad as it may be, but we do and not. For geeks. Right, for geeks. So Shelley was mentioning something to me the other day and I got, man, that's a good point.  Can you share a little bit about that, Shelley? Well, I think it's really pretty easy when you think about it. First of all, you know, why hack? Financial gain, power could be a nation state trying to get information, you know, I mean, that happens all the time. Government entities are targeted all the time. So, so threat actors are highly motivated. Their efforts results in what we all want, financial reward. And, you know, I was reading something in Security Magazine as I was preparing for this conversation and there are over 2,200 cyber attacks every day. That equates to one every 39 seconds. That's a lot. And threat actors have already found a way to manipulate and weaponize chat GPT and other AI systems. Some of the things that they're using include sophisticated automated phishing attacks using email, social SMS messages that are personalized and designed to be incredibly convincing. You know, the thing that I think that's worrisome about chat GPT is that by using this and other AI powered solutions, threat actors can stay ahead of what we're using in terms of malware detection engines and they're using AI to create what are basically sort of infinite variations of code. So they're able to use AI to kind of stay ahead of the law.  I'm using AI powered technology to be able to do that. So I think that that is, I think that's a big deal. And I know that hallucinations are another security threat. And when you think about that, you know, that's one of the knocks about AI is hallucinations. And sometimes you can't really depend 100% on the information that you get. And so hallucinations allow threat actors to manipulate LLM based technology. And that means they are able to create false or misleading information. And that can ultimately lead to people relying on that information that they're getting from AI engines within their organization to make business decisions. But those business decisions are then gonna be based on inaccurate information or it will help us spread misinformation. And, you know, another thing as it relates to, you know, what we're seeing cyber criminals do is that they can publish malicious versions of software. Software packages that an ALM and LLM might recommend to a user or developer who's looking to fix a problem. So think about this, just in terms of your everyday life, you know, you're a developer, you've got an issue, you're trying to solve an issue, you're looking at a latest software package from a trusted software vendor. And all of a sudden, this is a malicious version, you don't know it, of this software, you're using it to fix your problem. And then all of a sudden you've led attackers unwittingly deeper into your systems and you don't even know it. So that is enough to keep a CISO up at night. Yeah, it is, but you know, I'm a class half full girl and I, yeah, look, I think just as hard as the bad guys are trying to do bad, I think the good guys are trying to do good. And what I mean by that is the cybersecurity, everybody thinks AI is new, it's not new in cybersecurity, right? In fact, the cybersecurity vendors have been using AI for years and baking it into their tools to make the experience for that IT team a better one, right? And if we think about, you know, I have a couple favorites that I want to bubble up in case people aren't sure or haven't used the technology yet, it's kind of interesting. Dark Trace has a self-learning AI technology and it's really helped customers understand and adapt to the unique patterns of their networks as it relates to their users and devices. And what it does via the AI is the AI allows them to detect anomalous or novel behavior that might indicate a cyber attack, which is useful, right? I mean, that makes perfect sense. It's watching what your habits, what your tendencies are and it's learning as you go, right? And it's getting smarter every day. And so it's able to sort of be the frontline of defense there. I think that's, I love Dark Trace. I think it's a super tech solution. Yeah, from an endpoint perspective and just this is one of several that use this technology, CrowdStrike's Falcon uses AI under the covers. And one of the things that I like about it is this concept of contextualization. As AI gets smarter, it can help an organization pick out what's an anomaly that's a problem versus just a false positive. And that makes a difference, right? So it's looking for behavior that doesn't fit in with what you normally do. And it's contextualizing and bubbling that up to the IT team. And then I did not know this, but Zscaler has integrated an LLM with a massive data lake that handles more than 300 billion transactions daily. And it's continually learning, right? And so it's driving advanced AI outcomes for their customers. So I think that those are a couple examples of how these vendors are getting ahead of the bad guys. And I know that you had one that just recently came up in the news that you wanted to mention. Well, there's a couple of things. First of all, I can't ever talk about endpoints without mentioning Taneum. I'm such a fan of the company and their solution. And I'm sad that I missed their annual event this year. I was there last year, but Taneum is all about endpoint management and endpoint security. And endpoints are so important because that is sort of the last line of defense for the first place that threat actors attack. And so endpoint management and updating and patching and all of that stuff is just a big, onerous task. And so when you can use AI-powered solutions, some of what Taneum provides to make endpoint management and all of the patching and discovering everything easier solution, it is wonderful and goes a long way toward keeping your system secure. I spent a bunch of time at the Taneum event talking to some customers. And it's always interesting to me at a cybersecurity event because a lot of times customers don't wanna go on the record and they don't wanna talk about what they're using. And when I covered the Taneum event last year, I had this plethora of vendors who were so excited to talk about how they were using, how they were using AI and how they were using Taneum's endpoint management systems and everything else. And I just love walking away, hearing those kind of success, those real world success stories because you and I can talk about this stuff all day long with hearing from practitioners knee deep in the field about the solutions that they're using and the benefits they're getting, I think is to me where it's all about, where it's all about, I love that. What you were mentioning that Sentinel-1 is another security vendor who's in the news this week, this cybersecurity firm unites endpoint, cloud identity and data protection. And they announced this week the acquisition of a company called PingSafe which is a cloud native application protection platform startup. And so the addition of PingSafe to the Sentinel-1 family of solutions, I see this as being able to take PingSafe's CNAP solution, cloud native application protection platform which can deliver dynamic real time monitoring of multi-cloud workloads. It's super simple to set up. It's super simple to configure. I think that's exactly what customers are looking for today. It also boasts very low false positive rates, also important, and it will aggregate intelligence to help detect toxic and exploitable vulnerabilities. So again, going to your point, being able to use AI power technology to find and alert you to these vulnerabilities is incredibly important. This allows your security teams to make quick decisions. And the reality of it is it allows them to make quick decisions without having to rely on humans finding the problem and alerting you. So I see this acquisition by Sentinel-1 as a huge deal. I'm so excited for both companies and it combines the strengths of Sentinel-1's cloud workload protection, cloud data security, AI and analytics capabilities with the modern comprehensive CNAP. And overall, Sentinel in their press release when they were talking about this Sentinel-1, they said that they believe this integrated platform will provide better hygiene coverage and automation across an organization's entire cloud footprint. Cloud security, that's where it's at. We're going to see a lot of movement in this space. So I think that this was a really, it was a timely acquisition on Sentinel-1's part. Yeah, cloud native has been a whole from a securities perspective for a while. Absolutely. I'm really interested in these cloud native security platforms because if you were, the hyperscalers do a great job, but if you're running maybe containers, container security is tough. And this addresses some of the native cloud technologies, right? Which are kind of cool. I know we want to get into new AI threat vectors. And so one of the ones that maybe we can talk about that we're starting to see being exploited are the idea of fishing, fishing, and smishing. And that sounds like, they're funny words. I always think of the smurfs when I get to smishing.  And in case, you're not sure what some of them are, we all know what fishing is. We've all, that's been in the news and we've all read about it. So we're all pretty sure what fishing is, but we might not know what fishing and smishing are. So smishing is really done via text or instant messaging. So think WhatsApp or Telegram. And the scammer provides their victim with a link, which when clicked, then helps them steal their personal information or upload malware. One of the two things. And fishing, on the other hand, uses phone calls and voicemail to reach the victim. But AI is sort of up the ante here. These are old scams, but AI is up the ante. So why don't you tell them how AI is up the ante, Shelley? Well, I think too, I want to give you an example of smishing that happened to me just this last week. And so it's funny because I have been talking with a member of our team about getting together so that he could walk me through some functionality of some platform that we're using. And we had loosely talked about it and I got a text message from him that said, hey, Shelley, this is Alex. Do you have a little bit of time to get together? And so I messaged him and I said, oh, I'm finishing a call. I'll be free in about an hour. So we can definitely touch base then. And by the way, I had never texted with Alex before. I knew he and I just had a conversation about getting together. So I wasn't surprised to hear from him by way of text message. And then the next message that I got was, okay, well, I've got to run a couple errands, but I'm really in a gym. Can you do me a huge favor? Could you run out and get a couple Apple gift cards for me? Well, I knew instantly that this was a scam. And every part of, and these attacks are very coordinated. They are very personalized. They want you to think you're talking to the person that is reaching out to you. Another form of this is called CEO phishing or smishing. And that's when you get an email or a text message from someone that's the CEO of your organization or some person in a position of authority that asks you to do something that asks you to click a link that asks, and those things, we are wired to think, oh, Joe's my boss, I have to do what she wants. You know what I'm saying? We're wired to react very quickly to things like that, but it's like, I knew in an instant that Alex wasn't wanting me to run out and buy Apple gift certificates, but this kind of thing happens all the time. And again, what's creepy about that is that Alex and I were talking by email about doing this. And yet I got a text message from him that was so personalized, that was so on target for what we were talking about. And there was every reason for me to believe it was him except for the ask. So again, it kind of goes back to your employees are the lifeblood of your organization, but we're also always the weakest points when it comes to attack vectors. So there are other, we were talking about AI and being a part of a cyber criminals toolbox. There are all different kinds of things to worry about. AI impersonation technology, and it uses machine learning algorithms to impersonate people online. That's kind of someone that really, this is what happened to me, right?  And AI algorithms can analyze huge amounts of data like social media profiles and they're able to use that data and create fake profiles that are believable. AI can also impersonate a person's voice. And I know that we were hearing just in the last few months about you would get a call, so warning people that if you get a call and Joe, you answer the phone and I say, hello, is this Joe? And you say, yeah, this is Joe. And then I tell you, that I've been in an accident and I really need you to wire me somebody or whatever, whatever, but the fact that you responded and said, yes, this is Joe actually gives a cyber criminal your voice and they can take that voice and they can use it then in other attacks. And to me, that is just so alarming because think about yourself in any situation. Now if somebody has a voice recording that says, this is Joe and they can take that and use it so that they can make calls to people and manipulate your voice and get them to do things, that's pretty scary. It is and it brings me, my brain goes right to again, something you and I were talking about off camera, the idea of the law keeping up with this technology. Like our whole lives, we've been trained to think that if you see somebody on camera doing something, well, it's gotta be real. If you hear their voice and you recognize their voice, it has to be real. And this is introduced as evidence in law, like in courts of law, right? So we're all sort of our minds work that way. Oh, well, it's on camera, it's gotta be real. But the fact of the matter is that AI is changing that too. And the International Association of Privacy Professionals just put out a kind of year in review for AI and the law. And I wanna cover two of them. And I know you've got two of them that you wanted to talk about too. So the first one is in the U.S. and I wanna get this right, so I'm gonna read it. The Federal Trade Commission put businesses on notice that existing laws such as section five of the FTC Act, the Fair Credit Reporting Act, and the Equal Credit Opportunity Act applied to AI systems. And so what does that mean? Or what are some of the ramifications? Well, this past year, the FTC brought actions against ring, right aid for violative practices involving AI. So it was already starting, right? And then on October 30th of 2023, President Biden issued the Executive Order on Safe, Secure and Trust for the AI Development and Use of Artificial Intelligence, recognizing the benefits of the government's use of AI and he also detailed core principles, objectives and requirements that would help mitigate risk. What are a couple that bubbled up for you?  You know, the US is always behind the EU as it relates to, you know, sort of consumer protections and that sort of thing. I think that some of the parts of this Executive Order are interesting, some of the reporting requirements are interesting. We touched on that a little bit in our episode last week, but it'll be interesting to watch this evolve and it'll be in the other thing that I think that is important is that, you know, on this policy and regulation path, we actually have two, at least two camps, people who are pro policy and regulation and this is important and this is super important to keeping people in business is safe and then we have people on the other side of this and many people in the tech space who are like, no, regulation is bad, it's, you know, Stifle's innovation, let us do what we wanna do, all that sort of thing. So this'll really be interesting to watch evolve for sure. You know, and as you mentioned, so we're also seeing city and state AI policy throughout the US evolve. We've seen lots of different regional action on AI. Let's see, I've got a couple of data points here. Colorado finalized rulemaking on profiling and automated decision-making. California proposed rulemaking on automated decision-making technologies. Several other states have also passed laws that provide sort of an opt out for certain types of automated decision-making and profiling. Other state and city laws that have focused on specific applications of AI, including things like child profiling, writing prescriptions, employment decisions, insurance, all kind of really personal things, right? You know, we've also seen some states in 2023 establishing laws on government deployed AI, which is always a very sticky wicket. For example, Illinois and Texas established tasks forced with the goal of studying the use of AI in education and in government systems to see what kind of potential harms AI could cause to civil rights that kind of is, they just have to laugh a little bit like this because Illinois and Texas could not be any further apart on the political spectrum, I think. So that's really kind of interesting that both of them are looking at, you know, potential harm of AI to civil rights. I think they're probably coming at that from different directions. Connecticut also passed legislation that established a working group on AI and requirements for government. Pennsylvania's governor issued an executive order establishing principles for government deployed AI. So all of these things are in the works. We're going to see more of that. You know, the reality of it is, is that threat actors have always found a way. They've always been on the cutting edge of how to use technology to do dirty deeds. And if ACDC doesn't run through your mind, when you hear that, I really, I don't know what to say. So, you know, but when I say that in jest, you know, some early indicators of this some early indicators of this, sorry about that. You know, we've already seen fake news articles from leading periodicals. We've seen legal cases. We've seen instances where news videos or videos have already been altered, you know, and when you think about what's happening, videos can be altered, voices can be altered, ads can be altered, faux product announcements. I mean, our ability to determine what's real and what's not is going to be challenged in the days and months and years ahead in unlike anything we've ever seen before. And I think that's particularly alarming as we head into an election year here in the United States because, and so it's one thing to have a challenge of not knowing what and who to believe when it comes to sources, but that, you know, and being aware enough to know that we have to question these things, but when you have a whole segment of the population who really isn't in this, you know, no, I'm not casting any aspersions here, but there's a whole huge segment of the population who isn't paying any attention to this at all. And so they don't know that they have to, you know, make it more of an effort than ever before to discern between what's real and what's not real and how to do that and where to go for resources on that. And I think that's really gonna be a big challenge for us moving forward. Yeah, I do too. And in wrapping up here, I just wanna talk about something you mentioned when we started, you know, the ability of AI to write code, right? So we didn't, you know how to code a little bit before AI came along, now not so much. Yeah. You don't have to be a coder to code and AI can do it for you. And so that's gonna change things too. And there was some recent Stanford research, a professor Dan Bonet, Professor Dan, if I said your name wrong, I'm sorry. But they did, they share their findings on a study called, do users write more insecure code with AI assistance? And the authors found that participants who had access to an AI assistant based on open AI's codex, DaVinci 002 model, wrote significantly less secure code than those without access. So the authors concluded that AI assistance should be viewed with caution because they can mislead inexperienced developers and create security vulnerabilities, right? Well, and I think though, to me, the key thing here is, and I think we see this really when we're using AI in general, you have to approach it with a degree of caution and you have to approach it knowing that just because it's AI, AI-powered does not mean it's always correct. And I think, a point here, I was looking at the research that you shared and to me, what really jumps out is the people who were using an AI assistant believed that they wrote more secure code than those who did not have access to the AI assistant. So that's also, I think, an important part of this equation here is that you can't be tricked into thinking, I'm using AI, so everything I'm doing is 100% accurate. It is truly gonna change what we believe, what we think are true, right? So that's sort of the takeaway, isn't it? So I think, I hope we've given some folks some things to think about here. And as always, it's been really cool getting to spend some time with you. Well, absolutely, Joe. And as I mentioned at the beginning of this show, this is the first in a series of webcasts that we're doing talking about AI and the evolution of the AI threat. We started with three stages that we think it's important for you to be watching. In the next episode, we're gonna talk about network and kind of networking and the role of AI there and things to watch out for. And but we appreciate you spending time with us today. We hope you'll remember to hit that subscribe button, whether you're on YouTube or whether you're on your streaming service or whether you're reading this. Subscribe, come along on this journey with us. And if there's anything that you would like to have covered, message us. I'll leave our contact information in the show notes. And we always wanna hear from you. And with that, my friend, Joe Peterson, thank you so much for spending time with me today. And I'll see you next time.


So, Joe Biden recently made a lot of liberals incredibly angry because an article from Reuters came out recently that cited two sources close to Biden that indicated that he'd be seeking a more middle ground approach when it comes to the issue of climate change. And rather than taking bold action, he'd instead be doing more incremental things to mitigate climate change. So he'd rejoin the Paris Climate Accord, for example. Now the problem is that even when Obama joined the Paris Climate Accord, it didn't go far enough back then. But now we have even more data telling us that we need to act urgently, otherwise we will not be able to stop a climate catastrophe. The IPCC in last December just warned us that we have 12 years to get our act together. So to see this from a leading Democrat, it had a lot of people on the left justifiably outraged because if you're going to pursue a middle ground approach, then we will not save the planet. You will not stop the planet from becoming an apocalyptic hellscape pretty much. So Joe Biden saw that everyone was ripping him, and that same day, he walked back this claim that his advisors had put out, tweeting, I'm proud to have been one of the first to introduce climate change legislation. What I fought for in 1986 is more important than ever. Climate change is an existential threat. Now today, we need policies that reflect this urgency. I'll have more specifics on how America can lead on climate in the coming weeks. Now I don't think that this satisfied anyone because everybody knows that Joe Biden is willing to say and do anything to get elected. He takes policy positions much like Hillary Clinton for purposes of political expediency.  So Alexandria Ocasio-Cortez, someone who's been a leader on this, decided to take a thinly veiled shot at Joe Biden. So she tweeted out an article from Common Dreams that explains how CO2 levels for the first time in more than 3 million years hit 415 parts per million. And she says, this is why a middle ground approach to our climate crisis is unacceptable. This isn't like other issues where you can pretend you're a sober adult by cutting the difference between left and right. You're either fighting for our future or you're not. So it's obvious that she's talking about Joe Biden here. And before he jumped into the race, she made comments about him that suggested that she's not too happy about him running for president. In fact, she said something along the lines of she's not excited about a Joe Biden candidacy or it doesn't excite her. But nonetheless, she doesn't like what he's saying here because this undermines what she's been pushing for with the Green New Deal. She crafted legislation specifically specifically designed to meet the urgency of this crisis and what he's saying here in opting for a more middle ground approach is basically a slap in the face to that effort. It's a slap in the face to all of these climate change activists who have been begging Democrats to take bold action. So the problem is that Joe Biden will say one thing and then do another. So the fact that he walked back this middle ground approach, it's not going to persuade anyone because we know that he's going to govern as an incrementalist as a centrist, because that's how him and Obama govern for eight years, because he was the vice president. We don't have to try to speculate about the way that he would govern. We know how he would govern. We have the empirical evidence that dictates that he will pursue a middle ground approach if he does anything on climate change. Will he even push for legislation or will he just pursue executive action that can be undone the next time we get a Republican president? So obviously this won't suffice. And at a speech, Alexandria Ocasio-Cortez was talking about the Green New Deal and she very bluntly took another shot at Joe Biden. And it was phenomenal when they say that calling for a Green New Deal is quote too much or too extreme or too radical. No middle ground is right. Here's what's too much for me. What's too much for me is politicians looking and allowing babies blood to get poisoned in Flint for corporate profits. That is what is too much for me. What's too much for me. What's too much for me is coal barons coming up to Washington, DC, demanding bailout after tax break after bailout for themselves and then not even paying their own minors pensions and put their own minors health care. That is what is too much for me. That is too much for me. What is too much for me is the fact that ExxonMobil knew exactly that climate change was real and man made as far back as 1970. And instead of being part of the solution, they paid millions of dollars to lobby and lie and confuse the American public about it, endangering generations to come. That is too much for me. What is too much for me is the fact that in 19a was born the year that I was born, the year that many of us were born and in years after and right before that politicians were first informed by NASA, that Congress was first notified by NASA, that climate change was going to threaten my life and everyone hears life to come and they did nothing. That is too much for me. I will be damned if the same politicians who refuse to act then are going to try to come back today and say we need a middle of the middle of the road approach to save our lives. That is too much for me. That was really good. I'm going to read you that quote again. I'll be damned if the same politicians who refused to act then are going to come back today and say we need a middle of the road approach to save our lives. That is too much for me. That was amazing because she's right here. The reason why he is seeking out this middle of the road approach is because he doesn't want to take action when it comes to climate change. He may care about it, but he has a lot of special interests in his ear who will be persuading him to do otherwise. So he knows that if he says, well, look, we need to work with Republicans, that's going to give him plausible deniability. He's going to say, look, I tried to work with Republicans and they shot me down so I couldn't do anything. So I guess we can't do anything. But going back to her tweet, when she says that, you know, you're not acting like a grownup. If you're splitting the difference between left and right, she's 100 percent correct here because you're not being reasonable.  You're being suicidal here and you're putting all of our lives at risk by saying you want to seek out middle ground between Democrats and Republicans. One party believes in climate change and kind of wants to act. The other party doesn't believe in climate change at all. Donald Trump thinks climate change is a Chinese hoax. So even if you seek out middle ground and you concede to their insanity, even minimally, they still win. That's still a victory for them. So what AOC is doing here and calling him out is a public service because she has the popularity and the name recognition that will maybe make him realize that he's not going to win anyone on the left over if he's going to continue to pander to Republican voters, who he thinks he needs to win over, which we all know if you want to win, you've got to get non-voters to come out and vote for you. But again, this is Joe Biden, so he's dimwitted. But nonetheless, she's been taking these thinly veiled shots at him and he's now starting to take notice because a reporter from the Hill actually asked him about this at, I believe, a yogurt shop. He's always in these ice cream or yogurt shops, but nonetheless, he was asked about this and his response basically was me. Are you talking about me? Like he literally denied that she was even talking about him. Take a look. He never heard me say middle of the road. I've never been on the road on the Vana. And I tell her to check, you know, the the statement that I made and look at my record. She'll find that nobody has been more consistent about taking it on the environment and a green revolution than I have. And so, look, anyway, so I can't. I don't think she's talking about me. Ha, his response is to deny, deny, deny. What me? I've never said middle of the road. Have you heard me say that? Well, no, so I guess that's technically true. But people closest to you have said that that's what you are pursuing. And it's not like that's some absurd thing to believe.   So, of course, you're going to pursue middle ground when it comes to this issue and pretty much every other issue. But he says, oh, I've never said that. Well, come on, you're being disingenuous because we know that that's what your team knows that you're going to do. And that's why they said it. He also says, I've never been middle of the road on the environments. Well, you have a really weird way of showing that you know about the urgency with which we need to act because you were vice president for eight years and you didn't say too much when it comes to climate change. You haven't been a leader on the issue of climate change. And then he says, you know, if AOC is talking about him, then look at his record. I don't think you wanted to do that. But then he ends by saying, I don't think she's talking about me. Joe Biden is such a joke. And I'd be remiss if I didn't talk about his other recent denials. He denies that his crime bill led to mass incarceration. He's denied this or made this claim twice now in a week. He's a danger. If he wins the nomination, we are risking another four years of Donald Trump.


Hi, I'm Zor. Welcome to Unizor education. We continue talking about rocket science. It's kind of a nice education term. Today, we will talk about how this rocket calculations are related to gravity. So basically we are talking about a major component of space exploration, how the rocket should be calculated, how all these parameters that will speed, etc. If we are, let's say, leaving the Earth and are trying to launch the rocket on the orbit. Now before, when we were talking about ideal rocket equation, we were talking about space without any kind of external forces, external gravitation fields, for instance. Now we will introduce this component into the equation and we will see how it changes the equation. So that's the subject of this lecture. Now, this lecture is part of the physics for teens course of physics, which is presented on Unizor.com. I do suggest you to watch this lecture from the website. You just go through a directory. You go to physics and then from physics to mechanics and then dynamics and it will be part of the last topic on the dynamics. Now why? Because these lectures are not only on YouTube, because every lecture on the website has a very detailed notes, practically whatever I'm talking about is written. Plus the most important thing, I think, the website is logically structured. So all the lectures are follow each other in a logical sequence. Now the prerequisite for this course is mass for teens on the same website and you really have to be familiar with calculus and with vector algebra. So that's that's prerequisite. So I will be using relatively freely concepts of derivative, differential, etc. These are all parts of these rocket calculations. And the site is free, by the way. Completely free. There are no advertisement, no financial strings attached. Okay. Now, let me start from something which we already started in the previous lectures. Namely, the equation of how the speed of the rocket is changing. This is basically v of t at the end minus v at time the beginning. So these are speeds of the rocket in the beginning when it starts moving or its engine actually starts working. It may be on the surface of the Earth, which means this will be zero. Or maybe it's somewhere in space when engine starts working. And this is at the end of the period during which we are measuring the speed as a result of working engine. So this is what we are going to investigate. We did already use this and receive this formula. Now this is effective speed of the exhaust. So when propellant is exhausted, let's say backwards, then the rocket goes forward. Now we are always assuming that the rocket moves along the positive direction of some axis, let's say x-axis, which means we are disregarding y and z-coordinates. And the propeller, propellant is exhausted towards the negative end of the x. So that's why this speed, if we interpret it as a vector, is actually negative. And minus this is positive times logarithm of mass of t in the beginning divided by mass t at the end. Now the mass at the end of the period of acceleration is obviously less than the mass in the beginning of this period. That's why this ratio is greater than 1, logarithm is positive. Effective exhaustion speed is negative, but this is a minus, so it's also positive. And that's why we have this delta V of t positive. Right? Now this formula in many textbooks is not really written with this minus sign, which means they actually consider the E as positive. And that's why basically this is the result. Written in this way in a vector form, the formula is more, I think, flexible because sometimes we want to decelerate the rocket. For instance, rocket goes to some point and then it wants to decelerate. So it turns with its back towards its movement. And then starts working. I mean engine starts working. And obviously because we are exhausting towards positive direction of the movement, we are decelerating the rocket. And it's written here, actually, because if VE is positive towards the direction of the rocket, with minus it will be negative. And that's why the delta would be negative, which means we are reducing the speed with deceleration. So that's why I'd prefer to have this minus sign. But you should understand that it's not really that very important. Besides, in most cases we are considering when the rocket starts and accelerates. We don't think about deceleration for whatever reason. Okay, now I would like to introduce the gravitation. Now this is an equation in empty space. There is absolutely no gravitation fields, no drag from the air or anything like that. No resistance to the moving because the rocket moves in an empty space, basically. So this is this equation. Now I'm introducing the gravitation. And I will do exactly the same. I will use exactly the same logic as I was using when I derived this particular equation. So my first tool which I'm using is the conservation of momentum. So I will check what's the momentum of the rocket in the beginning of its movement and at the end of the movement. And they're supposed to be equal to each other. Except in this particular case, we have to consider that there is a force acting on the rocket. The force of gravity. Now, so we're assuming that the rocket starts from the surface of the earth and it starts usually with zero speed. But in any case, we will see that that's not really very important. But what is important is that there is a force which is directed against the rocket movement and the force, if the rocket works, if the rocket engine works during certain amount of time, this force has some impulse. And this impulse is supposed to be added to the entire momentum. Well, in this case, it's subtracted because it's opposite to the movement. Now, you remember this formula. This is the second law of Newton. Now, instead of A, we can have dV by dt. Because what is acceleration A? It's the first derivative of the speed, right? Or dMv of dt. So that was the formula when the mass was actually constant and we just put it inside differential. But now, if mass is not the constant, this is the correct form of this equation, which means that f times dt equals d of mv. And f might be actually even the force which depends on the time, too. Maybe. But it doesn't really matter. But anyway, this is the equation which equates impulse of the force during the moment, during the time, infinitesimal time, dt, and increment of the momentum of the motion. So this force, if it's gravity force, should also be added at the end of my equation, which combines my momentum before and momentum after. So before, force did not act. But during the time of my acceleration, my force was the gravity force and it was actually acting. And we have to take into consideration additional momentum, which it gives. Well, additional means with a minus sign in this case, because it goes against the movement. But anyway, this is something which we have to take into consideration. Everything else is exactly as before. So what was before? Now, before, I had my momentum being this. Now, in most cases, we can probably consider that at the time of the start, t equals t beginning. The rocket is on the launch pad on the earth. And basically, its speed is zero. And that means that my momentum is zero. Now, what happens if my engines are working during the time dt? This is an infinitesimal time from t plus dt. This is interval of time, which I am considering right now. So in the beginning of this, it was m of t times v of t. Mass is variable because we are exhausting propellant. V is variable because we are accelerating. But in the beginning of this time, I had certain mass and certain speed. Now, what happens during the time dt? Infinitesimal period of time. Well, we have exhausted certain amount of mass. Now, what kind of mass we have exhausted? Well, we have exhausted mass, which was at the moment t minus mass at the moment t plus dt. That's what we have exhausted, right? Now, what is it actually? Well, this is minus differential of m of t. Why? Well, because differential of function is the value of this function at the moment t plus dt minus the value of the function at the moment t. So right now, I would like my mass to be positive. So if I'm asking how much mass I have exhausted, it's supposed to be with a minus sign because differential is obviously negative in this case. This is smaller. This is bigger. This is after the exhaustion. This is before. So this is negative. So my differential is negative. And that's why the amount of mass which has been exhausted is supposed to be positive. And that's how I wrote it here. Now, this mass, which was exhausted, was exhausted with certain speed, right? Now, what is the speed of exhaustion? Well, my effective speed is ve. That's a speed of the propellant relative to the rocket. But rocket is also moving with the speed v of t, right? So we have to add basically the rocket speed with exhaust speed to get the real speed of the propellant. And this is the mass. So my momentum of exhausted propellant is its mass times its speed. So this is momentum of the propellant. This is its mass, positive mass, because it's minus and d is negative. And this is the speed with which we exhaust the propellant, the gases, whatever is burning. Now, the next component is the rocket itself. So gases are going one way and they have this momentum. By the way, in the beginning, if v of t is equal to zero, my ve is negative. So the whole thing is negative. So this is negative momentum, right? In the very beginning. When v of t is zero and my initial momentum, if we start from the moment zero, actually, when the rocket is in the launch pad, this is obviously zero. So this is negative. But the rocket has a positive momentum because the rocket goes to the positive direction of the x. So what's the momentum of the rocket? Well, the rocket has a mass m of t plus dt. That's its final mass, right? Which is equal to, look at this, mt of dt goes here, it's minus, it will be plus, d goes here. So instead of this, I can put m of t plus dm of t. That's the mass of the rocket. And what's the speed of the rocket? Well, speed of the rocket is v of t plus dt. But again, it's absolutely the same formula for differential. Instead of v at time of v plus dt, I can put v of t plus differential of v of dt. Again, if you feel some kind of uncomfortable about this, go back to the calculus. It's all there. It's very, very simple thing. So this is the momentum of the rocket itself, whatever remains of the rocket without the propellant, which has been exhausted. So this is, let's say in the beginning, when v of t is equal to 0, this is negative and this is positive. And that's why their sum is equal to 0, right? But now, not quite. Now we have to really overcome an impulse of the force of gravity, which is equal to what is the force of gravity? The force of gravity is m of t times g, right? Mass times acceleration of the free fall. And I have to multiply by the time during which this force was acting, right? So that's what basically the whole thing is. Now, if I will combine these three components together, I will basically have to, I have to get exactly the same thing as my initial momentum, because this is, in a sense, this is what actually the conservation of momentum is. This is momentum in the beginning of this period, from t to t plus, from t to t plus dt. This is the beginning momentum. And the combination of these three is the ending momentum. And the conservation of momentum says that they must be the same, right? So let's make this equation. Okay, so what is really the equation? First, I have to have this component minus dm of t times v of t plus ve. That's one component. Right? Now, second component is this one. This is the momentum of the rocket. New mass times new speed. And I have to add the impulse from the gravity. Force, mass times acceleration times time. So during the time dt, infinitesimal interval of time from some point t to some point t plus dt. So during this interval of time dt, this was in the beginning of this period. This was at the end of this period. And basically, that's it. So the only thing which I have added is this one, this component, relative to flying the rocket in a free space without any kind of forces. So let's just simplify that a little bit. Now, what follows is this. If I will open these parentheses, what will I have? I will have mt times vt. I will have vt times d of mt. I will have mt times dvt. And I will have differential times differential. And I will completely throw it away because this is an infinitesimal of higher order because I will be doing integration obviously after that. And this is infinitesimal of the higher order. And one integration will give me infinitesimal, which can be dropped at the limit. So instead of this, I can just put this. And now I can basically do the following. I can do this and oops, sorry, not this. This stays. And this. Right? Then I can do this minus dm of tvt and plus dm of tvt. So I can do this and this. So what remains, what remains is the following. I will have this one. I will have this one. And I can, and I have this one without this. So the final equation looks like zero. This is zero equals minus ve times dm of t plus m of t dv and plus this. So this is my final equation, which I can integrate right now to get the formula for total increment of my speed from t begin to t end on this time interval. So what will I do? I will obviously divide by m t and I will have this goes to the plus ve dm of t divided by m of t equals, no, I will put this also to the left, minus g, minus g times dt equals to dv of t. So this goes to the left. This goes to the left. This is the only thing which remains on the right. And I divide everything by m of t, by m of t, by m of t here, here and divide it here. So let me reformulate it a little bit more. dv of t is equal to, now what is this? This is obviously differential of logarithm, right? So the first derivative of logarithm of something is one over that something, that's m of t. And then you have to multiply it by derivative of the inner function, which is m derivative of t. And that's what gives you differential. And minus g dt. Now I can integrate it very simply. Integrate from t begin to t end, t begin, t end, t begin, t end. So what will be my result? Well, if I'm integrating differential of some function, the result will be function, right? So it will be v of t, v of t end, minus v of t begin. This is exactly delta v, which we are interested in. How much speed we will gain, right? Equals to, now this is the constant, so it goes outside. And then I will have again the function, logarithm of m of t end, minus logarithm of m of t begin. And minus integral of this is obviously g times t end, minus t begin. Okay, fine, that's done. Let me just simplify it maybe a little bit and that will be the answer. So delta v is equal to, now the difference between logarithm is logarithm of their ratio, right? Now ratio t end divided by mass of t end divided by mass at t begin. Well, the problem is mass of t end divided by mass of t begin. Well, t end is smaller, mass of t end at the end of the period is smaller than mass in the beginning, right? Because we are exhausting the propeller, which means that my ratio is less than one. When ratio is less than one, logarithm is negative, right? And I don't like to have, to deal with negative logarithm.  So as a result, I will have minus v e, logarithm of mass at t begin divided by mass of t end and minus g t end minus t begin. So that's my final formula, which is almost the same as my ideal rocket equation except this member. So this is the only thing which my gravitation added to the equation. My old equation was from here to here and now it's this way. Now it's kind of obvious that this is supposed to be this way. Why? Well, because as the rocket comes up, it also falls down because of the gravity. Now the gravity has acceleration g and the interval of time during which the rocket goes down and at the same time falls down is from t end to t begin. And that's why you have this minus g times the difference in time. So we could have come up with this without all these calculations, but I just wanted to make again the point that we're talking about conservation of momentum at the gravitation force has an impulse which is supposed to be taken into equation and that's basically why we have the same thing plus this particular member which is kind of obvious. Now what's important actually here? Well, important is that v e is again, v e is negative when the rocket starts, right? Because it's going against the direction of the rocket which we assume to be positive. So let's say this is a z axis and the rocket goes up along the z axis and obviously its speed vector of speed its velocity is positive and this one should be negative then with minus sign it will be positive. And unless by absolute value this thing exceeds this one, the rocket will not fly. It will just stay still on the launching pad. So you have to have a pretty substantial effective exhaust by absolute value to overcome this obviously. Now what else is important here? What is important is that there are complications. You see, you might think about this way, okay, we have taken into consideration the gravity and that's probably the biggest factor which influence all our calculations and must be taken into account. Now what has not been taken into account in these calculations? Well, number one, when the rocket starts from the surface of the earth there is an air resistance which drags it down, right? So that's, we would not take it into consideration at all. And the air resistance obviously depends on the rocket form shape itself but also on the density of the air and density of the air is changing the higher we go the less dense the air is. So we have to really take it into consideration which is not easy. Another thing which we did not take into consideration is that the gravity as we are moving off the earth higher and higher, the gravity itself is also changing because we are increasing our distance from the planet. So G is not actually constant in the real life situation. Which kind of complicates obviously our equation? I mean we have integrated equation basically, right? Now if we will take into account all these factors, the equation differential equation from which we started, which is what's happening during the time dt, this differential equation would be a little bit more complicated and sufficiently complicated not to be able to solve it in integrals. So we will not be able to come up with a formula like this one. Instead people basically do it numerically and taking into consideration all these factors actually does complicate the whole picture sufficiently to call rocket science in quotes as something which is really very very complicated. Yes you definitely can say so. There are many different factors. Another factor which I would like to mention is if you launch the rocket towards the east the earth's rotation actually helps to start from certain speed which is not really zero. So the speed in the very beginning V of T begin is not really zero. It's actually the speed of the rotation of the earth if you point it to the east. Now if it's at some angle maybe that's another story again. I mean you have to really take into consideration lots of factors. Okay now I do suggest you to read the notes for this lecture. It's in this website Unisor.com and just try to familiarize yourself and basically that's it. That probably completes my theoretical explanation of what rocket science is about. Again not covering completely all the complexity but giving you some flavor of basically this is the probably the most important part of it because all these additional things like the fact that the gravity is changing as we are going up or the density of the air etc. They are definitely contributing factors which the real calculations performed for launching the rockets must be taken. However for our purposes this is the major component because whatever we are adding is significantly smaller in magnitude and impact on the movement of the rocket. But still important and we have to take it into consideration when we are dealing with real rockets to launch. Okay that's it for today. Thank you very much and good luck.


Hey everybody it's Sam at Mixed Up Craft, thank you for watching today. I'm back with another scrapbook layout and this time I'm doing one of my hen party, well a few of the pictures I've got three. Now for some reason the beginning of the video has disappeared but it's fine. I've got a sheet of 12 by 12 and I've gone and cut strips of 2 inch by 12 in all different colors from the Fiesta Fever paper pack and then what I've done is I took a selection of my edger punches and I've got a Martha Stewart one, an X cut one and there was another one as well and you can see there basically along each of those different strips I have created a different border and I'm just going along with my glue and overlapping each one as I sit it down. So I started from the bottom and then slowly working my way up and I've got about half an inch that I'm leaving of each one. So I've actually got this idea from Paige Evans over on her channel and now hers is slightly different and she curled it all and it was very dimensional and things like that but I liked the idea of having lots of different colored strips of cardstock. So I just wanted to you know use the kind of last bits of this paper pack and I kind of clashed the prints with the plain so I've used the reverse of a lot of them so all the colors match everything ties in perfectly together but it is it's just a really fun effect. Now you know my hemp party was just absolute chaos it was without going into too much detail but it was a very very funny night and everybody was in a different fancy dress so we had Santa Claus, someone dressed as a toilet, someone dressed as a butcher with sausages around their neck, a turkey, a witch, a smurf. So everybody was clashing and colorful and just odd and I wanted to kind of create a layout that was that kind of way so again really you know really really crazy. So you can see now I've gone ahead and I've just covered that whole 12 by 12 piece of cardstock with those different strips. Now these are the photos so there's me as Santa Claus and then I've got one of me in let's say yeah the beginning of the night when we looked fresh so there's my mum me and my sister then there's my best friend in the top left with the turkey hat and then me and my sister and you can see she's the smurf and I never drink pints I've got a pint in my hand and I never drink pints but anyway so I wanted these three I just thought were particularly funny but I do have some other great ones but I just want to kind of frame them all mat and layer and all that kind of stuff so I'm actually doing it the reverse this time so I'm putting them on coloured cardstock first and then I'll mat them onto white so I'm just going through each picture there one on blue one on pink and then all of them I'm going to put on a white matte final layer just so that they kind of pop against the all of that kind of print because there's so much going on on this layout I wanted to you know make sure that nothing gets lost so you can see there the three and then just bringing in that white cardstock and it does it just really does you know like I said make it pop and you don't lose those photos so again this does create a bit more bulk to the layout but overall I keep the layout pretty flat this is probably really the most bulkiest part of these kind of pictures so one thing I've done is I've got this punch that creates this kind of I don't really know how to explain it but it allows you to be able to thread ribbon through now I'd never used it as a Martha Stewart one and I had this this ribbon here and I just wanted to have one with this punch along it so I'm just going along here and just weaving this kind of again I don't know what you call this this ribbon I know there's a name for it but it's completely gone at the minute but I just thought it would be a nice way to add a little bit of texture you know again just use the tools I've got I've had these things lying around for so long and I just think I don't know when I'm going to use it and when I saw this particular layout I thought actually yeah this is going to be a good good time to do it so I go along there it was a bit fiddly it did take me a bit of time but the overall finish did look really good and you can see it there just behind the picture of my mum me and my sister and yeah it was just nice it's again it's just texture it's kind of hard to pick up on in videos sometimes but it did look really good so the picture's already the background's all done so now it's just really a matter of starting to dress everything so I've got these puffy stickers from I want to say American crafts but I've got a feeling they're not I think they're hobby craft so again not doing very well with where I've got everything today but they are really nice puffy stickers but they looked really lost just putting them directly onto the layout background there so I'm just pulling this was a sheet from the beach life collection and I'm just kind of roughing up the edges there just ripping it freehand just to again just to give it a bit of something really so I'm going to run that strip just to the the left hand side there and that will give me just a nice blank background for my title I'm just putting my photos on some foam adhesive as I always do and then I'm going to stick down this strip first of all struggling there with the glue and this is on doubled the doubled the speed on this layout so you can imagine I was there shaking that bottle for a while so get the background bits stuck down first and then start positioning these photos so just get that one laid down there I haven't used three pictures on a layout for a while actually so it was quite nice to kind of combine more than one or two photos really so that's kind of what I stick to but just playing around there with the positioning and the title just before I kind of you know commit and actually stick down those other two photos so I'm starting to lay down the lettering here now now it's all in lowercase I don't think there's no there aren't any capitals on this one so again it just looks a little bit different as well which I liked so yeah hen party fun is the is the title of this layout and the colors worked really well as well again I've had these for a while but never quite had the you know the layout for them so everything does eventually get used which is good so you can see now how well that title really does pop and stand out and like I said it is on a foam so it's got a really nice fun texture to it as well so you've got the ribbon you've got the ripped kind of parts you've got all the layers of those strips and then you've got the foam from the title so lots going on then I'm bringing in some puffy stickers that one said woohoo I've got girls just want to have fun this is how we roll so lots of different ones and yeah just some fun little quotes so I'm bringing in some bit but I did go to use the purple on the left and then thought that didn't right so I've just made this nice orange bow which I end up sticking down later again just sort of look quite fun these are some of the cutouts that come on one of the street sheets in the 12 by 12 pack and that one just says yay so I've just fussy cut that one and then I start playing around deciding really where I want to do it this this layout actually took me quite a long time I remember I went away made a cup of tea come back again put it to one side so I just kept looking for different things to use so the top there that blue was just a bit too blank for me so I've just got these very thin washy tapes in an orange a pink and a green yeah again probably can't see it that well on the video but in the pictures you will I just wanted again something to break it up and then I remembered I had these neon do crafts strips sticky strips now they still sell these in the range I actually saw them the other day and I've had them for ages seriously I've had them for about three years and finally I found somewhere to use them so I just started laying these strips they're really really hard plastic but they bend and they're all sticky and they looked really quite good on this I thought yeah this is cool so and on the top I've done about four strips and I cut them all different lengths on that top left so you can just see me there kind of adding in more of those strips and they just they were just fun I just kind of you know pop them in anywhere really above the photos but mainly along the top left and along the bottom right you can kind of see there they've got some nice dimension shine they've got a bit glitter through them as well so yeah I was glad I got to use them so then I got some more of the cutouts from the paper pack this one says good vibes so again just fussy cutting that one out just kind of collecting as I always do bits and pieces you can see I've added in a little camera there just to the left of my best friend and me we were looking at a selfie that we'd taken on the camera so the camera little kind of chipboard embellishment looked really good there I'll put the good vibes up to the top left where there's the me my mom and my sister and then I've got these really nice enamel dots I'm adding a few of them into the on top of the photo there of me and my sister the bottom right just anything I had that was really colorful I've kind of added to this layout so I've got these fun rosy studio again kind of plastic stickers and just adding that slight little stars little hearts just lots and lots of stuff so just raid what you've got if it matches that it will work and yeah I just kept adding loads to this layout again you'll see it in the photos at the end but yeah so much texture and stuff it's really really cool and then at the bottom that was what I was saying earlier so girls just want to have fun I was adding glue onto the back of everything just because I didn't want these you know eventually peeling off because some of the adhesive's just aren't great on the stickers when you buy them so just making sure everything's stuck down there this is how we roll girls just want to have fun and again this is all rosy studio little sentiments and stuff so lots lots going on and then I'm just kind of working out where to put that bow so just having some hot glue there and I ended up popping it just above the hen title part there and I thought that looked quite nice again I don't tend to really add that bigger bow on my layouts because obviously it does create some you know height and bulk but it it was okay it still worked then we've got my trusty new video up so you know I'm coming to the end of the layout now and I added yellow pink blue light pink and green and then I went over and done it all again so there are tons and tons of Nuvo drops on this layout because again when they dry they just look so good and yeah they just again it's just another element to the layout and I really like them so that's why I've used them so yeah lots and lots and lots of Nuvo drops and there's the kind of dusty pink color again they just match so well with this this paper pack because there's so much color on that background you can pretty much get away with everything so there you go I can bring it up close now I've got celebrate woohoo good vibes girls just want to have fun this is how we roll and then you can see all those Nuvo drops everywhere and that lovely kind of strip all of the ribbon that I weaved the ribbon bow loads so I really had fun with this one and it's nice to just really use the stuff that we have in our stash even if it's just a little bit of it I've used it so I'm really really pleased and I absolutely love this layout and it just sums up the colorful fun you know hen party so I hope you've enjoyed this layout I will be back again with my regular layouts on a Sunday and until next week have a lovely weekend and I'll see you soon bye