We can begin. Hi. Good morning everyone. I'm Alice Kegrepova. I am a professor at Kablin Institute of Nanoscience in Delft in the Netherlands, where we have quantum method and AI lab. This is some pictures from our group life and my website if you want to check out more about our research.  So I try to go through things in a way that it will stay a bit interesting. I will try to not only talk about how machine learning works in quantum but also concentrate on these ideas of why and then connect it to the rest of the school with some experimental examples that we do tomorrow afternoon after you had your first introductory lecture into the cold atoms. So let's stop a little bit with this why machine learning because this is something that we should really stop and think about. It's easy to say oh this is kind of a problem I've been working on for the first year of my PhD but I can also do it with a neural network so it's probably going to be a PRA. And that's true but it's maybe useful to think about why should one do something like this. Because in physics we often understand nature by designing some minimal toy models that we can very well understand then analyze them and then derive some underlying understanding from that. And machine learning how you already work with it or you read about it somewhere is very different. You have this very data driven approaches that sort of extract features from data. And so if you think about it on the very very fundamental level these two things may seem a little bit contradictory. So it's maybe useful to stop and think about if we even have a big data in physics or in quantum physics. So can someone give me some examples of if we do do we. Yes that's a great one when we measure a quantum hardware we get a one projective measurement and we need to take many many of those if we want to calculate anything that's a great example I will come back to it later. Do we have more examples? Is the only big data set we have in quantum physics a shot on quantum hardware? That's another good one. Can we have also someone else make a suggestion so we wake up in the morning? That's a great one that's a great one. Anything can we think of anything that is not related to the experimental measurement? I cut it off very meaningfully please. I actually think it is and it's a great segue into the into the next topic right because the the wave functions themselves they are super huge objects so any numerical methods we develop to approximate them they will also yield some large scale data sets. Okay that's maybe let's take these two examples and let's see if we can come up with more during the talk but thank you for this DFT connection right because this is now a good segue for me to talk about why is quantum physics hard do we have someone who do not consider themselves a quantum physicist here? Great okay so this is going to be a smooth right so in in some quantum mechanics one-on-one someone tells you this right that if I have two quantum particles I need four numbers if I have ten I need a thousand and so on and so forth the number of amplitudes of a quantum wave function scales exponentially with the system size and that's the whole crux of the problem and or depends how you see it a great potential benefit of quantum computing so I prepared this actually super carefully in case we have some non-quantum people here but since we don't I will go over it super super fast the way you derive this exponential scaling is actually it's not super deep if I have two classical states whether I put this here or here it's either one or the other right but in a in a quantum I have a super position where I can be in a arbitrary normalized combination of those two states if then I add a second system if I would have a second sanitizer here I repeat the same exercise but if I start writing the numbers that I need to describe that state if I have two it's like one is going to be here one number the other one is going to be here the other number but if I have both of those in a superposition I need to start multiplying things so one superposition of a plus b and the other superposition c plus d once I multiply everything I get four number like this and for three systems I get eight numbers and for n systems I get two to the n and so this is just a super simple consequence of writing superposition and it's really important to remember that this has nothing to do with the speed up right we are just right we are just really writing the dimension of this complex vectors that we jointly decided at the beginning of the past century that we will describe the the quantum reality with and so we come back to this scaling and then somebody tells you usually or you can try on your own computer that once your numbers are start getting depending how like yes CPU and GPU are developing but when you are somewhere around 20 nowadays you cannot calculate things exactly just because you run out of memory on any classical computer because of this exponential scaling so there is a there is a thing to realize and that is that the the wave function itself is a really large scaling object even if we want to write a one-way function of like 20 particles it's already a disaster in terms of complex numbers that I need to store so this is very interesting and you come back to it because Philip will give you the whole lecture series about about how this works and then there is the other thing that you were also mentioning when I asked you the questions about the big data set and that is this experimental connection because of course I cannot go to my experiment measure the complex amplitudes and celebrate right we can only measure a real numbers so what I measure experimentally is some you know expectation values projections things like that and then someone needs to do the hard work of connecting those experimental measurements to the underlying theory models that live in these complex Hilbert spaces so we can complain all we want about how this abstract complex vectors scale badly with the size the experimentalists they have much bigger problems right because they don't get they don't even get this exponential number of complex amplitudes they get a millions of measurements that they need to map on this exponential number of complex amplitudes and it's also something that we are going to discuss later on and now there is this a question of like how what artificial intelligence have to do with it right so now I laid it on really thick so now this is not going to be any surprise basically we even though the way you learn physics in your maybe bachelor and sometimes masters program where you get all this pre reconfigured examples that you can solve exactly so this scaling problems do not sort of come up often in practice when you do science they do because we when we want to push the boundaries of knowledge we run out immediately of things that we can do analytically and then the numerical methods come in and then you want to analyze experimental data set this would go under this umbrella of like maybe discovered a new discovering new physics from data you want a process this huge measurement set that you get by measuring quantum computers you also want to automate the control of contemporary quantum devices because they are getting really really big I am gonna talk about that a little bit more tomorrow but you can also do some very fancy things like discover and optimize quantum algorithms or design new quantum materials things like that since we have a lot of people in the in the audience who said they are already worked with machine learning maybe we can have a three or four examples that someone say what they what they do with machine learning in one sentence that the rest of us can understand you have to listen to me for three hours like you gain nothing by being quiet right now like really okay let's go that's for it say again yeah that's a great one and thank you for that because we will talk about phase transitions first do we have another example also amazing one we will cover that tomorrow but apparently you already know another example great thank you Tom really that's my own group member everyone one more oh that's a very good one that's also can be seen as a Hamiltonian learning problem then okay let's leave it and somewhat good great now we switch gears forget all about this we now sort of motivated to ourselves that maybe somehow we should do we should do machine learning at quantum but let's do something let's do first something physics see to really get into the cracks of this the why of why we need the machine learning hands up who remembers an icing model from their statistical physics class it's like almost everyone that's good okay so presumably this is the Hamiltonian that you have seen before it just tells you that if you are on this two-dimensional lattices I showed you on a previous slide the nearest neighbor spin sigma i and sigma j they can be either plus one or minus one it calculates the energy of this nearest neighbor interaction with some parameter j and so if you just use this Hamiltonian you will realize that if the product of sigma i and sigma j is plus one both of them are up or both of them are down your total energy will be minus j and if they are not aligned your total energy will be plus j so if you want to go to the lower energy state you want to have them aligned right the phase transition that you learned about in your statistical physics course has to do with adding temperature to the system this is something called Boltzmann distribution and it just tells you a probability of each configuration at the given temperature but basically what happens is that when you start adding temperature the difference between this and this becomes more and more subtle and eventually it stops matter at all and that's what you when you get this temperature phase transition in icing model let's let's we come back to the temperature let's go back to this Hamiltonian that I write so let's do the icing test and I will ask you which one of these three configuration has a has a lowest energy shouldn't matter about open good question yes no like there is no there is no there is no true questions really if you have heard me talk about this before I always switch the configurations before every lecture so okay do we have suggestions yes great and why do you think it's B so now we saw not only the correct answer but also kind of smart way to arrive at it right because I wrote you the Hamiltonian right below so you could just do what I said use the Hamiltonian and just write all the plus and minus ones for all the pairs that you have in that configuration and just calculate which one has the lowest energy right but it's kind of annoying to do and it would take you like five minutes and then there is this other approach that you can say oh wait it's just the misalignment that matters so I need to find the picture where the boundary is a least so for example in the sea it looks like it's very blue but the one that flips everything is in the middle so the misaligned pairs are actually a lot so the one that has the least if you look at it is a B everyone is with me yeah okay great and but now we did actually something funny right because nobody's you didn't think about Hamiltonian when you explain this to me you thought about some pattern in the data so we actually did some kind of data inference already even on this minimal example and so if we go back to this temperature transition what happens is that at a different temperature you can draw this up down up down up down samples and then you at some point calculate this phase transition maybe someone taught you like on-sugger solution or some renormalization group stuff and you get this formula that you can get analytically for it in 2016 Leivang did something very simple but super brilliant and this is like my one of my favorite like machine learning in physics papers of all time is that he took this icing configurations that I just showed you use a super simple clustering algorithm and when you do that and you plot these configurations on the two axis where those are the two components of your clustering algorithm you get this plot where if you color the points by temperature you get the mid big cluster in the middle and the two blue clusters on the sides why is that too actually somebody tell me that yeah I mean that's correct but can we say it in like a normal human words exactly so this there is the C2 symmetry means that there is two ground states right like either everything is aligned like this or everything is aligned like this so we get a two we get a two clusters I don't want to yeah this is called principal component analysis I just tell you in a super super high level and we come back to it tomorrow if there's time because I don't want to get like yeah spend the whole lecture talking about singular value decomposition but basically what you do with this algorithm is that if you have some data points in some dimensions you can basically calculate minimal square following the minimal square distance in the data like to look in which direction the in which direction the standard deviation in the data is the smallest and that helps you define your new axis and then if you project the data into this axis you on this example I drew here it's it's meaningless but in this in this icing model you get a plot like this so basically what we do is that we take all of the square configurations make columns of all of them make a big matrix and then we just project that matrix into the two-dimension into the two directions of the of the minimal square distance now we are at this we are at this like a funny point right because to do the Leibang's thing I didn't have to do anything I just needed to know that the principal component analysis exists and you can actually just call it in Python without even knowing how it works actually who knows principal component analysis ah you are such a great audience like maybe we should just like skip this introductory lecture and just like go to the advanced stuff right okay so nonetheless so even if you know it it's even better right like then this plot should completely like value because I can to calculate a space transition in your statistical physics class you spent like two or three lectures right and that is a lot of writing and you need to understand about like partition sums and it's not it's not so easy and this I can just do I can just draw some like samples do the simplest clustering algorithm that we know exists and just celebrate right because here if I plug in the constant equal to 1 into this critical temperature formula I get something like 2.2 something if you look at the color in this plot of the transitional points and map them on the temperature temperature color scale you will see that it's kind of right in the middle between 2 and 2.5 so just like looking at the color alone I would guess like 2.25 is the transition temperature between those two clusters and that's a pretty good guess for someone who never heard about what's a Hamiltonian what's a phase transition right so that's that should be that should be very cool so we just don't go to the physics class anymore and do the just do just cluster everything right can someone think about like is there a problem with this or are we now done with physics yeah that's a great point that let's say that this critical temperature transition or where it comes from it somehow related to the physics that we want to study so actually having the formula would be good and we are not getting it like this anything else that's another thing that I cluster this and then if I have some weird clustering method that has a lot of artifacts I can make like a nature paper with my artifacts clusters and then be like a oops okay this is just the t-snay artifact and not the actual phase transition more thank you for that segue so what Felix is saying is that I can like try to cheat you here with the simplest icing model that we know of but let's try a harder one I am not doing anything fancy I am just going to add the product over the placard so instead of now just looking at the two nearest neighbors being aligned we are looking at the product over the placard and the same argument will apply if it's even then it's fine a IE I mean by fine I mean lower energy if it's odd it's a higher energy so let's repeat the same experiment as before which one now is the lower that's correct thank you and how did you find out great great so you literally had to check placard by placard now so this is becoming harder right because before we were just like we just look at the boundary and probably we can guess fine but if there is a single one in this picture that is wrong you don't know so if I would give you 20 plots maybe 40 times 40 lattice size we would be sitting here before for a long time before anyone can tell and this is the example of the type of spin model where if I do this kind of principle component analysis I am going to be disappointed let's say because you cannot get anything better than this and this is where the interpretability that some of you also raised before comes back because if you are a physicist somebody will teach you that you should map it on these Wilson loops and if they are broken it's a high temperature if they are not broken it's a low temperature just take me at the at my word at this point like that's how it works you get the loop by if you look at the bigger picture just if you try to draw the line between all the orange points and connect them then you get the lines that you see at the bottom picture and so if I get this kind of picture it becomes very it becomes very simple to look at even if I wouldn't give you the stars for the breakages you have this kind of dual image where you just look once and you see okay there is a one broken loop that's a then the then the gauge constraint was violated so so this is something that that it's like an open question that like maybe for now for it's not it's not as simple as just taking different configurations and different clustering and see what we can what we can see from them and then the question then the question of course is what to do next with that I am going to take a short break from this from this argument and let's just do this kind of detour machine learning primer there is many people who already saw this there is many people who didn't so I just I still wanna I still wanna go through it for those of you who are who are not familiar and for those of you who are I will just yell at you in 20 minutes when you can like stop looking at your phone so neural networks with these clustering algorithms that we saw there is a formula I make a matrix in a certain way I calculate singular value decomposition I calculate some project I apply it on my data done with a lot of problems you don't have this and so there is this idea that you that you use some kind of very efficient function approximator and people equated to neurons and a brain and stuff but actually this terminology is maybe a little bit little bit arbitrary even though it was helpful at the beginning of the field in the end what neural networks are they are just like parametrized and that said that can approximate a lot of functions and the approximation can be done effectively through some algorithmic means so how neural network looks like is like this that you have some input layer those are your data then the input layer is connected with this connections which actually is just a matrix and a vector that's a weights and biases to the next layer at which you apply some nonlinear function I will tell you in a second and then from the next layer you go and so on and so forth so in the end you end up with some output function which is the function of your second layer applied on a function of the first layer applied on a function of the data and all of this is a function of these weights and biases these W's and B's which are the so-called trainable parameters so yeah this is indeed this how this like a neural analogy started because you can think about this as like inputs that could be kind of like a synapses that are coming into some cell that are then outputted to the to the outside this is a picture I took from Phi Phi least Stanford machine learning for computer vision lecture which is by the way amazing if you want a more in-depth introduction to this since you want to stay with physics I'm going to be very superficial today but I will be referring you back to these to these in-depth sources okay so we are coming with the weights from the previous layer then the only thing that the neuron does is to calculate this linear combination this is something that you learned in your linear algebra you do some linear combination with the weights plus B to have a more general linear function for for bias and then you apply the so-called activation function I should have them here that gives you the nonlinearity because if you would only do a linear transformation in every neuron then yeah actually then what can I just get away with doing a linear transformation do I need this nonlinear functions for anything yes yeah exactly right so so the so if I would just have the linear transformation I would not be in a way not doing anything better than the principal component analysis that we just saw everything would be linear and okay I would express more complicated functions because I have a more variables but everything would just stay linear but if you want to express arbitrary function you need nonlinear function luckily for this F1 and F2 and Fn functions there is sort of standard choices that one can take that are already pre-implemented in all of these libraries that we use for machine learning these are called relu sigmoid or tangent hyperbolic those are some typical example of the nonlinear function that you can apply and that's really that's really the whole setup like you have some input layer connecting to the weights to the following layers all the weights and biases can be represented at matrices and vectors from which we just do linear algebra transformations plus we have this nonlinear function actors this is again another example from this from this 5.5 e-cores when you what happens when you are training the network I tell you in a second how do you actually train it is that the weights you are training should take some structure if you have a model that is looking like the picture on the on the left you probably you just have basically like a random weights and those models can be interesting to study in themselves but for this like a simple neural network application they are probably not good so what happens during training is that your weight matrices start picking up a very specific features that you can see if you plot them and that is then useful if you want to interpret what is your network learning now how do we train the network we need something called loss function which is the difference between what your network is giving and you wanted it to predict it's for now we will call it a function l and I will give you a concrete example in just the two minutes and what we need to do is to is to yeah minimize this function similarly like you would minimize the energy of the Hamiltonian you minimize some cost function or loss function that describes your learning goals meaning what you what is the function that you want the neural network to approximate and how you do that is that you adjust or you keep slowly adjusting all your weights and biases basically according to this formula that from every weight I slightly adjust by the derivative with respect to the loss function and that way I can slowly walk this optimization landscape until my loss function is the smallest the epsilon here it's called learning rate it just tells you imagine this if I have some multi-dimensional optimization landscape that is like some you know lots of local minima the rate tells you what is the size of the step so if the step is too big you are not going to distinguish or your fine structure and if your step is too small you will get stuck in a local minima so what this is the super important hyperparameter that you need to find what it should be for your specific learning problem now we need to figure out how to actually calculate this partial derivatives because it's easy for me to say okay you have some neurons it's connected by weights whatever comes out goes into the loss function that's some function that I want to minimize I minimize it by calculating derivative but I just told you that we need to calculate derivative to all of the weights and biases in the network which may sound like a daunting task can someone quickly remind us what what is the chain rule this is something that we surely had before thank you normally this is the question that I have to wait the longest to get answered but everyone saw this before right if I have a function that is a composition of multiple function and I want to differentiate it I do it like this that the derivative of my main function is this kind of product of the derivatives of the composite function exactly what we just heard from the audience okay but then it's simple right because I just take this formula and substitute it like to this picture and we write the loss function derivative with respect to the biases let's say in a first layer and then we decompose it like so so I differentiate basically from the backwards I first calculate the derivative with respect to the last layer then I calculate the derivative of the last with respect to the previous one and then I go to the previous one and take the weight that I wanted to differentiate with respect to in the first place and we keep multiplying like this and this is very general way to say it but this is all back propagation is it's just a chain rule and luckily you never have to think about it because again nowadays you will see in a second when we do the practical demonstration it's implemented for you in any package you will be using and there is a lot of like scientific needs why we need to maybe sometimes customize this algorithm but this kind of basic thing is always implemented for you so you never have to do it yourself but it's still useful to understand how it works so I will just repeat sorry for the slide that has a lot of text on it you take your network you calculate the forward propagation which is just linear combination from the previous layer nonlinear function linear combination from the previous layer nonlinear function then you calculate the backward phase meaning you estimate the error in the final layer you calculate this chain rule like I just told you and then you do this for many examples you combine all the partial gradients into the final gradient and then you update the weights by doing this W ij minus epsilon and the derivatives then you update all the weights and then you go again and again and that's pretty much that's pretty much on a conceptual level how it works let's take let's take a super concrete example because now I know I said like a lot of words so let's do the same but on a super super minimal example so first super prominent application of machine learning algorithm was just the image recognition if you remember like few years ago there were all these neural networks that are just recognizing like dogs from the cats on the internet and everyone was celebrating and so this is also a really great example of a neural network application because for example if we want to distinguish characters from these two movie franchises there is not one thing that I can say to describe this is not a problem this is to describe functionally right but this is exactly the kind of problem that is great for your network because I have tons of examples from each class that I want to describe so for to do this example let me say two things I told you before things about activation functions and I gave you some examples I neglected one and that is that for the last layer you want to use this activation function yeah I didn't write it before because the formula is kind of but what it just does is that it maps your output on a normalized probability distribution in this case binomial distribution probability it's a Star Trek probability it's a Star Wars and then you need some loss function and here for example we have this categorical cross entropy that calculates the difference between predicted probability distribution probability Star Wars probability Star Trek and the probability distribution that you wanted so let's take concrete example now with this categorical cross entropy loss function so Leia or Star Wars will be one zero vector so that's my label that's the probability distribution P hundred percent probability on Star Wars zero probability on Star Trek and Spock has the exact opposite and the network output the probability distribution Q will be a probability that the network is telling me probability I am in Star Wars probability I am in Star Trek then we can write out these formulas just writing out the loss function with the P and Q and just filling in the numbers one zero for Leia and zero one for Spock you will see that you get a smallest number if the Q class A and Q class B agree with your label right let's look at it on a concrete example here for Leia so we have a minus one logarithm Q of class A if class A is one then we get a zero and it's good but if it's a if it's a zero or a small number we are getting very big negative number multiplied by minus one very big positive number that's not a good loss and so on so what you really do it's it's as simple as this you just have the labels and you multiple you keep multiplying them with the probability distribution that comes from the network if your loss is not small or keep decreasing you repeat this back propagation step you do it for example a new set of images and you continue let's take a five minutes so you can digest it the people who are new to it you can come and ask me question and after that we will go back to spin models and we can also do some coding examples


Hi friends, welcome back to my channel and welcome if you're new here. My name is Jen. I'm a certified weight loss and nutrition coach and I'm on the WW or the Weight Watchers Blue Plan. It's Wednesday, so it's of what I eat in a day. Welcome to my car. I forgot to film my intro and outro and it is the end of the day. I just got done showing a house, which you'll see in today's video. So I wanted to pop on really quick and film my intro. If you're excited for another what I eat in a day, give this video a big huge thumbs up and don't forget if you're new or you haven't yet subscribed, I'd love to have you here. Hit the subscribe button and don't forget to ring the bell right next to it. So you never miss a single video down in the description box. You will find nutrition coaching. I do offer personalized to you macros and calories. Highly recommend this service so you know where you should fall every day to be successful. If you want to chat with me directly, I offer one-on-one coaching as well. Links, discounts to everything I shared with you in today's video, as well as all of my other favorite things and my Facebook group head on over and join us there are all down in that description box.  So let's jump in. For today, this is my meal prep. These are the protein sweet potato breakfast bowls, you guys, if you have not made this recipe from Monday's video, absolutely incredible. You can have it cold. You can have it warm. There is this delicious sweet potato mix at the bottom with some protein powder, some fresh fruit. It is absolutely incredible. So filling, so satisfying. So this is going to be my breakfast. I think I'm going to go ahead and head outside to eat. It's just such a beautiful morning. And then I'll chat with you guys for just a couple of minutes. Good morning guys, some outside with my breakfast. I'm telling you, if you have not made this meal prep, it's so good. My favorite way to eat it is to just warm it up in the microwave for just a couple of seconds, just to get it barely warm, but the fruit is still cold. It's so good. So I have a super, super busy kind of crazy day today. I have a coaching call at eight o'clock this morning. It's currently seven 30. So I decided I would go ahead and eat some breakfast. I've poured my first 20 ounce glass of water towards my gallon of water for today. And then I'm doing laundry. I need to get caught up on some computer work, get my meal plan done so that it can go out to everybody who signed up for my meal plan for the month of July. So I need to get that all done. And then I have a zoom call this afternoon at three o'clock with my challenge group over on my Facebook group. We're about to start our summer challenge. It actually starts July 1st. So if you haven't joined or you're not part of my Facebook group, come join us over there. We're having a really fun summer inspired challenge just so we can set some goals for summer, help each other reach those goals. I do zoom calls twice a month with that group. So I have that this afternoon. It's going to be over a hundred degrees today. So when Troy gets home from work, we are going to a barbecue for dinner tonight. So I'll be sharing that recipe with you. And then I have to go show a house at six 30 tonight. So I have a very busy packed day. So of course, I'll take you guys along with me throughout the whole thing. I'll share with you, of course, on my food today. And then tonight's dinner recipe. So things are just really, really busy. We have diesel surgery this Friday. So we're kind of gearing up for that, getting our house ready, getting our lives ready.  He has figured out a way to maneuver down off of our bed so that he doesn't have to actually jump off of our bed. He's found a little way off that is less of a jump. He's so smart and too smart, actually. So it's just busy getting that ready in the weather. Here has been in crazy, crazy hot, which is not fun, of course, for anybody. I posted this eyeshadow look that I'm wearing today on Instagram. Got a lot of questions. I will go ahead and post this palette down in the description box for you. It's such a pretty palette and super, super affordable, perfect for summer. I got a new pillow, so I want to show that to you guys. We just have a busy day. So I'm going to finish my breakfast and then we'll jump into the rest of our day. So I promised I'd share with you about my new pillow. I literally can't stop smelling it. This is the Suterra Lavender Zen Pillow. It smells absolutely incredible. If you love lavender, you will love it. It's lavender, but it's not overwhelming. And I ended up getting this pillow because I'm having a hard time sleeping at night. I've mentioned in a previous other videos that I've woken up with my neck hurting like my lower neck and sometimes even my shoulder area. I am generally a stomach or side sleeper. And I do put my arm under my pillow and sleep on it. So I wake up at night sometimes with my arm falling asleep. I also wake up with, you know, again, the shoulder pain or my neck pain. So I wanted a pillow that was proven for sleepers like me. I decided to partner with Suterra again today. I've partnered with them in the past on a couple of their other pillows that to this day I'm obsessed with. This is their new pillow, the Lavender Zen. So I want to thank Suterra for partnering with me for today's video. So let me tell you a little bit about my new delicious smelling pillow. The Lavender Zen is made of luxurious supportive memory foam that conforms to the unique contours of your head and neck. And that allows cushioning and pressure relief customized to your personal needs. This comforting design is perfect whether you sleep on your back, side or stomach. And that is exactly why I wanted this particular pillow, making it a premium option for all. Lush high density memory foam features micro channel ventilation technology in allowing increased airflow and breathability. So what happens with that, too, is it keeps it cool as you sleep. It doesn't get hot for you as you lay on your pillow and the outside case here is removable to wash it. You can even wash the pillow. It does come with care instructions, which I think is really nice about the pillow as well. So this is a versatile design for back, stomach and side sleepers. It can really benefit anyone that needs relief from pain caused from sleeping, whether that's like me and your neck or your back or your shoulder, the lavender essential oil will help ease your tension and support a restful sleep. So again, it has humidity and temperature control. That optimal flow technology for air, which I love. It's great for all sleep positions. It promotes a healthy spinal alignment, ultra plush memory foam for a full body support, which I think is really important, too, because when we're sleeping, we just don't need support for our head. We actually need support for our entire body. So I'm so thankful to partner with Suterra again. I love my other products from Suterra. I have their air purifier. I have their plug-in clarifier on. I have a lot of their products in my home. I will give you guys updates on those products as well. But I really wanted to share this pillow with you. I will link this down below with a special discount just for you.  Oh, you have a cool baby. Oh, so cool. Hi, Lola. Oh, look at Palmer. He has his baby. No, you're not taking. Are you taking it in? No, you're not taking it in. Pumpkin, let's get your pool for later. We'll have Daddy get your pool when he barbecues tonight. You guys, it's so hot out here. It's going to be over a hundred today. Pumpkin, are you cozy, buddy? It's time for my morning snack. I'm going to have the new flavor of the California Citrus Kombucha. I'm so excited to try this. I'll put it here on the screen, my thoughts, but I count this bottle as one point. WW counts. It is three. It is one to me. So I'm going to have that and some pistachios. I love these little pre-portioned out individual little packages. I love pistachios. I love nuts in general. I can very easily overeat them. So I love that this is pre-portioned out. So I'm going to have some pistachios and some kombucha. My Wicked Bayou candle subscription is here. I shared this with you guys last month. It was my first month receiving this subscription box. If you love candles, car air fresheners, wax mounts, you will love this box. Super, super affordable. It's a small business. I love it. This, in my opinion, is the best candle subscription box that I've ever ordered. So on the back of the little card here, it does tell you what comes in the June box, but I don't want to peek. Here is how it comes wrapped in tissue and then lots of fun, a full Luffy packing, which I save. And then I reuse it if I ever send packages out so we can go through what is in my box, starting with it. Looks like a candle. Okay. Hello. So first we have the Wicked Bayou candle in Bahama, Mama. And this says it has notes of orange and pineapple with hints of cherry. Oh my gosh. That is literal summer in a candle. I will tell you that I burned last month's candle. Amazing throw. It filled my entire office with scent and it burns down completely, where virtually there's nothing left in the container. So I'm super excited for this. Oh my gosh. How fun. This is the car freshener scent, pineapple margarita, notes of pineapple mixed with lime. And I have the sunflower one in my car from last month and it still smells. Now it's not as strong as it was when I first put it up, but it still smells. Look how cute this is. And this smells incredible. So these are really cute because they're fun to hang up in your rear view mirror because they are really pretty and aesthetically pleasing. And like I said, that scent has been in my car well over a month. Looks like we have wax melts. This is in passion fruit mojito, notes of passion fruit with hints of lime and mint. If I can get it open here. Struggle. Oh, that smells amazing. This literally smells like the mojito drink. I find that these wax melts also have very good throw and last quite a while. And lastly, which is super exciting is it looks like we received a second candle. This one is an island mimosa. I can't believe we actually got two eight ounce candles in this box for the price is insane. I will put the price here on the screen and I'll make sure that is linked down below for you guys. Oh my gosh. Ah, this smells so good. So this is notes of pink grapefruit and hints of Chardonnay. Incredible. Like so good. So recapping what we got. We received the island mimosa candle. The margarita car air freshener, the passion fruit and mojito wax melts and a second candle in Bahama. Mama. So again, I love this box. I think for the price point, this is exceptional. Last month, I received a couple wax melts, a candle and a car air freshener. So it does change up from month to month, but you always receive one eight ounce candle and sometimes two just depending on the month. I'm hoping I always get a car air freshener because I can't believe how well this lasted in my car and how cute this is just hanging from my rear view mirror. So again, I'll link Wicked Bayou candles down below in the description box so you can get your hands on this candle subscription.  I think he's up. Let's go get him. He's been sleeping for hours. OK, look at my house. It's just covered in dog toys. Welcome to having Palmer and several dogs. Do I see a little nugget? He's OK. OK. And I convinced him to come outside. Hi, buddy. How is your nap? Did you have a good nap? Now we just have the big one to come out. Yeah. Hi. Hi, cutie patooties. Hi. So here's my lunch for today. We are doing a what I eat in a day of meal preps, which just shows you that you can meal prep and it's great because everything's on hand for you to have for your meal. So this is the glazed poison meatball rice bowl that I also meal prepped. I went ahead and added a half of a cup of rice to mine. And then the meatball recipe with some carrots and green onions. You guys, this is absolutely delicious minus seven points. It is a three for the rice and four for the meatballs. Now you can just have the meatballs. You could change it up if you wanted to lower the points. But I'm totally fine with seven points and I'm also going to have my about fourth cup of water working on that gallon. So this is my lunch. I may have a sweet treat after. If I do, I'll definitely show you. So after my lunch, I decided I'm going to have one of my healthy eating all the time and go. Many bars. These are my favorite little nice, healthy, clean, sweet treats. They come in a box like this. They're perfect size. There are a hundred calories, three points on W.W. And like I said, the ingredients are super clean. There's protein, healthy fats. So I'm going to have one of those as the rest of my lunch and kind of my dessert. What do you think? Should mama have one? Yeah, mama should have one.  It's two thirty. I'm hungry. I'm going to have a snack. So I have this Chobani low sugar Greek yogurt in Gil cherry. This is my last one of these. These are amazing.  If you watched my how I cheat on W.W. video, I'll link it down below for you. I do not count the table spoon of granola. That goes on to my yogurt. However, it will be figured into my total calories for the day. So that's my afternoon snack for dinner tonight. We are grilling. It's over a hundred degrees here and we are feeling like a kebab night. The first thing I'm going to do before Troy comes home from work is get these kebabs marinating. So we're doing a Rosemary garlic steak kebab. So what I'm going to do is get the steak marinade ready to go. This recipe also marinades some tomatoes, which is pretty fun. So for the steak marinade, you're going to need some steak. This is just some top sirloin grass fed grass finished steak from my butcher box. You guys know how much I love butcher box. It is the best price and the most affordable for grass fed grass finished. So I'm going to chop these up into chunks and that's what will skewer on the kebab. I will link butcher box down in the description box with $30 off of your first box. You're also going to need minced garlic. The recipe calls for regular balsamic vinegar and honey. But I'm just going to use balsamic glaze because it's already thick and sweet. Like I did already add honey to balsamic vinegar. If that makes sense, I will make sure the original recipes linked on my website. Some stone ground spicy mustard and some salt and pepper. So I'm going to go ahead and chop up the steak into chunks and then I'm going to put it in as a block bag with all of the marinade ingredients. So the first thing I'm going to do is chop my steak. Now I'm going to go ahead and chop up the veggies for the kebabs. I have zucchini, a couple of potatoes, grape tomatoes, some mushrooms and then some fresh rosemary. I'm going to add all of this to a bag with a little bit of olive oil so that it can marinate as well. And there are veggies. So I added a couple of tablespoons of oil and a whole bunch of fresh rosemary. And then I'm just going to shake that up again. Let it marinate in the fridge for a couple of minutes and we'll start putting the veggies and steak on our skewers. All right, I'm going to start the skewers. I have some metal skewers. We'll skewer up some veggies and some steak. Put them here on the foil lined sheet pans so that they can go on the barbecue. So here are our kebabs. They look absolutely delicious. We have steak, potatoes, zucchini, mushrooms and cherry tomatoes. So we'll get these on the barbecue. We're not going to do any sides. I have to leave to show a house. And the kebabs are done. These look delicious. The recipe makes 12 servings and it is four points per serving. So basically per kebab. I'm going to go ahead and have two kebabs since this is all that we're having for dinner. How cute is my little margarita air freshener in my car? It smells incredible. All right, I'm off to show the house to my clients. She's in a really hard, hard, hard price point. I have a feeling this house I'm going to maybe the best that she's going to find in her price range. It's hot. It's 107 here. I did throw a skirt on so that I wasn't wearing pajama shorts to my showing. So we are off and running in the heat.  So I want to get some footage of it before that happened. So I brought the utopia snacks. You guys know I love this. This is the bananas for chocolate. I really, really like this one. It's so good.  This is four points. It has eight grams of protein. I love utopia snacks. As you guys know, I love this one and the espresso obsesso. And then my least favorite is the honey mustard. But if I'm craving something savory, I'll gravitate towards that one. I will link utopia down below for you guys with a discount. Highly recommend. Great for on the go. So here's the house I showed my client. It's actually really cute. So it looks like she's going to think about putting in an offer. So wish us luck. Thank you for joining me on another What I Eat in a Day on WW. I hope you enjoyed coming along with me today, seeing all my food, that really good dinner recipe, my new pillow, my candle subscription. It was a fantastic day. So if you enjoyed this video, don't forget to give it a big thumbs up. And if you're new or you haven't yet subscribed, I'd love to have you here. Hit the subscribe button and click the bell next to it. So you never miss a single video. Check out the description box down below again for nutrition coaching, links and discounts to everything I shared with you in today's video. And of course, my Facebook group head on over and join us there. Thank you guys again so much for watching. Have a beautiful day and I'll see you next time. Bye.


Hello, artist, friends, and visitors to Monet Café. Today I have a quick little lesson for you on how we can actually apply pastel, soft pastels, to not only watercolor paper, but watercolor painting. These are just a few little watercolor studies really that I had done a while ago, and I wanted to apply some pastel because I just love how pastels are so brilliant and they really make the colors sing and make the painting so vibrant. This is one that I have already done that to, and if I hold it up close, you can kind of see where I've added the pastel. You don't want to overdo it with this technique, but we're going to talk about that more right now. So let's get started. It's a pretty simple technique, and I think you're going to like it. Let's do it. Okay, so here are the two little watercolor studies that I've chosen just to describe and demonstrate this technique. I'm using two different products here. I'm going to show you two different techniques that you can do this. One is using clear gesso. It's basically, it's by Liquitex. It's basically just a liquid, kind of the consistency of syrup, that you can apply with a brush or a foam brush to a surface and give it more grit. If you've watched my channel much, you know that pastels typically need some grit to hold on to, and we use pastel papers which are sanded, almost like sandpaper. So watercolor paper is not sanded like that. It's got a little bumpy surface to it, which you could put some pastels down here, but they're not going to stay. They're not going to fix to it very easy or hold to it very easy. And so what we're going to do is create a surface that we can allow the pastels to not fall off and to get a little more vibrant color. So this is one of the ways, this product here, and this is another product. I use this one quite a bit in some of my videos. It's a spray fixative by Blair. I like this one recommended by Karen Margulis, and she uses a lot with her beautiful paintings. But I use it never at the end of a painting because it will darken your pastel painting, but just to add a few more layers or get a little more color to allow me to get more grit to that painting. And so this product can actually be used right on watercolor paper. So on one of these I'm going to use the Clear Gesso, and on one I'm going to use the Fixative. Both of them will give me a little bit more of an ability to put some pastels down. So let's get started with these techniques. It's so fun. All right, so the first one I'm going to do is with the Blair Fixative, and I'm going to do this one. And because I don't want to take this one down, I'm going to cover this one up while I spray it so I don't get the spray on here. I've also moved my camera back a bit because I don't want this Fixative to drift onto my camera lens. Also, with that in mind, you don't want to breathe this stuff, okay?  But if I'm doing a decent amount of this, I will take my artwork outside to do that, okay? So just keep that in mind. Some people ask about whether or not pastel dust is bad for you. Also, some people wear masks. They have a little reaction to it, but that's very rare. I have been doing this for years and I've never had a problem with it. But anyway, so back to the Fixative. We're going to just spray a light coat on this just a few inches back. I want to get enough on there to where it'll actually hold to it. Okay, that's good. Now I'm going to blow this dry and step out of the room for a second. Okay, now the Fixative is dry. Okay, and you notice it didn't darken the painting very much with watercolor, okay? So it's not really going to darken watercolor, but Fixative will darken pastels. Might be a hair darker, but not much. Now what we're doing with this is I'm not creating a pastel painting. I'm enhancing this with pastels, okay? So I don't want to just totally cover this up. I just want to use the brilliance of these pastels that I've chosen to just really create some intensity and some beauty to this little watercolor painting. So let's get started. So I'm just looking for areas of enhancement. I really like a little bit of this. That's a little too dark. Primrose blue. That's one of my favorite colors. It's like, is it a blue or is it a purple?   I just, you get to where you can find where corners are on the pastel. And it really helps to be able to feel your way with pastels. All right. I really love what's going on in these grasses down here. I've got some worms and coals, okay? So I'm going to represent that with, this is a little bit of a cooler green. A little bit of a cooler green. And so I'm just going to scumble. That's a word that just means to kind of, almost seems like it's just being messy. But there is a little reason to it. It's not all haphazard. So just getting in a little bit of these cool greens. My paper's moving around a little bit. I apologize for that. And maybe a few of them just kind of coming up and around. And I also like some of these warmer greens. Now this one might be a little dark. Let's see here. Oh no, I like that. Got a little warmer greens going on in here. So just scumble it all around. Maybe some back in here. We got some back in here too in these trees. So again, I'm just finding a spot, also a spot that's not dirty.  All right. So a little bit of this back here. Not too much. We don't want too much intensity of color in the background. All right. I think I need a little bit darker value of those cooler colors. Now this is more of a, just a, I love this color. Look at this brilliant cool blue somewhat teal green. And I'm gonna get a little bit more of these darks down in here. I'm gonna have to hold this paper as it keeps moving on me. Get some of these down in here. Okay. And I like some of this kind of brilliant purplish blues down in here. That's a little bit of that. Oh yeah, that's really pretty. And these, if I recall the reference flower, it just had all these pretty flowers just growing up along this fence row. And I wanted to keep this one so loose and not fixed or tight because the flowers just look so free. Now this is just a brilliant beautiful magenta pink. And see, it's just really some of those darks on there. Oh yeah, like that. And you want to be careful not to do patterns, okay? I don't want to do dot, dot, dot, dot, dot, dot, dot, dot, because life is random like that. I mean, there is order to life, but there's a lot of spontaneity, which is what creates beauty, I think. Now I'm just doing a little bit of these lighters. Now I might throw some of the lighters over in here off these flowers. I have a little ink drawing on this too, which sometimes I'll do. There's just a little bit of the ink pen I've used to indicate leaves, but keep them very subdued. I'm going to get a couple other little colors and we'll finish. All right, believe it or not, I don't want to do too much more. Again, I am just enhancing this, not doing a full pastel painting. I like some of these lighter pinks in here. I want to pop a few of those in here. One thing you'll notice real quickly you can accidentally do with watercolor paper is, with watercolor, you want to preserve the luminosity of the paper. Your lightest light should still be very bright because the paper is showing through. You have to be careful not to darken up your watercolor too quickly. All right, so now I'm just going to add in. I like this purple here. I don't want to do too much back here because I want to keep these looking far away and the less detail the more that's going to happen. Sometimes I have a problem with my left hand in this camera because it's awkward sometimes. All right, so I'm adding a little bit more to that shadow and a little bit more to the shadow under this window and going down into these grasses. All right, so now this one is the one where I'm going to apply the liquid gesso and more pastas. All right, with the liquid gesso I'm just going to shake it up. I'm not even sure if you need to shake it but I do and I'm just going to use a little foam brush here. This one I don't have to worry about breathing or moving my camera back because it's not getting in the air like the fixative was. All right, so I just put a little on my brush and we're just going to paint it on here. Some of it dripped. I'm going to make sure I get enough of it on there and this stuff doesn't dry super quickly so you've got enough time to just work it. Now this will, as you can see, it looks, it dulls out the painting a little bit but that's actually okay in this case and it's going to brighten up a little bit more when it dries but that's okay in this case because the pastels are going to be the the brilliance factor in this. So let me blow this dry and we'll get started. I wanted to point out because I've had this question asked a few times about what to do when your paper warps. Water color paper, when you apply water, it's going to warp or most likely it will and what you can do, see how this is curved, is lift it up, turn it over, however you have it, you know, it might be flatter here to something. You're basically just going to apply water to the back so just get your foam brush cleaned out of course and apply just a thin coat of water, not much, and it's going to curve that back in the opposite direction. So let me do that real quickly and then I'll get started. Alright, so that application of water did flatten it out a bit. There's still a little warping but it's not too bad. Now I've blow dried the the gesso so now you can actually hear it, the sanded surface. More so, well you can kind of hear that one too, but I can feel it with my finger that this one is is more gritty than the fixative. Okay, so the the gesso is going to give you a little bit more grit so all I'm going to do now is just enhance some of these colors and values that I think really make the painting work. We often want to leave the background more subdued and blurry to push it back in the distance and foreground things will get more of the brilliant color and typically more of the darker values so I'm gonna get started on this one.


Things that only real martial artists do. The very first thing you do when trying on a new pair of pants in a dress room is to test how well you can kick in them. The next step is to try a multitude of stances. You base your purchases off this dress test. Buying shoes also follows this rule. You first observe the traction that the shoe offers and then you test how light they are and if they will impede your kicking speed. New shirts and jacket must allow full shoulder rotation and cross body stretches. The next are acceptable, but only when accessorized with smoke bombs and blackface masks. Now regardless of the article of clothing, you flex and assume a fighting stance in the dress room just so you can try to assess the failure points. You all do that too. Don't even pretend you don't.


Hey everybody, this is Brett, and today I'm going to go over this 2022 Dodge Charger RT with the Daytona package on it. I'm going to go all the way around in this video. We're going to check out the interior, all the options. We're going to start it up, take a look under the hood in this video. First off, this is a 2022. The Daytona package is on the RT package. It's a package on top of the RT. It has the 5.7 liter V8 Hemi engine with the MDS capabilities where it shuts down four of the cylinders on the highway. This one's going to get you 370 horsepower and 395 foot-pounds of torque. The color on this one is frostbite. Exterior paint is what they call it. It's actually kind of a tint coat. We're going to go up to it in just a little bit and get a really good look at it. The paint code for this is PCA, if you were curious. This one's going to get you 25 miles per gallon highway, 16 city for a combined average of 19 miles per gallon. This particular car has the technology group. It also has the performance handling package, and it also has the driver convenience group. The other options on it are the sunroof and the red brake caliper group. We're going to go all the way around it. Let's start off by taking a look under the hood. Once again, under the hood we have the 5.7 liter V8 Hemi engine. It has the MDS system which shuts off four of the cylinders on the highway. 370 horsepower, 395 foot-pounds of torque. You can see that it comes from the factory with the Mopar cold air intake. It is a true cowl induction hood. Here is your emission sticker. Really tried and true to engine of course. Once again, 25 miles per gallon on the highway, so if you do a lot of highway driving, this might be the right car for you, and it achieves that by shutting off four of the cylinders on the highway to get you the better fuel economy, 16 city and an average of 19 miles per gallon. Let's take a look at the original window sticker and check out all the options on there and pricing. Here is the original window sticker. You can see it is a 2022 Dodge Charger RT Daytona Frostbite exterior paint black interior Daytona logo Napa and Alcantara seats. Has the 5.7 Hemi with MDS 8 speed automatic transmission. Everything on your left there is your standard equipment. Feel free to pause this. I'm not going to go over everything except the optional equipment here Frostbite exterior paint is a $95 option. The Daytona edition group is $3,995. Gives you the Daytona logo with the Napa and Alcantara seats, vented front seats, black edge premium floor mats, rear seat armrest with storage cup holders, everything there, heated seats, heated second row seats, and all that good stuff. When you get more into the real Daytona package where Daytona decals hood, roof, trunk, Daytona instrument panel, satin black charger, deck lid badge, Daytona front grille badge, black one piece performance spoiler, the heated steering wheel, power tilt telescopic steering column, the 20 inch by 9 inch low gloss granite crystal wheels and the carbonite interior accents which are really cool, we'll go over those in just a second. The tech group is a $1895 option, gives you advanced brake assist, rain sensitive windshield wipers, lane departure warning plus, automatic high beam headlamp control, full speed collision warning plus, and adaptive cruise control with stop. As a performance handling group which is a $1095 option, gives you the Brembo four piston fixed caliper brakes, the flat bottom steering wheel, high performance suspension, and then the driver convenience group is $1480, gives you blind spot indicator with memory power heated mirrors, and front and rear LED map pockets, bi-functional HID projector headlamps, deluxe security alarm, and locking lug nuts. Power sunroof which is $1295 and the red brake calipers are $595. Total MSRP is $53.55 on this car if you want to get your summit price with all the rebates and incentives on it in the upper right hand part of the screen is a link to our website so you can click that and check us out there. Three year 36 bumper to bumper, five year 60 powertrain, there your miles per gallon, and greenhouse and fuel economy ratings as well as your crash test ratings, so a lot of five and four stars up and down the board, so a very safe vehicle. Let's check out those rims and then we'll take a look in the trunk and then go over the interior. Alright so we have the 20 inch by 9 inch granite low gloss rims which are specific to the Daytona package and this car it comes with Goodyear Eagle RSA tires, these are 245, 45 ZR20s, you can see the heavy duty Brembo brakes there with the red calipers, gives it a really nice look, and the locking lugs must be in the trunk because this one just has the normal lugs on it but really good looking rims. I'm going to head to the back of the vehicle so we can take a look at the tread pattern a little bit on the tires, you can see that kind of a little bit more of a sporty tire on there, and of course four wheel disc brakes. Now coming around the outside here the Daytona stickers, you get this sticker, the one piece low gloss deck lid spoiler, of course the LED tail lamps here, you get the chrome tipped dual rear exhaust, and the other thing to note is that is wrapped as well, that's not paint, that's actually a wrap, and then you get the decal on the hood there. So those are all the Daytona specific stickers that they're talking about on this particular car, and we'll take a look inside the trunk here, I like that you press the button and the trunk opens up all the way instead of kind of stopping halfway, that's really nice. This is for your box for your pedals and stuff, this one comes with the tire inflator kit and this is also where your battery is located, those seats do fold down for extra storage. Let's take a look at that frostbite paint because it does have just a little bit of metal flake to it, it's kind of like a tint coat, but I guess you could consider it a metallic paint, it's really a cool color, I think they started using this color in 2000, let's go take a look at the interior. So here is the Napa leather with the Alcantara suede, this outside is leather, this interior is suede, you get the Daytona stitched into the backrest, really good looking and that is on both front seats, they're highly bolstered so they really hug you, they're heated and cooled power driver seat factory formats, this one does have auto headlamps, the power tilt and telescopic steering wheel, and you do get power windows, power locks and memory driver seat, it does have the Alpine premium sound system, you get the leather bolsters on the doors as well, and this nice thin gloss black trim on the doors as well. Now as we hop inside, before we take a look at that instrument cluster, I want to point out this carbonite trim, this is what, this is part of the Daytona package as well and specific to the Daytona package, really a cool design and it's not just a design, it's actually, there's texture to the dash so it's pretty neat and then of course you get your adaptive cruise controls, your normal cruise controls, bluetooth information center controls, the flat bottom steering wheel and you know the Dodge logo on there, the thumb pads on the steering wheel and then the paddle shifters on there, we'll turn the ignition on so we can check out the instrument cluster and then the radio and everything that this car has to offer on the interior here. Alright so you do get the digital speedometer on the 7 inch LCD display, pretty much everything is configurable on the corners, you can add miles per gallon, miles to empty, trip, all that good stuff to this instrument cluster, you can configure that, it has the heated leather wrap steering wheel, I'm guessing it's heated, it is heated and you can control that on the 8.4 inch radio here, this is the 4C radio, now you're heated and cooled seat buttons as well as your heated steering wheel, you get AM, FM and Sirius XM radio capabilities, you can do your climate controls here as well, I'll just turn this on so we can see how that works, now you can control everything up here or you can do it on the more tactile buttons down here, this one comes with super track pack which gives you the performance pages up there, you have a launch control as well, drive mode setup, you have all your different apps on here, that's your settings, there's your performance pages, you have projection manager, you can project your cell phone to the screen, so that's kind of the cool thing about this radio as well, this one doesn't have the factory navigation system on it, project your cell phone to the screen and if your cell phone has got Waze or Google Maps it will go right up on the screen and you can use it through the screen on your phone, it's really a cool system, we actually did a demo on an 8.4 4C radio with Android Auto, if you want to check that out that's in the upper right hand part of the screen as well, so a very very cool system and as soon as we're done in the interior here we're going to go start the vehicle up and do a final walk around with all the lights on, so definitely stay around for that 8 speed automatic transmission, your keyless entry with the remote start, you get that carbon night trim on the center console there as well which is pretty sweet, you get the Daytona badge on the dash, looks really good and of course this one has the power sunroof, up here you get map lights, home link buttons for your GradShore security systems and lane systems and assistant SOS buttons in the rear of your mirror. Let's take a quick look at the back seats and then we'll start it up and do the final walk around here, so the back seats have the same design as the front seats they just don't have the Daytona stitched into the backrest, you do get latch child safety system, these seats fold down like so and they have this little handle right here which releases the latch right there to let you pull that down and then you saw that there were cup holders right here, there's also a little storage bin as well, now these back seats are heated on the outboard side meaning the driver and passenger side are heated, you do get two USBs so like the center part wouldn't be heated, but the outsides would be. Then you get the floor mats back here, lots of room, very comfortable back here, a decent amount of head space as well and you do get child safety locks on the back doors. Alright we're going to start it up and take a final walk around with all the lights on. It sounds really good, that 5.7 Hemi, once again 370 horsepower 395 foot pounds of torque. Let's do the final walk around here, I would personally like to thank you for checking out the video today and hopefully you enjoyed the video, tried a little bit different style on this one and if you liked it give us a like and you can subscribe to my YouTube channel, youtube.com slash summit auto, new videos up just about every single day, you get the Daytona badge on the grill there, really a good looking car, fully functional hood scoop, then you get those HID headlamps, the LED running lights that go around the ring there, does say dodge on the side of those HIDs and then you get the LED fog lamps which are super bright as well. Now you can take these off, they're to be removed by the dealer at time of delivery so these don't get all scuffed up on curbs and whatnot but thanks for checking out the video, hope you liked it, remember to like, subscribe and share on the YouTube channel and to see more pictures of this car or one of our other 550 new and used cars, trucks, SUVs, minivans, Wranglers, sports cars, chargers, challengers, you name it, we got it, we got a lot of sports cars so go check us out at that website right there summitauto.com, full pictures and descriptions of every single vehicle from two locations all at summitauto.com if you'd like to check out more HD videos you can go to youtube.com slash summit auto, remember to like, subscribe and share on this video and all the videos that you see there, click the bell notifications and you'll get updates on the videos I do each and every day here at Summit Automotive. In fact in a second you'll see a link to subscribe to my YouTube channel, the upper left, a link to more Dodge Charger videos I've done in the upper right, a link to this vehicle in our website in the lower left and a link to one of our latest YouTube videos in the lower right, click those, check us out and we're super excited to be offering the brand new 2022 Dodge Charger RT Daytona package and Frostbite Clear Coat. Thanks again for checking out the video remember to like, subscribe and share on the YouTube channel I really appreciate it, thanks again


I'm Bianca Renee and you're watching Bianca Renee today and today. I'm so excited to announce that I've officially hit over a hundred and fifty thousand subscribers words cannot express how thankful grateful and Blessed I feel to have you guys watching my videos. So of course I like to thank you all by doing a giveaway, this is my 150k giveaway And I am going to be showing you all the prizes that one of you like literally possibly you watching right now My win now if you've been following me on snapchat and Instagram you saw that I've been using curl keeper a lot lately And that's that's how I got these amazing day five curls So because I love the curl keeper products so much I'm going to be giving one of you all of my favorite curl keeper products Including the curl keeper slip the 30 second detangling spray the flexi brush for detangling those curls my all-time Favorite the curl keeper gel the curl keeper original and the curl keeper water bottle, which is what I used to refresh my hair Every day. I'm also going to throw in the curl keeper styling cream. I Don't know where it is. I literally pulled it off my shelf to put in this video and now it literally just disappeared Now although I can't find it right now It does look like this and this is also going to be one of your prizes if you aren't familiar with any of these products I have videos on literally all of them I will put links to all my curl keeper videos in the description box below and at the end of this video Okay, so now that you know how awesome the prizes let me tell you how to enter It's really quite simple. I just want you to leave a comment telling me two things The first thing I'm going to tell me is what was the first beyond grenade today video that you watched that made you push That subscribe button. I'm just curious on how you became part of the family The second thing I want you to know is what are you following me on? Are you following me on snapchat? Do you follow me on Twitter? Do you follow me on Instagram? Do you follow me on all of them? I'm just curious Now if you don't have other social media, that's totally fine I'm not going to like be mad at you for not having Twitter or whatever then just say you only have YouTube that you watch me every Sunday But wait, there's more. I'm also going to do an Instagram giveaway I'm so close to hitting 30,000 followers on Instagram, so I want to do an Instagram giveaway I'm actually doing a collab with high Felicia if you're not following high Felicia You definitely need to on YouTube and on Instagram She is like my curly sister that has the same goal as me, which is to help all you guys with your curly hair She is someone that really went through the struggle of having damaged hair and revive them to a whole new Level so definitely follow her on YouTube to watch her tutorials and also follow her Instagram for weekly curly hair tips So I will be sure to put one her YouTube channel down below So you guys could subscribe to her YouTube channel and really get some great curly hair tips And I'm also going to put her Instagram because she has a prize and I have a prize So let me show you what's going to be in my Instagram giveaway My Instagram winner is going to receive full-size bottles of the myel styling gel the detangling Co-wash and the edge gel you're also going to get the tally would jeed shade cocoa Condition daily leave-in conditioner as well as the shade cocoa two-in-one conditioning co-wash I'm also going to include some makeup like the beauty blenders by the cream shop and real techniques You're gonna get the very popular lights camera lashes mascara by tart I'm including a bunch of different lip glosses lipsticks eyeshadows another eye shadow palette by nix with some darker colors as well as some face masks and One of the most exciting things is a brand new full-size Morphe 35 oh Palette this palette right this was a tough one to give away because it's so beautiful But let me just show you. Let me give you a little sneak peek. Look at those colors You guys see that these are like really beautiful fall colors your neutrals your brown some shimmers I have this palette myself. I got two of them, so I'm giving one away to you guys and Oh, and then once your hair and makeup are on the leak, you're definitely gonna want to take some selfies I'm gonna include this ring light for your cell phone So you always could take the perfect selfie now if you want to enter the Instagram giveaway Make sure you go to my Instagram at miss beyond grenade And you will see a giveaway post with all the rules and all the prizes then you also can go to high Felicia's Instagram page follow her and then read her instructions for her post So you now have three Chances to win some awesome prizes by one leaving me a comment on this YouTube video to win my curl keeper prize Then you can go to my Instagram leave a comment on that picture to get all the prizes I just showed you and you can go to high Felicia's page into her giveaway and win some other Amazing hair products as soon as I hit 30k at Instagram Felicia and I will be choosing our two winners and Someone is going to get all these awesome Prizes I always say you either don't enter at all and have a zero chance of winning or Enter on all three and have a chance if you are excited about this giveaway go ahead and give me a thumbs up and Subscribe I post two new videos every week once on Friday and once on Sunday, so I hope to see you all next week Thanks for watching beyond grenade today


Hello and welcome to the session, I am Deepika here. Let's discuss the question which says choose the correct answer in the following. If probability of A upon B is greater than probability of A, then which of the following is correct? Probability of B upon A is less than probability of B. Probability of A intersection B is less than probability of A into probability of B. Probability of B upon A is greater than probability of B. Probability of B upon A is equal to probability of B. So let's start the solution. Now we are given if probability of A upon B is greater than probability of A, then we have to find which of the following option is correct. So if probability of A upon B is greater than probability of A, this implies probability of A intersection B upon probability of B is greater than probability of A, provided probability of B is not equal to 0. Now this implies probability of A intersection B is greater than probability of A into probability of B. Again this implies probability of A intersection B upon probability of A is greater than probability of B. Now this implies probability of B upon A is greater than probability of B. Now this is our option C. So C is the correct answer.


Open up Superstar KO. I have not opened Superstar KO since they had the college teams in it. And that was an, dude, that was sick. That was so much fun. But finally, bow knows. Bow knows Superstar, challenge your friends and I like betters with new Drap Pool Edition, Bow Jackson. There is a Bow Jackson. Right now, it's gotta be a legendary. Legendary Bow Jackson in the pool in Superstar KO. But I know a while and you know what? Campus Legends is still in. I thought they were gonna take it out but they didn't respect it. We'll play infinite. So once we get this Bow Jackson, we can literally play until we lose. I don't know what abilities he's gonna have.  Also, you know what I just remembered? There used to be, there used to be the John Gruden Rhythm. They've switched it to coach Dean Strauss. I think they still are gonna give Gruden a new team. But instead of the John Gruden Rhythm, it's gonna be called the John Gruden Racism. And I really wanna play as that team. I feel like I had to- The best case scenario is Lamar and Bo. And then I could run just read options like crazy. I feel like Backyard Heroes could be pretty good. But we'll go with Ground and Pound. Presumably they have some read options in there, but.  I have been here for so long. Bow Jackson! Bow Jackson had back Bow knows high chance to win interactions versus the first defender. He has his own Superstar KO ability.  It's literally called Bow knows. That's hard.  That's so, dude, I don't even know who I drafted first. Oh, that was my first pick. Okay, that was my first pick. So now, now we take Julio. We have a double MIY receiver in case like, we end up in fourth and 30 somehow. Having Zeke, I mean Zeke's the good pick here, but having him does nothing. I think we take Kittle and I assume he'll block better than whatever gold I have in there. None of it matters. I'm running the ball every time. I don't know if you guys will recall this when Chandler Jones or Levante did. Or, ah, no, you gotta go Miles Gear. A sample of Force Miles Gear is nasty. I don't know if you guys recall, a year and a half ago or something like that, they dropped the Giannis on set of Kupo into Superstar KO. I sat here and sweated for like 30 minutes to draft him.  This game is crucial. I have to win this ship. I can't go down to swinging right now. Let's go Avalanche, Jamal Adams, so broken. If you hit stick someone coming down towards them, it's a fumble. I can't wait to use this bow knows ability.  Also, of course, I wanna give a huge thank you to Manscaped for sponsoring today's video. Christmas came early this year. I had a package at my front door. It was from Manscaped. It is the brand new performance package.  True words have never been spoken. This is the world's first all-in-one grooming kit. Let's start out with this beast, the Lawnmower 4.0. A waterproof cordless trimmer built with advanced skin-safe technology so you don't cut yourself while shaving. Got a cool little LED light to help guide you. The best ball trimmer on the market. The Crop Preserver Ball Deodorant. Amazing stocking stuff for if you ask me. Goes perfect with the Crop Reviver Ball Toner. These two need to end up in your stocking this Christmas. And the most slept on product, the Weed Wacker. This is an ear and nose hair trimmer. If you've never shaved your nose hair, take this as a sign to start right now. You may not have that angle to see what's up there, but other people do, especially girls who are shorter than you. And Manscaped is no longer just for shaving below the waist, they have the Shears 2.0 all-in-one nail kit. It's got a nail file, nail clippers, scissors, tweezers. I keep this in my travel bag, I'm so glad I have. This package is all you will ever need or all your friend will ever need if you wanna gift it to him this Christmas. And for a limited time, there are two free gifts with your order, the Shed Travel Bag and the Manscaped Anti-Chafing Boxer Briefs. You will be the ultimate gift giver. So don't wait, go to manscaped.com forward slash MMG to get 20% off plus free international shipping and those two free gifts. You can always just click the link in the top of the description. Manscaped, thank you for sponsoring guys, enjoy the rest of the video. Bo Jackson is a 90 overall. So his abilities are leap frog, so you can't fumble when you hurdle. I might try that. Bruiser Evasive Tank, that is so broken. Those are like the five best abilities.  He has Juiced Hittsticks and Stiff Arms. All right, well, if anyone's wondering why I'm gonna do it. He literally fell on his own accorded guy. This is a questionable play call. Pitchers are just not that good this year. I'm going for it anyway. Ooh, I think he pitched down. Ooh, we gotta get through. I kinda got through the corner. All right, we're going with the stretch. Definitely there, bo get through one, get through two. I gotta say it is super fun to try out leap frog because you can just hurdle with no penalties at all. I'm gonna start trying it.  I think I just noticed it. High chance to win interactions versus the first defender. I think that means everything. It's a combination of freight train and first one free.  He's gonna run through them. Yup, we're gonna get this edge for sure, I wanna go. I wanted to try a hurdle there.  Let's get this verse down. He's gonna clog the middle. So we really gotta make a play here. Let's go bow. Uh-oh, uh-oh, we need two. Can we just go power strong, lead dive? I feel like he's just so built for this. Five yards out of bow, Jackson. Eight rushes, 50 yards.  This formation is called Maryland Eye Heavy. Let's get the edge. I've been hitting the middle so much. Yup, people it's, hold your blocks, yes sir. Switch on, switch on, come on. Come on.  He literally shrugged them off like he was a pee-wee football player. You know what, why don't we try and aggro catch out of bow? Yeah, I'm just gonna send him right here.  Damn, he's got Derek, Henry, Lamar, Jackson and maybe Travis, Kelsey, Grudge, Kittle. I don't know who that is. But he's kind of open on the left side. Oh no, lock, it's gonna snag this one. Big hit.  Big hit. Oh no, that was Jamal Adams. I think that was Jamal Adams.  Okay, Derek, Henry. I know he'd throw this. Come on. Is that not an avalanche? Big hit? I think the angle screwed me up there. If he was at a different angle, I think that was gonna be a pump. He's got the corner. He's gonna throw here. He's gonna throw here. Make a mistake. Make a mistake. That is not a mistake. That is a great play. Rifles one in. We gotta stop this. I don't think he runs this. Can't audible. Come on. That's okay though.  So let's go back, get bow Jackson again but get a better playbook. I feel like record breakers had really solid plays but I also, let's go backyard heroes. I think they have options. Megatron is still in this? Oh my God, I saw the orange. I thought I got bow bro. A team though, could have Meg. Did I have drafts so many times?  I really like that my apologies. Yeah, I've been here a while. I apologize, right? I didn't even know what our team was either. I just saw it. We have Russell Wilson, Darren Waller, bow Jackson and we are the record breakers. Again, I don't fully remember the playbook but I have used record breakers a lot. I know I've liked it so I know at least they have some solid run play. Plus Russell, I mean Russell Wilson's not Lamar but he's pretty fast. He got a solid defense too. Go Jamal Adams again. Wow, we don't have a single comment on this team. We got two rares, a legendary and three rares, I believe. All right, ball. You have a better playbook. I have no excuses now. I didn't really have an excuse in the first place. First in 10, we have a solid inside zone. Let's see how this looks. First run, looking very good. Oh my God, he's got avalanche, doesn't he? I can't believe with avalanche, okay. Well, he is truly the best head back in the game and I have gotten pretty unlucky here in these last two.  I would love to go overtime with this guy and I'll go right back at him. Just gotta keep Miles Garrett coming off the edge. I got Junon. Oh, he's got bow as well. What do you know? Damn, his team is cracked too.  He might have been doing exactly what I was doing. Yup. Oh, it's a play-action. Get to him! I would love if you would pick that off, but okay. Fourth and one. One yard of a bow Jackson. It's low key, very easy. He does not hand it off. He's throwing deep. I love that. Let's go. Let's see it over time. You got lucky on that first one. Bow's not gonna make that mistake again.  I'm getting on the QB. Thick, six. Let's go, baby. Let's go! You don't even need bow, I guess, but you know what this does? This six is the next game. That game was ugly. It's over though.  I'm gonna try and hit bow Jackson on this playmaker here. So let's bring bow right there. Oh, he caught it! Really not what I was trying to do. I just hit hurdle. I hit hurdle and you just spun out of that tap. Ooh, he's sending a house. Let's just hurdle once we get up to this line, yeah? We're double duke!  I think he's gonna keep clog in the middle. Let's try and get to the edge, dude. This, this. This is either a two yard loss or a lot of yards. Let's see which one it is. I didn't ran one over. That just, that all just said. Bow is running around here. An interesting looking round. I'm just gonna playmaker him. Oh, I don't think he's really that open. Air trucks, dude. The latency is killing me right now, but he did get really solid yards. And we were in this same position before. All we did was we got to the line and we hurdled. Think we gotta try it again fourth and one. You know exactly what I'm doing. It doesn't matter. It doesn't matter. Let's go. Oh yeah, come up the middle. Great block. Great block. Give me a one on one. You know he's going through that. Oh, and that stiff arm was nasty. They was an extra five if we had stayed in bounds, but still an extra two or three. Oh yes, right side. Yes sir, get through him. Jamal Adams. He had hit me. I was gonna fumble. That was an avalanche right there. Yeah, he's coming up the middle. This has gotta be there. I should have a one on one with an E.V. here. Oh, so low. Turn, E.V. Second and goal. Bo right up the middle. Get through one. And I don't know about the rest of that animation, but that was three yards. Get there Bo. Now I almost think we gotta get in the air. Do I have anything where Bo can get this touchdown? Cause that'll be way cooler. Inside cross. Ew, this could be a Bo Jackson touchdown, but it's gonna be sketchy. So Bo Jackson's got basically that four verticals route. I'm gonna block Eifert. He's following it. We're throwing it anyway. Go Bo. Russ, you have to catch Darius lay. Oh no. Where is Russ?  What's wrong with you?  Oh, and I have Lamar. I have Lamar. I have backyard heroes. This should be, I think there's at least triple option in this playbook. I think at the bare minimum, we have that. All right, Matthew's sick. Okay, so Chris Jones momentum shift, it doesn't work anymore.  So I really can't take that. There's just no point. So I'll take your baby's wife. The double Jackson backfield. I'll show you a double Jackson. I think the move is probably just to give to Bo Jackson first year for sure. You're done. What's crazy about this read option is if I keep it with Lamar, he has trust. I can't fumble. I feel obligated to continue to look at the full. Lee Frog. He's not switching on the tackles. I don't think Lee Frog will ever work. Jump on, jump on Juicy Juice. Okay, he doesn't, but the pitch key is there. Bo's got it and you're done for. Juke. Yes. Pitch. Oh, they counted that. They let that through. Come here. They're gonna switch on and go low. I'm going for a spin. Oh, he switched on. Can almost just keep it again. Look at the left side. There's not a soul over there. Just gonna keep it. And now he'll switch on, right? No. That's randomly Juicy, but the Juke from Lamar takes us in. I guess it doesn't really matter which of our Jacksons gets the touchdown because one of them is gonna get it. And that's got my Jackson hard. Let's just give this one to Bo. That O-line has been absolutely dominant up front. And I literally didn't even run into anyone.  Well, five wide action, Jackson. I'm going left side. Ooh. I missed. Jenaevious White just lost to Eric Ebron. It's superstar KO. You can't kick field goals here. You gotta get that Tuddy or it doesn't matter. Oh, I'm on him. I'm on him. Rodgers is gonna go down. Ooh. Where? Rodgers! Wait, we can get that. We have it. What? I will personally hand you $5 if you've ever seen that happen.  All right, finally. Dude, I literally have had Bo Jackson for three games now and I've won for three. If there's more than three or four minutes left on this video, buckle in, get your popcorn out. You got a good one coming. Triple option. We got a read key on the right side. Bite on Juicy juice. He bites. Lamar's got room. We go with the pitch. Whoa, you are way far back there, Bo. I don't know if you ever play football, but it's five and one. Okay, one yard back, five yards to the right. Not five. Boring. Third and four. Gotta get the pitch. Oh my God, he's wide open. I'm trying to pitch. Don't tell me I'm getting saw stuff like this, bro. I think I just gotta hand it to Bo. This is against Dot City. We're giving it to Bo. Let's go, buddy. Yes, sir. That's how you know you got a run game team. If it's more than seven, you're going to the ground.  Wait, he broke the tackle.    Ah! Whoa! Did I just run over Ed Reid? Doesn't he have avalanche? That is Ed Reid with avalanche.  He has enforcer avalanche. Oh my God.  And I'm a big boy! Five rushes, 34 yards. This is so sad. Yeah, he bites. Pitch!  Are you taking us over? To pitch!  Lamar. Oh my God.  All right, let's make the read. Let's make the read here, because if he bites on Bo, oh, yep.   He was showboating and broke the tackle. That's messed up. Daylight?   I am going to sack Tom Brady. I'm going to sack him right on the lips. Yep! Right on the lips. He liked it way too much, dude. Honestly, the play is probably to send another screamer here. Oh, oh no. Oh no. Oh, slant man. Slant man could not break the tackle. Thank God. He's throwing underneath. He's way too scared to throw tall. Yup! Yup! What? No, you did not catch that. Basically the same thing. He's going to throw left side. Oh!  He's not going to run with Tom Brady. So let's just keep you spied everybody. Right side. Right side. Let's go! Got another one. We got another shot with Bo, baby. Goal line stop. Keeps us moving. Let's get it. Is that RPL Peaks on Bubble? The RPL Peaks on Bubble. No, they don't have it anymore. They took magicians out for whatever reason. Oh, okay.  Is that Leveon Bell?    Easy.   Bro, you better hope. You better hope I don't get the two-point conversion. So I can promise you I'm scoring. Better hope I don't get it. There's some nasty stopping goes, but he's set the house on that one. Edge set. Gets through one and that's a first.  Great blocking. Oh my God, a pancake. Amar is going to juke inside. We're moving now. First and 10. Bite on Bo one more time. Bite on him, bite on him, bite on him. He bites. He bites. Amar is off to the races. We got a little juke. One goes down, two goes down. Lamar, I see you.  And he will not be denied. First and goal, three yards to go for Bo. Ooh, look at that. Bo'll run. We might have to pass. He's literally gonna run, Command. Ooh, wow. I thought for sure I was gonna get that. Clean touchdown. Clean touchdown. I gotta do the same thing. We are not in tug-of-war yet. I still had to get my two points. For some reason it's acting like we're in tug-of-war. Ooh, I kind of wanna look there and waller. I'm hoping that's a blitz. Blitz, blitz, blitz. It's not a blitz. Get around him. I tried to stop and go him and I couldn't get a great play by him. He switched on and made a great play. We made a valiant effort though to get back in that one. Bo Jackson back in Madden, baby. Good time. I love you guys. I can't wait until it comes out on Ultimate Team. That'll be the real test. Either way, I love you boys. Thanks for watching as always. I'll see you in the next video. Peace out.


Since the Mueller report was released, which showed no collusion and had no indictments for obstruction, the media and the Democrat party have been foaming at the mouth to convince us that no, there really was collusion. We've seen a few attempts to quell the media hysteria by people like Rod Rosenstein who defended A.G. Barr saying quote, this notion that he's trying to mislead people I think is just completely bizarre. Rod Rosenstein as far as we know is no fan of Trump so it's pretty damning when he starts calling Democrats and people in the media bizarre. In this case we have former Attorney General Michael Mukasey who is brilliantly exposing Chris Cuomo for the hack he is even outright telling him that he's misleading his viewers. Something we've been saying on this channel for years now. Did you see what happened there? Chris Cuomo is so used to spewing his misinformation in his bubble that he wrongly thought that he could pull one over on someone who actually knows what they're talking about. Mukasey is right that the report spells it out. There was no collusion and I'll read it for you right here on page 181 quote, the investigation did not establish that the Russian contacts amounted to an agreement to commit any violation of federal law including foreign influence and campaign finance. Did you catch the part where it said there was no collusion to influence the election? The report even says that there were Russian attempts to collude with the Trump campaign but that they all failed meaning that the Trump campaign people rejected it. There was no collusion none zero. Chris Cuomo is a hack liar who's just desperately trying to spin his way out of being wrong for the last two years. But this is a special counsel and it was put together by Rosenstein because he wanted it separate from the DOJ because of what he saw as potential counsel.  Typically that means they're not listening to you. In this case Chris Cuomo is spewing a bunch of DNC spin disguised as hard hitting analysis and he's hitting a roadblock when the sensei smacks him down. No Cuomo you didn't know and you're about to get schooled. We have three branches of government. I understand. This is within the executive. I understand. We don't sprout a new branch of government. But what your friend did is not just buy the book. This is where propaganda clashes with reality. AG Barr decided not to indict based on the complete lack of evidence after two years of investigation. That's his job. Chris doesn't care about any of that. He just wants to advance his narrative despite it being a completely debunk conspiracy theory. I find it interesting that earlier in this same interview he defends the legitimacy of the investigation by citing Rod Rosenstein saying this is a special counsel and it was put together by Rosenstein. But then a few sentences later he's attacking the attorney general as having done something outside the norm. Despite the fact that Rod Rosenstein defended the attorney general and called his critics bizarre. I think bizarre is a fitting adjective for Chris Cuomo.    Sure they've all lost credibility but they never really had a need to begin with. I think what they might actually be worried about is being exposed for their part in this entire fraud once Barr shed some light on the corruption behind the investigation. That's why they're trying to discredit Barr and I think you'll find that any time the media is trying to discredit somebody it's almost always somebody who's a threat to Democrats or the media. Hey thanks for watching please like share and subscribe. If you weren't aware I'm also posting on Bitshoot now. Hit on over there and subscribe if you want to see some of those clips that I know many of you miss. You can find all the links in the description or in the pinned comment. Thank you.