Hello everyone, welcome to theCUBE's presentation of the AWS Startup Showcase. This is season three, episode one. The focus of this episode is AI ML, top startups building foundational models, infrastructure and AI. It's great topics, super relevant, and it's part of our ongoing coverage of startups in the AWS ecosystem. I'm your host, John Furrier with theCUBE. Today we're excited to be joined by Jay Marshall, VP of business development at Neural Magic. Jay, thanks for coming on theCUBE. Hey John, thanks so much. Thanks for having us. We had a great CUBE conversation with you guys. This is very much about the company focus. It's a featured presentation for the startup showcase. The machine learning at scale is the topic, but in general it's more, we should call it machine learning and AI, how to get started, because everybody is retooling their business at companies that aren't retooling their business right now with AI first, will be out of business in my opinion. You're seeing massive shift. This is really truly the beginning of the next gen machine learning AI trend. It's really seeing chat GPT, everyone sees that, that went mainstream. But this is just the beginning. It's just scratching the surface of this next generation AI with machine learning, powering it, and with all the goodness of cloud, cloud scale and how horizontally scalable it is. The resources are there. You got the edge. Everything's perfect for AI because data infrastructure is exploding and value AI is just the applications. This is super topic. What do you guys see in this general area of opportunities right now in the headlines? And I'm sure you guys, phone must be ringing off the hook, metaphorically speaking, or emails and meetings and Zooms. What's going on over there at Neural Magic? No, absolutely. And you pretty much nailed most of it. I think that my background we've seen for the last 20 plus years, even just getting enterprise applications kind of built and delivered at scale, obviously amazing things with AWS and the cloud to help accelerate that. We just kind of figured out in the last five or so years how to do that productively and efficiently kind of from an operations perspective got development and operations teams even came up with DevOps, right? But now we kind of have this new kind of persona and new workload that developers have to talk to and it has to be deployed on those IT ops solutions. And so you pretty much nailed it. Folks are saying, well, how do I do this? These big generational models or foundational models as we're calling them, they're great, but enterprises want to do that with their data on their infrastructure at scale, at the edge. So for us, yeah, we're helping enterprises accelerate that through optimizing models and then delivering them at scale in a more cost effective fashion. You know, I think one of the things the benefits of open AI we saw was not only as an open source, and you got also other models that are more proprietary is that it shows the world that this is really happening, right? It's a whole nother level. And there's also new landscape kind of maps coming out. You got the generative AI and you got the foundational models, large LLMs. Where do you guys fit into the landscape? Because you guys are in the middle of this, how do you talk to customers when they say, I'm going down this road, I need help. I'm going to stand this up and this new AI infrastructure and applications. Where do you guys fit in the landscape? Right, and really the answer is both. I think today when it comes to a lot of what for some folks would still be considered kind of cutting edge around computer vision and natural language processing. A lot of our optimization tools and our runtime are based around most of the common computer vision and natural language processing models. So you're YOLOs, you're BERTs, distill BERTs and what have you. So we work to help optimize those. Again, who've gotten great performance and great value for customers get trying to get those into production. But when you get into the LLMs and you mentioned some of the open source components there, our research teams have kind of been right in the trenches with those. So kind of the GPT open source equivalent, OPT, being able to actually take a multi-hundred billion dollar parameter model and sparsify that or optimize that down, shaving away a ton of parameters and being able to run it on smaller infrastructure. So I think the evolution here, all this stuff came out in the last six months in terms of being turned loose into the wild. But we're staying in the trenches with folks so that we can help optimize those as well and not require again, the heavy compute, the heavy cost, the heavy power consumption as those models evolve as well. So we're staying right in with everybody while they're being built, but trying to get folks into production today with things that help with business value today. Jay, I really appreciate you coming on theCUBE and before we came on camera, you said you just run a customer call. I know you've got a lot of activity. What specific things are you helping enterprises solve? What kind of problems? Take us through the spectrum from the beginning, people jumping in the deep end of the pool, some people kind of coming in, starting out slow. What are the scale? Can you scope the kind of use cases and problems that are emerging that people are calling you for? Absolutely. So I think if I break it down to kind of like your startup or I maybe call them AI native to kind of steal from cloud native years ago, that group, it's pretty much part and parcel for how that group already runs. So if you have a data science team and an ML engineering team, your building models, your training models, your deploying models, you're seeing firsthand the expense of starting to try to do that at scale. So it's really just a pure operational efficiency play. They kind of speak natively to our tools, which we're doing in the open source. So it's really helping again with the optimization of the models they've built. And then again, giving them an alternative to expensive proprietary hardware accelerators to have to run them. Now on the enterprise side, it varies, right? You have some kind of AI native folks there that already have these teams, but you also have kind of like AI curious, right? Like they want to do it, but they don't really know where to start. And so for there, we actually have an open source toolkit that can help you get into this optimization. And then again, that runtime, that inferencing runtime, purpose built for CPUs, it allows you to not have to worry again about do I have a hardware accelerator available? How do I integrate that into my application stack? If I don't already know how to build this into my infrastructure, does my IT ops teams, do they know how to do this? And what does that runway look like? How do I cost for this? How do I plan for this? When it's just x86 compute, we've been doing that for a while, right? So it's obviously still requires more, but at least it's a little bit more predictable. It's funny you mentioned AI native, born in the cloud was a phrase that was out there. You kind of now you have startups that are born in AI companies. So I think you have this kind of cloud kind of vibe going on. You have lift and shift was a big discussion. Then you had cloud native kind of in the cloud, kind of making it all work. Is there a existing set of things people throw in this at? And then what's interesting AI native and kind of providing it to existing stuff? Because we're seeing a lot of people take some of these tools and apply it to either existing stuff it's not really lift and shift, but it's kind of like bolting on AI to something else. And then starting with AI first or native AI. Absolutely, that's a great question. I think that probably where I'd probably pulled back to kind of a lot of kind of retail type scenarios where for five, seven, nine years or more even, a lot of these folks already have data science teams. They've been doing this for quite some time. The difference is the introduction of these neural networks and deep learning, right? Those kinds of models are just a little bit of a paradigm shift. So, I obviously was trying to be fun with the term AI native but I think it's more folks that kind of came up in that neural network world. So it's a little bit more second nature whereas I think for maybe some traditional data scientists starting to get into neural networks, the complexity there and the training overhead and a lot of the aspects of getting a model finally tuned in hyperparameterization and all of these aspects of it. It just adds a layer of complexity that they're just not as used to dealing with and so our goal is to help make that easy and then of course make it easier to run anywhere that you have just kind of standard infrastructure. Well, the other point I'd bring out and I'd love to get your reaction to is not only is that a neural network team, people who have been focused on that but also if you look at some of the data ops, lately AI ops markets, a lot of data engineering, a lot of scale, folks who have been kind of like in that data tsunami cloud world are seeing, they kind of been in this, right? They're like been experiencing it. No doubt. I think it's funny the data lake concept, right? And you got data oceans now, like the metaphors just keep growing on us but where it is valuable in terms of trying to shift the mindset, I've always kind of been a fan of some of the naming shift. I know with AWS, they always talk about purpose built databases and I always liked that because you don't have one database that can do everything. Even ones that say they can, like you still have to do implementation detail differences. So sitting back and saying what is my use case and then which database will I use it for? I think it's kind of similar here and when you're building those data teams, if you don't have folks that are doing data engineering, kind of that data harvesting, pre-processing, you got to do all that before a model is even going to care about it. So yeah, it's definitely a central piece of this as well. And again, whether or not you're going to be AI native and as you're making your way to kind of, on that journey, data is definitely a huge component of it. Yeah, you would have loved our super cloud event we had talked about naming and around data meshes was talked about a lot. You started to see the control plane layers of data. I think that was the beginning of what I saw as that data infrastructure shift to be horizontally scalable. So I have to ask you with neural magic and your customers and the people that are prospects for you guys, they're probably asking a lot of questions because I think the general thing that we see is how do I get started? Which GPU do I use? I mean, there's a lot of things that are kind of, I won't say technical or targeted towards people who are living in that world, but like as the mainstream enterprises come in, they're going to need to playbook. What do you guys see?  Absolutely, and I think where we hook in specifically tends to be on the training side. So again, I've built a model. Now I want to really optimize that model. And then on the runtime side, when you want to deploy it, we run that optimized model. And so that's where we're able to provide. We even have a labs offering in terms of being able to pair up our engineering teams with a customer's engineering teams. And we can actually help with most of that pipeline. So even if it is something where you have a data set and you want some help in picking a model, you want some help training it, you want some help deploying that, we can actually help there as well. You know, there's also a great partner ecosystem out there, like a lot of folks even in the startup showcase here that extend beyond into kind of your earlier comment around data engineering or downstream IT ops or the all up ML ops umbrella. So we can absolutely engage with our labs. And then of course, you know, again partners which are always kind of key to this. So you are spot on. I think what's happened with the kind of this, they talk about a hockey stick. This is almost like a flat wall now with the rate of innovation right now in this space. And so we do have a lot of folks wanting to go straight from curious to native. And so that's definitely where the partner ecosystem comes in so hard because there just isn't anybody or any teams out there that literally do from, here's my blank database and I want an API that does all the stuff, right? Like that's a big chunk. We can definitely help with the model to delivery piece. Well, you guys are obviously a featured company in this space. Talk about the expertise. A lot of companies are like, I won't say faking until they make it. You can't really fake security. You can't really fake AI, right? So there's going to be a learning curve. There'll be a few starts will come out of the gate early. You guys are one of them. Talk about what you guys have as expertise as a company, why you're successful and what problems do you solve for customers? No, I appreciate that. Yeah, we actually, we love to tell the story of our founder, Nir Shavitsa. He's a 20 year professor at MIT, actually was doing a lot of work on kind of multi-core processing before there were even physical multi-cores and actually even did a stint in computational neurobiology in the 2010s. And the impetus for this whole technology has a great talk out on YouTube about it where he talks about the fact that his work there, he kind of realized that the way neural networks encode and how they're executed by kind of ramming data layer by layer through these kind of HPC style platforms actually was not analogous to how the human brain actually works. So we're on one side, we're building neural networks and we're trying to emulate neurons. We're not really executing them that way. So our team, which one of the co-founders also XMIT, that was kind of the birth of why can't we leverage this super-performance CPU platform which has those really fat, fast caches attached to each core and actually start to find a way to break that model down in a way that I can execute things in parallel not having to do them sequentially. So there's a lot of amazing like talks and stuff that show the kind of the magic, if you will, a part in the part of neural magic. That's kind of the foundational layer of all the engineering that we do here. In terms of how we were able to bring it to reality for customers, I'll give one customer a quote where it's a large retailer and it's a people counting application. So a very common application and that customer has actually been able to show literally double the amount of cameras being run with the same amount of compute. So from a one-to-one perspective, two-to-one, business leaders usually like that math, right? So we're able to show pure cost savings but even performance-wise, we have some of the common models like your ResNets and your Olos where we can actually even perform better than hardware accelerated solutions. So we're trying to do, I hate to just dumb it down to better, faster, cheaper but from a commodity perspective, that's where we're accelerating. It's not a bad business model. Make things easier to use, faster and reduce the steps it takes to do stuff. So that's always going to be a good market. Now you guys have deep sparse, which we've talked about on our CUBE conversation prior to this interview, delivers ML models through the software. So the hardware allows for a decoupling, right? Which is going to drive probably a cost advantage. Also, it's also probably from a deployment standpoint, it must be easier. Can you share the benefits? Is it a cost side? Is it more of a deployment? What are the benefits of the deep sparse when you guys decoupled the software from the hardware on the ML models? No, you actually hit them both because that really is primarily the value because ultimately, again, we're so early that and I came from this world in a prior life where I'm doing Java development and the WebSphere, WebLogic, Tomcat open source, right? When we were trying to do innovation and we had innovation buckets because everybody wanted to be on the web and have their app in a browser, right? We got all the money we needed to build something and show, hey, look at the thing on the web, right? But when you had to get into production, that was the challenge. So to what you're speaking to here, in this situation, we're able to show we're just a Python package. So whether you just install it on the operating system itself or we also have a containerized version, you can drop on any container orchestration platform. So ECS or EKS on AWS. And so you get all the auto scaling features. So when you think about that kind of a world where you have everything from real-time inferencing to kind of after hours batch processing inferencing, the fact that you can auto scale that hardware up and down and it's CPU based, so you're paying by the minute instead of maybe paying by the hour at a lower cost shelf. It does everything from pure cost to again, I can have my standard IT team say, hey, here's the Kubernetes in the container and it just runs on the infrastructure we're already managing. So you have operational cost and again, and many times even performance. So that's, I can throw CPUs if I want to. Yeah, so that's easier from the deployment too. And you don't have this kind of, kind of blank check kind of situation where you don't know what's on the back end on the cost side and you control the actual hardware and you can manage that supply chain. And keep in mind exactly because the other thing that sometimes gets lost in the conversation depending on where a customer is some of these workloads like, you and I remember a world where even like the round trip to the cloud and back was a problem for folks, right? We're used to extremely low latency and some of these workloads absolutely also adhere to that. But there's some workloads where the latency isn't as important. Now we actually even provide the tuning that if we're giving you five milliseconds of latency and you don't need that, you can tune that back so less CPU lower cost. Now throughput and other things come into play but that's the kind of configurability and flexibility we give for operations. All right, so why should I call you if I'm a customer or prospect, Neural Magic? What problem do I have or when do I know I need you guys? When do I call you in and what does my environment look like? When do I know? What are some of the signals that would tell me that I need Neural Magic? No, absolutely. So I think in general, any neural network, the process I mentioned before called sparsification. It's an optimization process that we specialize in. Any neural network can be sparsified. So I think if it's a deep learning neural network type model, if you're trying to get AI into production, you have cost concerns, even performance wise, I certainly hate to be too generic and say, hey, we'll talk to everybody. But really in this world right now, if it's a neural network, it's something where you're trying to get into production. We are definitely offering kind of an at scale performance deployable solution for deep learning models. So neural network, you would define as what? Just devices that are connected that need to know about each other. What's the state of the art current definition of neural network for customers that may think they have a neural network or might not know they have a neural network architecture? What is that definition for neural network? That's a great question. So basically machine learning models that fall under this kind of category, you hear about transformers a lot or I mentioned about YOLO, the YOLO family of computer vision models or natural language processing models like BERT. Yeah, if you have a data science team or even developers, some even regular, I used to call myself a nine to five developer because I worked in the enterprise, right? So like, hey, we found a new open source framework. I used to use spring back in the day and I had to go figure it out. There's developers that are pulling these models down and they're figuring out how to get them into production. So I think all of those kinds of situations, if it's a machine learning model of the deep learning variety, that's really specifically where we shine. Okay, so let me pretend I'm a customer for a minute. I have all these videos, like all these transcripts. I have all these people that we've interviewed, CUBE alumni's and I say to my team, let's AIify, sparsify theCUBE. What do I do? I mean, do I just like, my developers got to get involved and they're going to be like, oh, I uploaded to the cloud, do I use a GPU? So there's a thought process and I think a lot of companies are going through that example of let's get on this AI. How can it help our business? What does that progression look like? Take me through that example. I mean, I made that CUBE example of it, but we do have a lot of data. We have large data models and we have people and connected to the internet. And so we're kind of seeing like there's a neural network. I think every company might have a neural network in place. Well, and I was going to say, I think in general, you all probably do represent even the standard enterprise more than most because even the enterprise is going to have a ton of video content, a ton of text content. So I think it's a great example. So I think that that kind of C, or I'll even go ahead and use that term data lake again of data that you have, you're probably going to want to be setting up kind of machine learning pipelines. They're going to be doing all of the preprocessing from kind of the raw data to kind of prepare it into the format that say a YOLO would actually use or let's say BERT for natural language processing. So you have all these transcripts, right? So we would do a preprocessing path where we would create that into the file format that BERT, the machine learning model would know how to train off of. So that's kind of all the preprocessing steps. And then for training itself, we actually enable what's called sparse transfer learning. So that's transfer learning is a very popular method of doing training with existing models. So we would be able to retrain that BERT model with your transcript data that we have now done the preprocessing with to get it into the proper format. And now we have a BERT natural language processing model that's been trained on your data. And now we can deploy that onto deep sparse runtime. So that now you can ask that model, whatever questions or I should say pass, you're not going to ask it, those kinds of questions, it's a GPT. Although we can do that too, but you're going to pass text through the BERT model and it's going to give you answers back. It could be things like sentiment analysis or text classification. You just call the model and now when you pass text through it, you get the answers better, faster, cheaper. I'll use that reference again. Okay, we can create a QBOT to give us questions on the fly from the AI bot, you know, from our previous guests. And I will tell you, using that as an example, so I had mentioned OPT before kind of the open source version of chat GPT. So, you know, typically that requires multiple GPUs to run. So our research team, I mentioned earlier, we've been able to sparsify that over 50% already and run it on only a single GPU. And so in that situation, you could train OPT with that corpus of data and do exactly what you say. Actually, we could use Alexa. We could use Lex to actually respond back with voice. How about that? We'll do an API call and we'll actually have an interactive Alexa-enabled bot. Okay, we're going to be a customer. Let's put it on the list. But this is a great example of what you guys call software-delivered AI, a topic we chatted about on theCUBE conversation. This really means, this is a developer opportunity. This really is the convergence of the data growth, the restructuring of how data is going to be horizontally scalable meets developers. So this is an AI developer model going on right now, which is kind of unique. It is, John. And I will tell you what's interesting. And again, folks don't always think of it this way. The AI magical goodness is now getting pushed in the middle where the developers and IT are operating. And so it, again, that paradigm, although for some folks seem obvious, again, if you've been around for 20 years, that whole, all that plumbing is a thing, right? And so what we basically help with is when you deploy the deep sparse runtime, we have a very rich API footprint. And so the developers can call the API, IT ops can run it, or to your point, it's developer friendly enough that you could actually deploy our off the shelf models. We have something called the sparse zoo where we actually publish free optimized or pre-sparsified models. And so developers could literally grab those right off the shelf with the training they've already had and just put them right into their applications and deploy them as containers. So yeah, we enable that for sure as well. It's interesting DevOps was infrastructure as code and we had a last season series on data as code, which we kind of coined. This is data as code. This is a whole nother level of opportunity where developers just want to have programmable data and apps with AI. This is a whole new way. Well, great stuff. Our news team at SiliconANGLE on theCUBE said you guys had a little bit of a launch announcement you wanted to make here on the AWS startup showcase. So Jay, you have something that you want to launch here? Yes, and thank you, John, for teaming me up. So I'm going to try to put this in the vein of like an AWS main stage keynote launch, okay? So we're going to try this out. So a lot of our product has obviously been built on top of x86. I've been sharing that to past 15 minutes or so. And with that, we're seeing a lot of acceleration for folks wanting to run on commodity infrastructure. But we've had customers and prospects and partners tell us that ARM and all of its kind of variants are very compelling both cost performance wise and also obviously with Edge. And wanted to know if there's anything we could do from a runtime perspective with ARM. So we got the work and it's a hard problem to solve because the instruction set for ARM is very different than the instruction set for x86. And our deep tensor column technology has to be able to work with that lower level instructions. But working really hard, the engineering team has been at it and we are happy to announce here at AWS startup showcase that deep sparse inference now has or inference runtime now has support for AWS Graviton instances. So it's no longer just x86, it is also ARM. And obviously also opens up the door to Edge and further out the stack. So that optimize once run anywhere, we're not going to open up. So it is an early access. So if you go to neuromagic.com slash Graviton you can sign up for early access but we're excited to now get into the ARM side of the fence as well on top of Graviton. So that's awesome. Our news team is going to jump on that news. We'll get it right up to get a little scoop here on the startup showcase. Jay Marshall, great job. That really highlights that the flexibility that you guys have when you decouple the software from the hardware. And again, we're seeing open source driving a lot more in AI ops now with machine learning and AI. So to me that makes a lot of sense and congratulations on that announcement. Final minute or so we have left. Give a summary of what you guys are all about. Put a plug in for the company, what you guys are looking to do. I'm sure you're probably hiring like crazy.  No, I appreciate that so much. So yeah, join us on neuromagic.com. Part of what we didn't spend a lot of time here are optimization tools. We are doing all of that in the open source. It's called sparse ML and I mentioned sparse zoo briefly. So we really want the data scientist community and ML engineering community to join us out there. And again, the deep sparse runtime, it's actually free to use for trial purposes and for personal use. So you can actually run all this on your own laptop or on an AWS instance of your choice. We are now live in the AWS marketplace. So push button deploy, come try us out and reach out to us on neuromagic.com. And again, sign up for the Graviton early access. All right, Jay Marshall vice president of business development neuro magic here. Talk about performance, cost effect and machine learning at scale. This is season three, episode one, focusing on foundational models for stars building data infrastructure and AI. AI native, I'm John Furrier with theCUBE. Thanks for watching.


Hello and welcome to the session. I am Deepika here. Let's discuss the question which says A formal mix is two brands P and Q of cattle feed Brand P costing rupees 250 per bag contains three units of nutritional element A 2.5 units of element P and two units of element C Brand Q costing rupees 200 per bag contains 1.5 units of nutritional elements A 11.25 units of element B and three units of element C the minimum requirements of nutrients A, B and C are 18 units 45 units and 24 units respectively Determining the number of bags of each brand which should be mixed in order to produce a mixture having a Minimum cost per bag. What is the minimum cost of the mixture per bag? So let's start the solution Let X and Y be the number of bags of brand P and brand Q in the mixture respectively so Obviously X is greater than equal to 0 and Y is greater than equal to 0 Now according to the question of formal mixes two brands P and Q brand P contains three units of nutritional element A and brand Q contains 1.5 units of nutritional element A and The minimum requirement of nutrient A is 18 units So according to the question plus 1.5 Y greater than equal to 18 now this is a constraint on Nutritional element A that is 2X plus Y greater than equal to 12 Again brand P contains 2.5 units of nutritional element B and brand Q contains 11.25 units of nutritional element B and the minimum requirement of the nutrient B is 45 units So again, we have 2.5 X plus 11.25 Y greater than equal to 45 now this is a constraint on nutritional element B that is X plus 4.5 Y greater than equal to 18 or This can be written as 2 X plus 9 Y greater than equal to 36 Now again according to the question brand B contains two units of nutritional element C and brand Q contains three units of Nutritional element C and the minimum requirement of nutrient C is 24 units So now we have 2 X plus 3 Y Greater than equal to 24. So this is a constraint on Nutritional element Now again, we are given the cost of each bag of brand P which is rupees 250 and the cost of each Bag of brand Q which is rupees 200 Now according to the given problem we have total cost in rupees is equal to 250 X plus 205 Let Z is equal to 250 X plus 205 Hence the mathematical formulation the given problem is minimize Z is equal to 250 X plus 200 Y Subject to the constraints Plus Y greater than equal to 12 2 X plus 9 Y greater than equal to 36 2 X Plus 3 Y greater than equal to 24 X greater than equal to 0 and Y greater than equal to 0 Now Z is equal to 250 X plus 200 Y is our objective function Let us take this as number one. Now we have to minimize set Subject to these given constraints. Let us number these constraints as two three four and five Now we will draw the graph and Find the feasible region subject to these given constraints Now the equation of the line corresponding to the inequality 2 X plus Y greater than equal to 12 is 2 X plus Y is equal to 12 So we will first draw the line representing the equation 2 X plus Y is equal to 12 clearly the points 0 12 and 6 0 like on the line 2 X plus Y is equal to 12 so the graph of this line can be drawn by plotting points 0 12 and 6 0 and then joining them Let us take a as a point 0 12 and B as a point 6 0 So a be represent the equation of the line 2 X plus Y Is equal to 12 Now this line divides the plane into two half planes We will consider the half plane which will satisfy to So the half plane Which does not contain the origin will satisfy too So we will consider that half plane only Now again the equation of the line corresponding to the inequality 2 X plus 9 Y greater than equal to 36 is 2 X plus 9 Y is equal to 36 Now clearly the points 0 4 and 18 0 lie on the line 2 X plus 9 Y is equal to 36 So we will draw the line representing the equation 2 X plus 9 Y is equal to 36 on the same graph by plotting the points 0 4 and 18 0 and then joining them Now let us take C as a point 0 4 and D as a point 18 0 So CD represents the equation of the line 2 X plus 9 Y is Equal to 36 now CD divides a plane into two half planes We will consider the half plane which will satisfy 3 So we will consider the half plane which does not contain the origin In a similar way We will represent 2 X plus 3 Y greater than equal to 24 graphically by drawing the line 2 X plus 3 Y is equal to 24 Now the points which satisfy this equation are 0 8 and 12 0 So again, we will plot these points on the same graph and then we will join them Now let us take E as a point 0 8 and F as a point 12 0 So E of represents the equation of the line 2 X plus 3 Y is Equal to 24 now again this line divides the plane into two half planes So we will consider the half plane which will satisfy 4 so clearly The half plane which does not contain the origin will satisfy 4 so we will consider that only Again X greater than equal to 0 and 5 greater than equal to 0 implies That the graph lies in the first quadrant only Now the lines a b c g and e f Intercept each other At three points. Let us take this as l This is m and this is m So clearly the coordinates of l r 3 6 the coordinates of m r 9 by 2 3 and the coordinates of n r 9 2 Now here the yellow shaded portion in this graph is the feasible region Satisfying all the given constraints now clearly the feasible region is unpounded with corner points on one side as a l n 90 so here the feasible region is Unbounded with coordinates of the inner points 0 12 3 6 with coordinates 9 2 and D with coordinates 18 0 Now according to the corner point method Minimum value of set will occur at any of these corner points So we will evaluate set at each corner point now at the point a with coordinates 0 12 Z is equal to 250 Into 0 plus 200 into 12 which is equal to 0 plus 2400 and that is equal to 2400 Now at the point L whose coordinates are 3 6 Z is equal to 250 into 3 Plus 200 into 6 which is equal to 750 plus 1200 and that is equal to 1,950 now At the point n whose coordinates are 9 to Z is equal to 250 into 9 plus 200 into 2 which is equal to 2250 plus 400 and that is equal to 2650 now at the point D Whose coordinates are 18 0 Z is equal to 250 into 18 plus 200 into 0 which is equal to 4500 plus 0 and that is equal to 4500 hence minimum value of Z is equal to 1,950 which occurs when x is equal to 3 and y is equal to 6 but here the feasible region Is unbounded So 1,950 may or may not be the minimum value of Z So to decide this issue We will graph the inequality X plus 200 y less than 1,950 To check whether the resulting open half plane has points in common with feasible region or not if it has common points then 1,950 will not be the minimum value of Z. Otherwise 1,950 will be the minimum value of Z now here the green shaded region in this graph excluding the line 250 x plus 200 y is equal to 1,950 or 5x plus 4 y is equal to 39 represents the open half plane 5x plus 4 y less than 39 or Z less than 1,950 Now clearly it has no point common with the feasible region hence Z is not less than 1,950 in the feasible region except at 36 hence 3 bags of brand P and 6 bags of brand Q should be mixed in order to produce a mixture having a minimum cost per pack that is rupees 1,950 So the answer for this question is three bags brand P six bags of brand Q minimum cost of the mixture is rupees 1,950 so this completes our session. I hope the solution is clear to you. Bye and have a nice day


Two of the studies talked about backlash, and they were persuasive. Can you speak to a sense of, have you looked at the dynamics of the backlash? Do you see backlash as being a transient phenomenon, more long-term phenomenon? What do we know about the timeline on which backlash happens, and is there optimism that it would subside? That would go in line with what Ashwini was just saying, right? That if there is backlash, it's a sort of adjustment cost, or how should we think about it? So I guess. So actually, I didn't mention this, but in my paper, that result I showed you where there was backlash is for people who've experienced quotas more than once, I think at least once. So then when you've experienced quotas two or three times, then this backlash goes away. So we show that at least this is a short-term backlash, but in the long-term, we kind of argue, and we show a little bit, that norms update and change, and consistent with the fact that it's only short-term. So that's not something I have tested yet. I shall. But it's indeed consistent with, I mean, I expect to find result consistent with what Joseph is pointing out, and it's also consistent with other papers that show that norm update with time, so that we need to have this repetition, such that you have also a lower interaction and implicit association taste and things like that. So that would make sense. Yeah, I think, I mean, Joe's results are absolutely what we find also in India, which is both for gender and for caste. What started as a more kind of a formal mechanism has now created a set of individuals who are respected and valued more than other members of their community are. And so I definitely believe that it's a transient phenomenon, the backlash. Yeah, well, one of my questions just got answered, but I'll sort of restate it. So I was trying to sort of figure out, Prof Deshpande was saying that there's no efficiency effects in the railway sector over time, yet the backlash studies show there's some sort of, for example, an effort effect. And so perhaps the way to make the two consistent would be that backlash is a short-term effect. That's what I sort of understood from this discussion. My other question is, so to Joe, is when you say beliefs about skill gaps or beliefs about disadvantage, for lack of a better word, when you say beliefs and skill gaps, it seems like it's sanitizing sort of racial beliefs. Because racism has this inherent idea of these are the skill gaps, and they're sort of biologically determined. And you could just call them skill gaps. But at the base would be something that's much more, it's not really sort of an old quest, right? And so how do you think about racism in this sort of perspective? I was wondering if you thought about that. Another way, I guess, you can term that skill gap is statistical discrimination. But it could be other forms. But I think it could, in likeliness, be just statistical discrimination. And I guess, yeah, it's hard to justify because there's lots of different contexts where the skill gap could exist. But for example, if you think of the gender context, we're currently working on a study to measure this skill gap in the IT sector to kind of understand the differences in at least beliefs between males, beliefs about people's skill in the IT sector. So I think, yeah, it mainly seems to us from our current studies that it's based on statistical discrimination. And a lot of the time, there's not necessarily these differences. These differences don't necessarily exist. It's just, yeah, complete perception. If I may just add up on that. So in the case of the household survey, what I observe would be also kind of inconsistent with this notion that there's a decrease in productivity. Because if you look at the trust data, even member of the non-SCST, they don't decrease their trust in the pancayat. At the moment, there is the SC quota. They don't say that there's more crime or feeling of safety in the village at the moment of the quota. So that would be also inconsistent. Very interesting presentations from all the panelists. But I'm wondering, now we get into the point where we are beginning to see a gestation period for the effectiveness of affirmative action. And a gestation period that may differ from one sector or one activity to the other. And I'm saying this because with education, I think we are beginning to see positive results from affirmative action after perhaps a generation or two. Whereas with race, we are actually going through cyclic motions where you have positive impacts, which seem to be reversed over after a certain period. So that's my first point, and I'll be interested to know what you think. The second one is whether we are also experiencing a shifting of the goalposts, particularly with reference to meritocracy, as we look at the outcomes of affirmative action. And certain sectors seem to suggest that this may actually be happening, particularly in industry. And I'm looking at the financial sector where if you look at banking staff, where women dominated the lower ranks, and as women became more qualified, interestingly, they stayed in the same positions in many of the banks with higher education. Because the goalposts have shifted for rising within that. These are some of the complexities that I'll be interested in knowing what your observations are. Thank you. I want to take that first. So responding to your first point, I definitely think there is a gestation period in terms of race. And you mentioned a generation. We haven't observed a full generation that has been subject to affirmative action legislation yet. We are starting to see effects in higher education where there is no official affirmative action policy in South Africa, for instance. But where you start seeing the composition of higher education changing. And this should feed through into the rest of the economy. So I think there's an overlap and a complementarity between the changing in the education sector, but also how that allows affirmative action to take effect in the labor market. So I think when you mention a gestation period, I think at least from a labor market race perspective, it could be a generation. So I just wanted to go back to the backlash question. And I thought it was very interesting that you said that after playing a couple of rounds where you change after being exposed to quotas a couple of times, people become more accepting of quotas. But actually in real life in India, don't you agree that we are seeing the opposite? We have had affirmative actions for what, 60 years now. And yet now it is only in the past couple of years where we are seeing upper-cast seeking reservations as a backlash. And I would turn that as a backlash for quotas for SCSTs. So in my mind, I was just trying to reconcile these two findings and what could be the explanation. So I would say, based on my model, that maybe beliefs changing in maybe after some time when you've had quotas for such a long period of time, people maybe start to believe that these people don't deserve quotas anymore because maybe they observe that there's a lot more people in, say, the upper class. But that would be consistent with what I would believe based on my model. But I don't have any data to show that.


So we've gotten as far as developing a model for the geometry of a diatomic molecule and we've determined that rather than thinking about a molecule with two different masses and two different atoms at two different positions, we can get away with thinking about a molecule that's in the same orientation but only a single point with mass, a mu, the reduced mass, a distance r from the origin with again the same angles theta and phi. So the other advantage of using this coordinate system in addition to reducing the number of variables that we have to think about is it also helps us distinguish pretty clearly between the two different types of motions this molecule can undergo, vibrational motions and rotational motions. When the molecule vibrates, if it keeps the center of mass where it is and changes its bond length by vibrating, in this model that just corresponds to changing the length of this coordinate r, the distance away from the origin. On the other hand, if the molecule rotates, if it changes its orientational angle, then that's a change in theta or phi or both of those at the same time. So rotations are described by theta and phi, vibrations are described by changes in r. And we're actually going to treat those two problems separately. We'll postpone vibrations for a little while and let's think first only about the rotations. So the way we'll do that is we'll require that r be constant, r is not going to change. So when this molecule rotates, it does so with a fixed bond length. So in other words, it's a rigidly rotating molecule, it doesn't change it's not flexible but it's rigid, it doesn't change its bond length. So r is constant, we are going to allow theta and phi to change. So those two variables can change and therefore the way that we'll describe the state of this system, the two variables that can change are theta and phi and the state of this system is going to be described at least quantum mechanically by a wave function that depends on theta and on phi. So in order to describe this system quantum mechanically with a wave function, we're going to need to start talking about Schrodinger's equation. So let's remind ourselves of what Schrodinger's equation is. In general, Schrodinger's equation is a kinetic energy term which looks like some constants minus h squared over 8 pi squared mass, but remember now our mass, the mass of this particle that we're studying is this reduced mass mu times the second derivative in the form of this Laplacian acting on the wave function. Our wave function only depends on two variables theta and phi and then we've got a potential energy term multiplying the wave function. Kinetic energy plus potential energy must equal e total energy. So h psi, Hamiltonian acting on psi gives us energy multiplying psi. So that's Schrodinger's equation in its general form. In this particular case, if we think about the potential energy term, for this diatomic molecule this potential energy term is asking how different is the potential energy for this diatomic molecule if it has this orientation or this orientation or this orientation and if you think about a gas molecule changing its orientation, we don't expect its potential energy to be any different than any one of these orientations. So we will assume that the potential energy is equal to zero for this model that we're calling the rigid rotor model. So if we make that assumption, Schrodinger's equation simplifies quite a bit. Leaving out the variable, the coordinate dependence, kinetic energy term minus h squared over 8 pi squared mu del squared acting on psi is equal to e times psi. In other words, kinetic energy term is equal to e times psi. That looks an awful lot like what we had when we solved the 3D particle in a box problem. Really the only difference in the equation is I've got a mu here for a mass instead of an m, but there's one important difference that we need to solve this problem in spherical polar coordinates, theta and phi, whereas we solved the 3D particle in a box problem in Cartesian coordinates, x, y and z. So let me summarize so we don't get confused the properties of this rigid rotor model. So we've assumed that for our diatomic molecule the bond length is constant, it stays rigid as it rotates, that's why we call it a rigid rotor. We've assumed that the potential energy is zero, that's the same assumption we made for the particle in a box, potential energy is zero. That means we've only got two variables to worry about, theta and phi, so our wave function is going to depend on theta and phi. This is a reminder that we're doing this problem in spherical polar coordinates, theta and phi, rather than x, y and z. The other important difference with the 3D particle in a box model is the boundary conditions. Remember for the particle in a box we can find a particle in a box and the wave function had to reach zero as we got to the edges of the box. For this case there is no edge, the coordinates we're talking about are theta and phi. If I take the variable theta and I keep increasing it, the molecule bends down away from the z-axis. If I keep increasing it there's no edge of the box, the molecule can just spin, can I have any values of theta and phi, well I want, if I increase theta from zero to pi and keep going it just does circles. So rather than an edge of a box that we have to worry about the real periodic boundary conditions we have to worry about are the fact that in particular if I take phi, if I take this molecule, if I start increasing the value of phi, the molecule will spin around the z-axis and when I spin by a full two pi radians around the z-axis I get back to where I started. So what that means is if I evaluate the function either at an angle theta and phi like I've drawn it here or at an angle theta and phi where I've spun it by a full revolution around the z-axis and get back to where I started the wave function before and after I spin it around has to be exactly the same. So we're going to require that our wave function obey this boundary condition. The wave function at theta and phi has to have the same value if I rotate phi by an angle of two pi. So that's the requirement we're going to place on our wave function. So with those things in mind we need to rewrite this Schrodinger equation now not with del squared equal to what we used in Cartesian coordinates so just as a reminder we won't be using this right now but in Cartesian coordinates the Laplacian del squared is the second derivative operator d squared dx squared plus d squared dy squared plus d squared dz squared so that's what we did for the 3D particle in a box. In spherical polar coordinates del squared is still a second derivative operator second derivative with respect to these r and theta and phi coordinates but it looks a little bit different. It looks like let's see the second derivative with respect to r looks a little bit convoluted has the d dr separated by a little bit likewise there's a second derivative with respect to theta but the two d d theta derivatives are separated they have this sine theta sandwiched in between them and they have some terms out front and there's a third term one over r squared sine squared theta the second derivative with respect to phi does look like an ordinary second derivative. So those three terms all together you have probably seen in a calculus three class at some point that's what the Laplacian looks like that's the second derivative Laplacian in spherical polar coordinates it gets a little bit simpler for us because once we've made this assumption that r is constant the derivative with respect to r those terms go to zero so we don't have to worry about the d dr terms specifically because we're not allowing the value of the bond length to change so it can't have a derivative so what we're left with is just the second two terms if I then take this expression for the Laplacian and plug it into Schrodinger's equation and that'll be the last thing to write on the board for this lecture so the rigid rotor Schrodinger equation the one we'll want to solve is the Schrodinger equation with r constant so this term goes away with v equals zero so this term goes away and with the Laplacian in spherical polar coordinates so I use these two terms for the Laplacian so I've got minus h squared over eight pi squared mu let me notice also that both of these terms that I'm about to write down this term and this term they both have a one over r squared in them so let me go ahead and put the r squared here from both of those terms and then I've got one over sine theta d d theta sine theta d d theta that's the remaining terms from here and then I've also got one over sine squared theta d squared d phi squared those things acting on the wave function which remember as a function of theta and phi must equal energy times the wave function which is still a function of theta and phi all right so this expression that I've just written down that is the Schrodinger equation in the form we need to worry about it to describe a diatomic molecule so remember what that means is we're looking for some function some wave function psi of theta and phi that obeys this particular equation that when I do this stuff on the left to it I get back a constant times the same wave function that I started with so the next thing we'll tackle is trying to find wave functions that obey this Schrodinger's equation.


Yeah, we on boss talk one on one. One on one. Yeah, we gonna talk. The way that the music moved, man. Then, like I said, when I seen you, I was like, man, did DJ M, did he have by heart a way or what was it to deal with that? So what happened with the DJ M6? At first he didn't have, it wasn't, you came off with it first. Yeah, like I dropped it. Yeah, you dropped it. Like really, I didn't even drop it.  He sent it to a DJ. I don't remember who got it first. I want to say it was DJ Bitt Tiny, man. Who we slipped the two first and then DJ... What was that? What was y'all that? Man, what's the name of that club? What was it right there?  The V-Li, V-Li, down here? V-Li had a lot. Yeah, they had the three, three stores in there. I went in that thing. Yeah, what they had the folks.  Magic City for show, we dropped it.  Let's just go out and do it, like his own. Next thing you know, it started getting big in the clubs, in the streets, niggas round, round, playing it. DJ Envy came down. My DJ, DJ Ann Durtle was playing it in 1145.  Yeah, like Craig, like, whoa.  It was that moment, like.    Favor, man, that's favor, bro. You feel me? That's favor. And the crazy thing, we go home. Like we, I was still, we weren't even, you know what I'm saying?  So you hadn't did the video yet or nothing like that? No, I haven't. No.  Wow. And DJ Envy called my brother home. How did he get his number? I don't know, you know what I'm saying? I'm in the room, sleep. He coming out like, hey, bro. Some nigga named DJ Envy just called me. I tough up. DJ Envy. He like, yeah, you know who this nigga is?  I love it, man.   I said, man, whatever. I roll over and go back to sleep. He call back. He say, bro, it's a DJ, nigga, DJ Envy.  I don't think he believed it either. So I finally got up, call him back then. He called him. He was like, yo, what's up guys? It's DJ Envy. I'm like, you knew the voice, nigga.   I'm like, what up? You favorite? He like, yeah, well man, I like the rest of the world. I'm like, hmm, for real. Oh, I'm on the pre-sale. How you getting my brother in on him? You know what I'm saying? You're getting hot on that nigga, man. But nah, I had to, I'm trying to open them up and see if it's real, like, and it was real.  Hey, I called my manager. Hey, bruh, nah, that's him for real, bro. We got, what else?  He wanted to do, what did he want to do? So what we did, I don't know initially what he wanted to do. Maybe he did want to buy us on, but that's something I don't know. I didn't have that discussion. But what happened was, we did like a partnership on the record, 50-50 partnership, and we redropped it. Wow. You see what I'm saying?  Went crazy, man.   Maybe Birdman playing this motherfucker. This might be one. But man, only you ain't know a whole bunch of people who experienced this and what you saying. You know what I'm saying? It's dope though that you, will you ever have, will you be able to make a song bigger than that? Well, of course. Have you made a song bigger than that? I don't think I made it today due to the normals, but I will. I'll make plenty more bigger than that. How much pressure do you put yourself under to make something bigger than that? I don't put myself under no pressure because I honestly feel like God gave me many times to do it the first time. And I did that song on the spot. Like it wasn't, I ain't sitting down, think about it or nothing. It was like, mm, I went in, did it. And the truth about all the way, right? I had did a song already, I was like, well, at least a hook. I did a hook like years ago. And when he put me on the spot, London playing the beat and there's a lot of us in the studio. So my manager like, get in there, what you scared of about you? Now you can go out to talk, get in there, buy you a jukebox, just make some. I go in there, I'm thankin' and I hear them make presents in the top month. What take it so long, bro? Say something. So I called my engineer, done salute. You know what I'm saying? Hey, bro, you remember that song I did when I was talking about magic, all the way, pin it all the way.  So now I step behind the thing in the studio behind it. So it don't pick up on the mic. I'm listening all the way, I'm listening all the way, I'm laying on the man, all right, back, boom, I hang up. And I go in there, all the way, all the way. You know what I'm sayin'? Tryin' to make it go to the beat. I ain't nah, nah, niggas with that. It just came out, I'm lookin' in the room. I'm sayin' niggas like, Diggs was over that door, all that. I ain't nah, nah, niggas with that. So I was like, and to be honest, it was a lot of niggas on all the way at first. Really? Hell yeah. Like, you know how you do a song in the studio? Yeah, yeah, yeah, a lot of people. And then niggas just boom, boom, boom, boom, boom, put a verse on there. It was a lot of niggas on there.  Can't do that. Nah, you trippin', bro. This, you need to do this. You need to go do a second verse, bro. You trippin'. And I went and did a second verse, and I was with, I was at a, I forgot the studio I was at, but your scooter was in, he was like, this the one. God damn, Alibaba, this the one.  You feel what I'm sayin'?  I ain't goodbye to none. I ain't never thought this deep about all the way. And that's all. Man, we went in on every one of my favorite songs. That's what, that's all that's happenin' right here. Die, die! I ain't ask now, nigga, for nothing. I took the heart away. I put up with me overcomin' with the dope. They put my heart away.


Hey, Psych2Goers! Have you ever stopped to think whether what you're feeling in your relationship is genuine? Perhaps you're thinking in a way that has you questioning your true feelings for your significant other. This video discusses the differences between a codependent relationship and authentic love to give an insight into what people may experience. But if you are having codependent thoughts, that doesn't mean you aren't genuinely in love with another person. What codependent may sound like? I need you and I know you need me. I can't love without you and I know that you can't live without me. What authentic love may sound like? I choose to be in a relationship with you and you choose to be with me. I enjoy being in your company and appreciate spending time with you. However, I am also happy having my alone time. I do not rely on you alone to make me happy. In a codependent relationship, there has to exist a level of dependency, either from one person or both parties involved. Making somebody else feel responsible for your happiness and your well-being is a form of emotional manipulation. Choice is an important factor in any relationship. When individuals feel that they are making a choice in any relationship, this allows an individual to feel that they have a sense of control. When people don't feel like they have a choice, this can cause pressure and individuals may feel trapped or that they cannot actively be in control of what is happening in their relationships. People should be in relationships with each other because they want to and not because they feel that they need to. Number two, dependent. What codependent may sound like? I need you to feel okay, otherwise I will not be okay. What authentic love may sound like? You are your own person and are allowed to experience feelings without judgment from me. People's feelings should not be dependent on others and this could come across as emotional manipulation because people should be free to experience their own emotions and feelings without being made to feel that they're moved or how their feeling is based on how their partner feels or that they should be okay in order for their partner to be as well. When your identity is based solely on people pleasing and you feel responsible for everyone's well-being, you might find yourself reacting to situations rather than by your own choice. Number three, communication. What codependency may sound like? You should know what I need. If I have to explain it to you then you clearly don't listen to me or understand me properly. What an authentic love may sound like? I will communicate my needs to you openly and not just expect you to know what I need. A codependent mindset makes it hard to communicate effectively as people are often unaware of their own wants and needs and when people are aware they may be reluctant to express them. Dishonesty can also develop as a habit when people are more interested in maintaining a sense of control than actually communicating. In order for any relationship to be successful individuals must learn to communicate honestly and effectively. Number four, support. What codependency may sound like? If you do not support me I will guilt trip you so you understand that I am not happy. What authentic love may sound like? I will ask for support from you and others when I need it. I will not take my anger out on you if you can't support me in the way that I need it at the time. Stress can play a huge factor in any relationship especially when there are communication and boundary issues. Codependent partners may feel insecure about being abandoned, being alone and not being supported by their partner. As a result they may end up taking their frustration out on their partners and blaming them unnecessarily which can cause relationship stress. Number five, boundaries. What codependency may sound like?  What authentic love may sound like? I respect your boundaries and do my best to discuss them with you if I or step them. In the same way I will inform you about my boundaries and communicate how I want to be treated and spoken to. People in both roles in a codependent relationship tend to have problems recognizing, respecting and reinforcing boundaries. Having boundaries is about having respect for each other and recognizing that individuals are not responsible for other people's happiness. Setting and maintaining boundaries is an important skill that cannot be ignored in any relationship. Number six, control. What codependency may sound like? You would do what I asked if you truly loved me. What authentic love may sound like? I understand that there will be times when we disagree on things but that does not dictate whether you love me or not. We will communicate those differences openly and resolve any differences with love and respect. Typically neither person in a codependent relationship has very good self-esteem which will often involve seeking approval or validation from others and wanting to have a sense of purpose. If these factors are not met, this can lead to further insecurity, controlling behavior and emotional manipulation. And number seven, self-worth. What codependency may sound like? I need to feel wanted and needed by you. I don't feel valued by you if you don't show me that. What authentic love may sound like? I am valued and worthy without needing approval from others. My role is to be a supportive partner, not a therapist, more to try and fix other people's problems. One of the major signs of codependency is either feeling a sense of responsibility towards others to take care of them or expecting others to take care of us. An example of this may stem from childhood when the caretaker learns there may be negative consequences for failing to take care of a parent's needs. This fear of something bad happening causes people to take care of others rather than it being out of genuine affection, which may indicate codependency. Can you relate to any of these signs? Let us know in the comments below and share this video with others who might benefit. As always, the references and studies used are in the description below. Until next time friends, take care and thanks for watching.


I just want to take this short time right now to speak to you on a topic that I had to face with in my life going, living my life in Nigeria and coming back here and just as a church, as a whole, as a leadership team and as our pastors have been facing with this issue. I just want to be able to talk to you shortly on how to overcome your doubt. Tell your neighbor, overcome your doubt. So each and every single person in this place, we face doubt in our lives. It's something that each and one of us, we fight on our daily basis. It could be in your finances, it could be in your relationships, it could be in your finances, but we always come to a point where things just do not add up and we are faced where so many people are facing. We are faced with a situation that we do not know the outcome of it. As we, as many of you guys went to school leaders this Friday, our pastor shared a story of how when this church was beginning and how our pastor was faced with the situation that he had doubt. He did not know how things would turn out. He had a plan A, how the church would grow. It failed, had a plan B where it, how the church would grow. That plan failed and he was faced with an option of C of raising up new leaders, but that option was just, it was so, literally it was like impossible to achieve. So our pastor, he said how much doubt he had, but in the midst of that doubt, he always believed that God can make a way where there is no way and how God can come through. And as I had a chance to live in Nigeria and to be able to learn, to be able to be an intern and to learn from the life of Prophet Ibi Joshua, there was many things that I was faced with that I did not understand where I did not believe and I was challenged. I had much doubt.  I can see the hand grew out. So I'm like, okay, that's it.  And they said, the Prophet says, you are healed. And I'm expecting, you know, the flesh is to just grow back together. And I'm like, this guy is healed, you know. So as I was there and I remember Prophet Ibi Joshua would come to one person and be like, you are healed and he would stretch his hand and I would watch the hand and I'll watch the guy and I'm like, watch the hand, watch the guy and I'm like, nothing is happening. And Prophet Ibi Joshua was like, you are healed. Go home. And this guy is just, nothing's happening. So he's still limping. He's still hurt. There's still, you know, blood coming out of his leg.  So I'm like doubting. I'm like, I don't know. This guy is not healed. And the person's like, am I healed? I'm like, I don't know. I'm new. I'm new. Okay. I don't know. I'm not a Christian. I'm new. I don't know these things, you know. So I too had doubts. You know, I just didn't understand it because I always heard stories of people say God healed me and I had cancer. Now cancer is gone.  And that's in my mind. That's how I see healing. But when I came to the ministry of profit to be Joshua, I was just amazing. I had these doubts of when they're being proclaimed. They look, you are delivered. You are free. You are healed. And nothing would take place at that moment. I would begin to have doubts in my heart. And I begin to question God, is this real? You know, we read in the Bible and we've seen people say, we see the people being sick in the Bible and how Jesus healed them and we write away, imagine this thing that just bam, just quick thing just happened and we have this idea how God would do for us. If we are sick, we believe that the prophet or the pastor prays for us and we are healed. That's it. I must get up right now and all the pain is going to be gone. But God works in different ways. I remember many times in even this church, people would testify and they would say how the pastor would come and pray for them and they said, God has healed you. But at that moment, the pain would still be there. But the people are like, you know, I'm going to proclaim, I'm healed. I'm going to proclaim, I'm delivered. And as they went home, they went to sleep, the next day they woke up and they're like, the pain is gone. So now it's, we are faced with the situation and we are faced with the circumstances where we begin to put God in the box and say, God, you should work this way. God, you should do this way. But the moment God begins to work outside of our box, we begin to doubt it and we begin to question it. And this is what I want to talk to you about this morning. Is that many people in the Bible and some of the greatest pillars of faith that we know in the Bible became heroes and became champions that we read about today in the greatest moment of doubt. In the greatest moment of their doubt, they became champions and the heroes of faith, that's when they were faced with the most difficult situation.  At that moment, Peter did have doubt.   He said, Jesus, if you only said your word, then I will come to you. And we know with Peter, he had doubt many times. Many times he proclaimed that Jesus is the Christ and other times Peter have denied Jesus. But at his weakest point, at his moment of doubt, he became the greatest apostle, but because he sought Jesus in the midst of his doubt. One thing I want to let you know this morning that it is okay to have doubt. I will tell you, neighbor, it is okay to say it a little bit louder. It is okay to have doubt. Now the question is, which kind of doubt are we talking about? There's one doubt, there's two types of doubts. There's one doubt that leads you closer to Jesus Christ and there's another doubt that leads you further away from Jesus Christ. And I just want to let you know on first one, first doubt as we talked about this morning when our pastor was starting a church and there was just nobody, there was just few families to start a church with, you know, all the other relatives left and he had a dream, he had a vision and he believed that God wants to use our pastor to start a revival in tri-cities to use to start a church and to bring a movement into cities but there was just nobody to start a church with. He had doubt. But in the midst of that doubt, he sought Jesus and said, God, give me a way. I know that you can do it. We want to reach out to an American speaking people. We want to reach out to Hispanics. We want to reach out to black, to Chinese. We want to reach out to everybody. We don't even speak English but God, I know you can do it. I know you have called me, pastor had doubt. But in the midst of that doubt, he sought Jesus. He's crying out, God, give me a way. I know I'm facing an impossible situation but give me a way. And as you know that today, we have a church that way. We have a hunger generation. We have a church that it's not known just in tri-cities but actually it's known all over the United States. And it became so influential that it's not just in these four walls of the church but it goes beyond that. And this is what happens when you have doubt but you begin to seek God in the midst of that doubt. So I want to encourage you this morning that it is okay to have doubt. It is okay to face an impossible situation where you do not know an answer. You do not know what might happen. But in the midst of your doubt, begin to seek God for an answer. Begin to seek God, God, explain to me. I do not understand it but I know you can make a way where there is no way, amen? And the second doubt is which leads you further away from God. And this is the doubt that eventually becomes sin. We've seen that God comes to Abraham. He says that I'll make you a father of many nations. I'll give you, I'll just, you're going to have so many children but Abraham begins to doubt. Abraham begins to doubt God. God, how can this happen? I'm of old age. My wife is of old age. She's barren and I just don't know how it's going to happen. So Abraham begins to take matters into his own hands and that doubt begins to lead him to sin. And we know that God had another plan for his life but that doubt led him away from Jesus Christ. Begin to doubt God's word while God said to him and that doubt eventually becomes sin. In our church, we, in the beginning we were praying and we're asking God, God, we want to see miracles. We want to see healings. We want to see deliverance in our church. And we had this vision, you know, that our pastors are going to pray for people. Our pastors are going to do these things. But the way God began to work in our lives and our ministry was through the medium of the anointing water. That's how it was at first. So it was, it was different because we imagined in a way where how God used to do before. We imagined that, you know, the pastors will pray, we're going to see healings through the stretching of hand. But the way God has planned it was much different. We see that when we came into contact with the ministry of Prophet Hubei Joshua, God started using the medium of the anointing water to be able to heal the sick, to be able to see deliverance in our churches. God had a different plan for our lives. So it was those kind of, when people would see, you know, the anointing water, when they see Prophet Hubei Joshua, us looking to different ministries, they begin to doubt and say, you know, this is not of God. And they, many of the people, they canceled their own healings. They canceled their own breakthrough, their own deliverance because they doubted in the way God moved. They doubted. And I know many people who were sick and they were just saying, you know, God cannot heal this way. God cannot just, you cannot get healed through praying with somebody through TV. You cannot do it. They just said, no, I don't believe it. I know the only way I know if somebody prays to you, that's the way it's going to be healed. I just don't believe it. And many of the people that we know of today, they canceled their breakthrough. They canceled their own healing because they chose to believe that God can only work one way. And they doubted everything else. So I want to let you know that the way in the manner God will execute his plan in our lives will differ. The way God might answer a prayer for you will differ. The way God will answer a prayer for somebody else. So I remember when my mom was six, she was bleeding for a constant month just straight.   My dad would pray for her, but she did not receive her healing until she prayed with the pastors through Emmanuel TV. So it's one thing to be able to say that, God, you did it for Vladimir this way and I want you to do it this way for me too. But the way in the manner God will do it for you is different. I remember one story, one testimony, one guy, he said that he had a testimony. He said, you know, I donated a car.  God has given me so much finance.  So another guy who heard the testimony, he said, you know, hey, that's cool. I'm gonna go buy a bus. I'm just gonna donate. I'm gonna take a loan. I'm gonna buy a bus.  He went by the bus, got a loan and till today, he's still walking on his feet. So the way in the manner God will work for somebody else, it differs. So you cannot say that just because pastor did it this way, it has to work for me. Our dependence and our faith lies in God. God can do miracles every different type of way. You know, it takes God to save your brother when he begins to go into, let's say, sports and God can reach him out through the area of sports. Some people, they go in an area of music and God can reach out and save people through the area of music. So you can't say that because I need to bring my brother to church and he's gonna run to the altar, he's gonna save only through this way. No, God can do it differently for each one of us. Amen. So that's why we have to be dependent on God, trust in God, that God can work his miracles. His ways are much higher than ours. We can't put God in the box and say, God, I want you to rescue me this way and if you don't do it this way, everything else, I will doubt. Amen. Tell your neighbor, overcome your doubts. So this is why we have school leaders on every Friday night. We have where you are able to be trained, you'll be able to be equipped to know these things where maybe if you have doubt, you don't understand certain things. We encourage each one of you. Go to school leaders where you'll be equipped, you'll know how God works. You'll be able to go to the Scriptures and you'll be able to understand that God does not just work one way. He has many different mediums that he can express his love and his power in our lives. Amen. So I want to just go to the Scriptures right now. Matthew, if you have your Bible open to Matthew 11 and we're just going to read chapters 11 verses 1 through 6, we want to take a look at a case of somebody who had doubts. And chapter 11 verse 1 says, Now it came to pass when Jesus finished commanding his 12 disciples that he departed from there to teach and to preach in their cities. And when John had heard in prison about the works of Christ, he sent two of his disciples and said to him, are you the coming one or do we look for another? Jesus answered, said to them, go and tell John the things which you hear and see. The blind see and the lame walk. The lepers are cleansed and the deaf hear. The dead are raised up and the poor have the gospel preached to them. And blessed is he who is not offended because of me. We see the life of Apostle John where he had doubt. He had been preaching about the coming of Christ before and when Jesus comes on the earth, he just begins to do things differently. And John begins to doubt. He says, I don't know, I've been preaching about the Messiah that is coming and how do you know if you are the one? So he takes his two disciples and says, look I'm in prison, so you guys go and find out from Jesus. Is he the one to come? Because I don't know. I'm doubting right now, I just don't know because Jesus is just doing things differently to the way things I believe. He goes to Jesus and Jesus begins to say, look, look at the things that are happening. John, he had doubt. But in the midst of that doubt, he begins to seek an answer from Jesus Christ. He begins to ask God, are you the one? Can you please prove yourself? I want to be able to understand that is the doubt that led him closer to Jesus Christ. He sought God in the midst of that doubt. It is not that John had less faith. It is not that John did not have faith at all. He did have faith. He just wanted to have proof that God, I want to have my faith to be concrete. I want to know are you the one? And that's why he sent his disciples and they found out that he is the Christ. In our lives, there's many things that are happening in this church that many of us we will doubt. We don't serve a God who does things the same way as he did yesterday. He's not going to just, many of us we expect and we put God, if I will tithe, God will bless me.  He will just put on your heart and say, I want you to give so much, this amount of money to this one person.  For others, they will keep tithing and God will bless them through that. Many of us will receive healing as we will pray with ourselves and just say, God, have this pain in my body. I ask you for healing. God might heal you this way. For others, it will be when they come to church and they'll be prayed by pastor and they'll receive their healing that way. For another people, they'll come to the prayer line and that's how they will receive their healing. For others, maybe you would have to go to a different ministry outside of this church to receive their healing. I do not know, but what I want to encourage you this morning is that our God is the same yesterday, today, and forever that he can still heal. He can still bless, but the way and the manner he will do it for you will differ from somebody else. When we come in the midst of doubt, let's seek God for an answer. Let's seek God in the midst of our doubt and that doubt will strengthen our faith and we will receive that thing that God's word has guaranteed. Amen. We've seen that if you can open with me to judges. Judges 6 verses 36 is a story of Gideon, how Gideon, God said to Gideon that he will win this war, that God will give him a victory. Judges 6 verses 36 let's read it. So, Gideon said to God if you will save Israel by my hand as you have said look I shall put a fleece of wool on the threshing floor. If there's a dew on the fleece only and it is dry on all the ground, then I shall know that you will save Israel by my hand as you have said. God says to Gideon I'll give you victory, you will save Israel. But Gideon in that moment he doubted. He said, God I do not know, I just I'm weak, I'm limited, I just have my limitations, but I want you to be able to give me a sign. I want you to prove to me, if you're going to do it for me please do this and this and this and God came through for him. Gideon began to see God in the midst of his doubt and that's when God has came through for him and God has brought a victory and Gideon has overcome. It is not that these people had less faith, it is that their faith was being challenged in a new way. In our spiritual walk with the God with the Lord, we our faith will be challenged. I will tell you this thing right now. There's certain things that you believe and there's certain things that you understand but you will come to a point where your faith will be challenged in the new direction. It will just be challenged. I remember when when we we wanted to we wanted to be able to expand a church and we wanted to see different healings and deliverance. We wanted to see the power of God move. Our pastor continually told us look for ministries outside of our region where God is moving. Look what God is doing and churches there and churches there and churches there and for some of us we just did not understand it. We thought God is, if you pray 24-7 God is going to move and this is going to happen but things are just not working out. Our faith began to be challenged. We began to look for ministries and for mentors outside of a church where God is moving. We came to a point where we had doubt. God, is it really that you called us to do this? We don't know. We wanted to close down the church. Years were going by. Nothing was just happening. We just came to a point where we had doubt. Our pastor in the midst of that doubt began to say God will come through for us. There will be a revival in tri-cities. God will begin to heal through your hands. God will begin to save through your hands. You will see this place back. Come on, put your hands together for Jesus. Our faith was being challenged in a new way. We did not know. We thought that first year we were going to open the church. Bam, revival is going to happen. American people are going to come. Mexican people come. The Russians everything is going to flood. It wasn't happening that way. It was just completely the opposite. The people that we started with would just begin to leave. Our faith was being challenged. And I want to let you know that whatever you're expecting from God have an open mind. God might bring you an answer that you may not understand, but do never be too fast to open your mouth and say I do not believe it. Always have an open mind. Say, God, I do not understand it, but I trust you that you will come through for me. I just trust you and believe you that you will come through for me. I mean, I remember with our church when we first started with praying with anointed water. It was just unrealistic. It was just unheard of. Nobody ever prays with water for people's oil. It's oil. Get oil, you know. Get more oil and just pray. We didn't understand that. We didn't understand it, but I love the heart of our pastor where you say, you know, we're going to see God in the midst of our doubt. We do not understand it, but we're not going to say that this is not from God. We know that God can use any medium to express his power or might. And we thank God for the life of our pastor. Come on, put your hands together for the life of our pastor. And I remember when I was in Nigeria and there was certain things I did not understand. I remember Prophet Josh always at the end of the day saying, examine all things in the light of God's word. Whatever I'm telling you today, don't just be too fast to believe it.  Oh, pastor said that this is it. Go into the Bible and find out the truth for yourself. Don't be too easily to persuade and do one thing or another. Grab the word of God and begin to examine. God, did you do it like that? People are, you know, we've seen testimonies that are happening, you know, through praying through the TV, through the medium of the anointing water, sometimes through just fasting. Go into the Bible to begin to see did God do it like that there? Did God use different mediums? We read in the Bible that God uses spit to heal people. So it's like it's weird, it's different, you know. But God did it. God healed them. You know, sometimes we hear that He used the staff to be able to split the seed to do this and that. You know, it's different. I don't understand it, but that's how God expressed his power or might. Whatever situation that you're facing today in your family, is it in your marriage? Is it in your finances? You may be praying that God come through for me. God, bring me an answer.  But because of our doubt and say, no, God needs to do this way, we could cancel that answer. So I want you to be able to, when you don't understand certain things, don't be too quick to say this is not from God. In the midst of your doubt, see God and God will come through for you, amen. Whatever you criticize, you will never have. Whatever you criticize, you will never have. So it is so important that when you see God is doing something for other people, and don't be too fast to say, oh, this is not from God. Whatever you criticize, you will never have. We're honored today to be able to look up to so many ministries where God is doing mighty things. Where churches are growing, where churches are expanding, where we see God doing mighty things, and we're looking up to them. We're not too fast to say, well, this is not from God because they clap. Well, this is not from God because they dance for six hours straight and they have worship for six hours straight. This is not from God. No, we just know that God can execute this plan differently in every single person's life. Amen. What happened was we wanted to, you know, when our pastor was starting the church, we wanted to see revival in this church happening through mighty leaders. We wanted to see people who can speak English eloquently.  We were 14 years old and God chose to bring revival through young people. When pastor was first starting this church, we literally had people who did not speak English. We had people who did not understand anything, who stole at the point of our ministry. You know who were doing bad things when we were in church. We didn't understand, but God chose to use the foolish things of this world to confound the wise. Other people would be able to probably, you know, say, God, I want to bring revival in tri-cities and, you know, so the pastor would go look for somebody out of college to be able to graduate with bachelor's degree in speaking and have a degree in pastorship if there's a thing like that, you know, to be able to lead this revival. But God chose to use 14 year olds at the time when we were beginning the church. Just a bunch of kids were able to bring his move. And today, many families are restored because of those 14 year olds. Today, many people received their marriages became to behold because of those 14 year olds that were beginning. Today, many people are healed in their bodies because of those 14 year olds that were beginning the ministry. We might have a view of saying, God, I want it to be done this way. But when God does completely the opposite, don't begin to doubt. See God in the midst of your doubt. Amen. Remember the story of Naaman in the Bible. You know, he wanted to be healed by prophet Elijah. And when he came to him, Elijah said go and dip yourself in this dirty river seven times.  But God had a different plan for him.  Imagine that. Imagine you put yourself in a position where you're asking God for an answer and God says, go do something completely opposite. But he obeyed in the midst of that doubt. He even, you know, we read the Bible, he was just mad. He's like, I don't know what this is, you know, this is crazy. But in the midst of that doubt, he saw God for an answer and we see how he was healed. So whatever that we're facing today, whatever doubt that we have in our lives, whatever that we're looking, maybe there's a career that we do not know where we're going to go. Maybe it's a marriage that is falling apart. Maybe it's finding that you're lacking. Your business is just not taking off. In the midst of that doubt, begin to see God for an answer and God will come through for you, amen. Tell your neighbor overcome your doubts. Tell your other neighbor overcome your doubts. One thing that we have to know is that Satan always and always makes us to doubt what God's word said. Satan wants to slip us into unhealthy doubt where we begin to focus on instead of God's promises. Satan wants us to be able to question everything that God has said and to begin to point our faith into our own selfishness. To be able to see that, look, you're weak, you cannot do it. Look, you're not holy enough. Look, you're not righteous enough. Look, nobody in your family has made it. Look where you're coming from. You're not able to do it. That's what Satan's aim is to be able to doubt God's ability and God's desire to be able to use us. I mean, we see in the Bible so many people who were just disqualified by outward appearance disqualified by the things that they've done, but God used them to bring a breakthrough in our lives. The case of Moses, he was a murderer. I mean, imagine somebody getting up to speak today. I mean, today would be weird. I know back in the day it was much easier. But who was a murderer? And God used a murderer to bring a mighty revolution of Israel out of captivity.   And this is why we have this community today. That's why we have church because Peter has overcome his doubt. Don't begin to limit yourself about what you can do, what you can say, what you can be. Begin to focus on what God has said in his word for you. That with him, all things are possible. That I am an overcomer. That I can do all things through Christ who gives me strength. Amen. When we begin to worry, when we begin to doubt we cripple the ability for us to think, to act and to exercise faith in the present. When we begin to doubt God's word, when we begin to look upon our own selves, we cripple the ability to think, to act and to exercise our faith in the present tense. Every time you begin to doubt you cannot have faith that God will come through for you. You cannot have faith enough to know that God can work a miracle in your life. When you begin to trust God, say God, I don't understand it. But a belief that you said in your word that those who believe will make it happen. You begin to stand upon God's word and God will make it come through. But when you begin to doubt God's word God's ability and desire to make it come to pass in your life you will not be able to exercise the faith to make that thing come too fast. The best the best weapon against doubts is testimony and God's track record what God has done in your life. It is so important for you to begin to surround yourself with testimony that God is doing around the world. I remember where pastors just always saying that begin to surround yourself with what God is doing. There's people that are being healed at that church. There's people being saved by hundreds, by thousands of doctors. Begin to look there. Begin to surround yourself by testimonies knowing that God can use you and God will be able to do the same thing in your own church. Begin to surround yourself by the testimonies and by the evidence that God will do it today because God will do it in your church. We've seen those people that have been here long enough they've seen the changes in our church when we begin to surround yourself with churches where God is doing something it was just a matter of months where we see the same thing happening in this place. It was a matter of months if you're sick in your body begin to surround yourself with testimonies those people who are healed. If you need a breakthrough in your life begin to look for testimonies God who did you bless? I want to be able to know where is this something that somebody did something and their business begin to flourish where God is just power is moving when you surround yourself with testimonies and evidence you will have faith enough that God can do it for you too. We see when David faces a goliath. Everybody was just scared and it's not that David was just had more boldness or anything. David surround yourself with testimonies saying God you help me to overcome with the lion you help me to overcome with the bear this is just going to be another one that I can overcome. David begins to surround himself with testimony he begins to surround himself with evidence and we see how God begins to step on his side and David has conquered and he's defeated the goliath. Many goliath in your life will be conquered the day you begin to surround yourself with cloud of witnesses of what God is doing around this world. When you see the power of God many people died of cancer but yesterday I saw somebody being healed from cancer. Today I can be healed. Somebody says 50% of people get divorced. Yesterday I saw a testimony of marriage being restored in an impossible situation and marriage just got put together by God's grace and today they are happily like a brand new marriage. When you begin to surround yourself with testimonies that doubt will begin to diminish and you will have faith enough to know God can come through for you God can do for you. He is the same he can do what God says he can do and I will have what God's word has guaranteed for my life. Amen. Unhealthy doubt only comes when we fail to observe all evidence that God has given us. Unhealthy doubt comes when we not take the time to observe what God is doing in our lives. I mean if you begin to say this guy just got set free from drugs and we say no it doesn't happen there's just one in a million that's when unhealthy doubt comes and that's when it leads you to sin. When we fail to observe all evidence in our lives many times we complain that God hasn't given us this. We complain that God has not given us this in my business. But you forgot how God has kept you healthy all the way of your life. You forgot how God has given you a good family. You forgot that God has always provided that you always had food on your table. You forgot that God has given you this. Now you're focusing on what you don't have and you begin to slip into unhealthy doubt. You begin to doubt God's goodness and God's ability to make it come to your life and that's when unhealthy doubt comes and that is when it becomes sin. So when we look at what God has done on our lives, when we begin to review God's track record in our lives God will come through for our lives, amen. And I remember when we, when there was a point in our church in our lives where we had nothing going on in this church there was just nothing happening, no people being saved, nobody was getting healed I mean nobody was just coming to our church just, just nothing was happening here.  Whatever the situation that you're facing tonight, it may be impossible every odd may be stacked up against you, but when you begin to observe all evidence all the testimony what God is doing God will be able to come through for your life, amen.