Hi. Welcome back guys. What happened? Did we pass the drop date or something? The class shrunk. Well, it's good to see you, the ones that are here. Today I want to talk to you guys about a concept that was fairly instrumental in my own career, which was the idea of generalization. The idea that when you look at a biological system and you see how it learns, can you say something about the region of the brain that might be involved in learning that's taking place? And the mechanism by which we made progress was toward this concept of generalization, which means that the learner is learning from error, makes a guess, sees an observation, forms an error, updates his belief, and then you look to see how does he change, he or she changes his or her belief about other things that it hasn't seen. And the way it generalizes says something about the shape of those basis functions. And those basis functions are what was interesting to us because we wanted to say something about different parts of the brain, different parts of the brain have different kinds of basis functions, and so can one make estimates of what part of the brain is being used. So to start out, there was one thing that I remember from yesterday's on last week's lecture that I wanted to go back to because I think it's an important idea that you may want to know since many of you guys will decide to take your oral exams with me when you want to pass your qualifying. So I want to distinguish between two concepts with you. When we have a random variable, x, that's made up of x1 and x2, each one a random variable, when we say what's the variance of x, well, what we do is that we find the variance of x1 plus variance of x2 plus two times the covariance of x1 and x2. And this is something that we've described, but that's very different than writing a probability distribution that's made up of two different distributions. So for example, on last week we talked about having a probability distribution, p of x, that was made up of row one times a normal distribution with some mean mu one and some variance sigma one plus row two, another normal distribution with mean mu two and sigma two. So for example, you know, we have a distribution that looks like this, right? So here what I mean by variance is very different than in this case. And just to show you that, I want to go through the math to describe what is the variance and expected value of a random variable that's described as a sum of two distributions, which is very different than a random variable that's a sum of two different random variables. Okay? So let's go through this to understand what this means. So what's the expected value of x in this case? Well, what is the definition of expected value? It's x times the probability of x and what's the probability of x? Well, it's row one times a normal with mean mu one sigma one squared plus row two. And of course, by this, if this is a proper distribution, this plus this must be equal to one, right? So row one and row two are both less than one or at most one and the other one is zero. So that's what we mean when we say expected value and because this integral, I can take the expected value inside and divide it and separate it. What I have is that x times a normal. So that's just equal to row one times expected value of x, which in this case is mu one plus row two mu two. So that's fine. The expected value of x is just a weighted means of these two distributions. What about the variance of x? Variance of x is equal to the expected value of x squared plus expected value minus expected value of x quantity squared. So what's expected value of x squared? That's just equal to row one integral of x squared times a probability of normal mu one sigma one squared dx plus row two integral of x squared normal mu two sigma two squared dx. And these integrals are from minus infinity to infinity. That's going to be equal to row one mu one squared plus sigma one squared plus row two mu two squared plus sigma two squared. So therefore variance of x is going to be equal to this minus this squared. And let me just check to see if this makes sense. So if I set row two equal to zero, variance of x should just be equal to sigma one squared, right? And that's, I'm missing a squared here squared. Well, I don't know. This, I have to go check my math. This doesn't, this didn't quite work out. This seems like those should be squared for this to come out right. Row one and row two need to be squared for it to come out right. But they are not squared here. Row two is zero. Sorry. I'm not sure what's wrong. I don't know why this didn't work out. I have an, I have an issue with my rows. That is true. So then it doesn't matter, does it? Yeah, that's true. No, I was only going to check to see if it makes sense. If, if, if I only have one distribution, then the point is rows one, so it doesn't matter if it's squared or not. Yeah. Well, not five. It has to be less than one. I mean, it can only be a, so it's not a distribution unless rows equal to one. This is integral has to be one. Yeah, yeah, yeah, yeah. So it may be right. I don't, I don't see, I mean, I don't have, I don't, I don't find an error in it. And you're right. If I only have one distribution, then it's correct. I may be right on this. I'm not sure. I checked it before on some, some, some other distributions and it works. But I was just a little confused here because of having a single distribution. I thought that, I thought algebraically things would cancel, but of course they don't cancel unless rows equal to one. Which has to be, otherwise it's not a distribution. All right, I will check this and I will come back to you guys on Wednesday. I think it's right. But not 100% certain. So anyway, the point being that when you have a random variable that is a sum of two random variables, its variance is very different than if you have a distribution that's a mixture distribution. And this is a mixture distribution. It's a mixture of two different, two different Gaussians in this case. All right. So let's go back to another thing that we talked about yesterday on Wednesday, which was that when we looked at the loss function, from the experiments that we saw from that paper where they estimated the loss function for individuals, they said that it looked like this, y tilde to the 1.75. So the error is not quite being squared. It's being raised to a power less than two. So I want to show you what this means from the point of view of how much you learn from error. And I want to show you that what this says is that your sensitivity to error is particularly large when you have small errors. You learn a lot from the percentage wise point of view when your errors are small, but when your errors become really large, you don't learn as much. That's what this equation means. This kind of a loss function means. So if we had a quadratic loss function, what it would mean is that I'm going to learn 20% of my errors regardless of whether the errors are small or large. But when I have an error function that looks like this, what this implies is that I'm going to be more sensitive to small errors and I'm going to discount large errors. That's just the intuition that I want to show you guys with this particular error function. So what this means, of course, is that we're going to look at the difference between y and y hat, and in this case raise it to some power q. So let me just do this, call this q my power that I'm raising it to, and suppose that I write my estimates as I have some basis set that is evaluating the input x, and I'm going to sum it up with some weights w to form my estimate y hat. So I'm going to have my learning rule where let's just worry about the first derivative where I have the derivative of the loss. So whatever is my derivative with respect to the w, I'm going to move in the opposite direction with it so I can rewrite that equation. Find this derivative with respect to my estimate, do the chain rule and write it like this. So I'm going to define sensitivity to error as how much I change my weights from before when I made a prediction to after I made the prediction. So I'm going to say w hat of n plus 1 minus w hat of n is the change that I made in my belief divided by the error. So how sensitive am I to that particular error? I'm going to call this variable sensitivity to error. This change divided by the size of the error that I had. So if I do that, yeah. You need to like take the numerator and add the action. I'll show you. It's going to be a function. It's going to be a function because the weight is a vector, the w's are vectors, y is a scalar. So it's going to be a vector in this case. Okay. So that's just equal to this representation which I can analytically find. So the derivative of the loss with respect to y hat is assuming that I'm going to write it in this form is going to be equal to minus eta times q times its absolute value raised to the q minus 1. Then derivative of y hat with respect to w is this function g, vector g of x. And then I have this final quantity 1 over y tilde. So if you look at this, my sensitivity to error as a function, this is a vector g, as a function of, I can plot it as a function of my particular error size. And you see that it depends on two quantities. Error raised to the power q minus 1 divided by error itself. So this, if q is 2, this is just something raised to the power of 1 divided by itself which means that the sensitivity to error is just going to be constant. So if I plot this quantity as a function of error for a quadratic cost function, it's going to be some constant equal to minus eta times q for q is equal to 2. But for this particular one where q is less than 2, what's going to happen is that this is going to be a number that's going to be q minus 1 is going to be 0.75 divided by q. You're going to get a function that looks like this. It's going to be high here and it's going to fall as y increases. So this is for q is equal to 1.75 and for functions that are larger than being raised to a power greater than 2, you're going to see things that, you know, kind of looks like this. This is q is equal to 2.5 and it's going to be a line for q is equal to 3. So how much you change your weights for a particular, at a particular x that doesn't depend on g of x depends on the size of the error and as the error size increases, this sensitivity to error decreases for the particular function of 1.75. Yeah, yeah, yeah, peas, yeah. So if they should like over there and they had a huge error, wouldn't that correspond to a big change in their behavior? Yeah. So a bigger or less force them to change a lot of their prediction. Right, right. But what we're talking about is that as the magnitude of error increases, do you learn the same percentage of it? So say that you're going to learn 20% of the error. If the error is this you're going to change your behavior by this much. 20% of it, say. Now if the error is small, do you also learn 20% of it? If you have a quadratic cost function, that's what you would do. You always learn the same percentage of it. But if your cost is being a power of less than 2, loss is less than 2, what you actually, what it means is that you're going to learn as a percentage wise a larger proportion of small errors than large errors. Effectively you're going to ignore very large errors as being outliers. That's what people seem to be doing as well. I have no thread there later but I still find that all of this information might work in this case but not in another case. Absolutely, yeah. So the reason why I wanted to show you this is because this paper was the original paper that described this particular loss function was published in 2004 or something like that. Then a few years later we did an experiment where we actually gave errors, we controlled error sizes. Given a particular distribution of perturbations we controlled the error size and we asked what percentage of each error were people learning. And what we saw was that they were more sensitive to small errors than they were to large errors. Which then made us go back to that study and say well that's actually consistent with that study that the loss function is not a quadratic but something smaller. It's discounting very large errors basically. Possibly implying that very large errors are unlikely to be sort of your fault, just outliers. So this idea simply comes from this particular loss. Alright, let me switch gears and I want to talk about generalization and how we're going to estimate generalization. So I want to give you the framework that I want to pursue. So I describe some basis set G here.  All we can see is that the learner makes an estimate.  You give the truth to them. So there's an error between the two. And so then they estimate their weights. Basically they change their weights. And the idea is that they will take that error and change their weights everywhere. Not just at the particular X that you gave but it will affect everything. And the question is well how are you going to understand how that information got spread. So you may have only given information to the learner at one particular X but they will have generalized that to everywhere. And you can't track it. You can only ask them to say okay, give me your estimate at some other X. So the learner can't tell you everything he knows. He can only tell you what he knows at a particular location. But his model will change everywhere. So the question is how can one estimate this process of learning from those individual questions. How can I ask what these basis functions are given that I've only been asking them from this location than that location and the learner is going to change from every estimate. And every trial the learner is going to change everything he knows. You can only ask what do you know at this particular location. Give me Y hat for this particular X. As soon as you give the actual Y for that location they change their W's everywhere. So there's no way for you to know what that whole system looks like. You only can tell for the particular location. So how can one estimate G's. Now why is it important to estimate G's? Well if you look at how biological systems learn there's consistency in them. Meaning that they don't just randomly pick some basis set and then use it to make some learning. They come to the learning problem with a particular basis set and those that seems to be consistent among the samples of the population that you try. So from that point of view it's interesting to ask what can I say about their basis set and why did they choose that basis set. One idea being that maybe there was some part of the brain that they used and that part of the brain had receptive fields that had a particular shape to it and by looking at how that learning was taking place and how they generalized I can say something about the basis. So that was the idea. So back about twenty some years ago when I was a graduate student like you guys sitting on an undergrad I guess it's sitting among sitting in a class there was this idea that if we look at learning not just from the point of view of the learning curve but something about how it generalizes we might be able to say something about what part of the brain is being used. Because we know something about the receptive fields at that location. So those are the G's. What do those G's look like. So a few years later we came up with a very simple technique to estimate not G's but something that's related to G's which is called the generalization function which is the way that information that you got at a particular X gets spread out to the other parts of the model that you have. And that's what we're going to do today. And by the end of the day what you guys are going to end up with is a simple set of tools that you're going to use. So I've given you a data set for your homework where all you have are basically what a learner would have. You have X input, you have Y hat the learner's estimate and you have error. And you have a sequence of examples like this and from that you're going to estimate what the generalization function looks like. How do they learn that experiment. So okay let's try to formalize our problem. We want to say something about G's and what they look like. In a very simple case you know they may be narrow, they may be broad. So we have Y hat is equal to W transpose, this is a vector G of X, this is a vector G. And you know we have our simple learning rule which plus if we want to use the Newton-Raphson technique it would be the second derivative of the loss. Something like this. So when we write it in a single trial it looks like this times the error times G of X evaluated at X of N times G transpose of X. So this is a vector. Okay I can write the change in my weight vector as this function. Okay so if I now project the change in my weights onto the output space, the Y space so now the change in Y is going to be equal to change in my weights times G of X and this is a function basically it says you figured out this vector, this change in your W projected onto your G space at any X and I'll tell you how much your change, how much change did you get in your output Y? Sorry this is Y hat. So to give you a sense of things, so here's some function that I'm trying to estimate here's X. Let's say I ask you now to tell me something at this location, X of N. You say here's my prediction. My prediction is this number here. This is Y hat at X of N. On trial N. So here's your error. This is Y tilde. You're going to learn from that error and you're going to change your estimate now. Next time you're going to become a little bit better. Maybe move up to there. So this difference here is delta Y hat in trial N plus 1 but it's not going to just change your belief there. You're going to generalize it to other locations. So if your prior belief maybe look like this, if this was the function that you had before, afterwards it's going to become different over some space over this region. So there's one location where I gave you the error.  That's what you generalized. And the difference between Y in N plus 1 after the weights changed and Y at time N before the weights changed is what you generalized. Is what you learned. Which is this quantity. So it's my change in weights times the basis at G that gives me my new Y hat. And that Y hat now is a function. So the difference between the red and the black is in some region. And that's what I've learned. And the width of that and shape of that somehow depends on what. It depends on these G's. So if I were to write that, so what is this delta Y hat of X, is this function a times the error G of X of N times this normalization minus 1 times G of X. So I'm going to call this term here. Let me write it like this. This is a function. I'm going to call it B of X and X of N. X is the place that I'm evaluating my new belief. X of N is where I saw the error. So before I started to learn, you asked me to tell you what is your belief about X of N. I gave you Y hat, this red point here. Afterwards, you gave me the error and I learned from your error. You changed my belief everywhere. So now I get this function. And that's this function here. It depends on something that I'm going to call a generalization function. This generalization function depends on two things. Where did I see the error? And where are you asking me now to generalize to? X is anywhere along this line. X of N is the particular location where I saw the error. So the change in Y depends on this generalization function. And that's what we're interested in understanding. How do we quantify this function? So, any questions before I continue? Okay. So you're going to have some data. And you're going to ask yourself, alright, well how do I quantify a function that looks like this? Well, we need to parameterize things. It's a two-dimensional input space. X and XN. Because you're going to have an input that you're going to learn from and you're going to generalize that to anywhere along this line. So X can be anywhere, XN can be anywhere. So we have a two-dimensional space to represent for input B. And so I'm going to write my function B of X and XN. I'm going to write it as a matrix. And this matrix is going to have rows and columns, B11, B1 size P, and BPP and BP1. It's going to be some numbers there. We're going to have to estimate what they are. And what is the rows? The rows represent the quantity X. The columns represent the quantity XN. This is, XN tells me the location where I received the error that I learned from. X is the location where you're asking me to generalize to. So to describe this, what we're going to have to do is take my input space, take input space X and divide it into P equal locations. So we can just digitize your input space into P different places. And if you do that, what you can then do is that you can write your Y, Y hat at some time point N as a vector. This is a function that is evaluated at any one of those locations. So this is Y of X1 of N, Y of XP of N. So take my function there. And write it up so that at any particular X that takes one of P values, I can tell you what Y is. And by generalization function, what I mean is this matrix. The matrix that tells me if I were to experience an error at a particular location X of N, what fraction of that error will I generalize to any other location P? And we're going to have to try to estimate that from the data. Let me show you how to do it. Suppose I define a vector K to be made up of P elements only one of which is a 1. This is going to be a row vector that's going to select the location P or location I, let's call it, where input X is queried. Somewhere along my input space X, you're going to ask me to make a guess and that location is going to be the location where this K selector is going to have a 1 in it. Everything else is going to be 0. So what that means is that when I ask you to tell me at trial N what you do is you take K and you multiply it by this vector Y hat of N. So this is a scalar. This is your guess in trial N. Let me write it like this. Y hat of X of N. You're going to take this matrix, this vector, multiply it by this and that's going to give me your output at that particular location. What I want to do is to show you how we can estimate this matrix from the sequence of data that you have. And the idea is as follows. You have a guess from the learner at a particular location. Then the next time you're going to test them in this location, that location, this location, that location, and so forth until at some other time point later you're going to come back to the same location. During these periods of asking to make guesses the learner is learning. The learner is learning from this error from this error from this error so forth and each time he's learning he's generalizing to this location. Each one of those generalizations is a number in this matrix. So all you have to do is to keep track of the places that you've asked the learner to guess the errors at each one of those locations. And what you end up with is a single equation with the unknowns being the elements of this matrix that are the distances to the location where you asked. So you get one equation with as many unknowns as the number of places that you asked. Then you do it again. So every time you come back to a same location you have one equation which is composed of all the generalization in between the two trials. In trial 50 you're in location here. In trial 59 you come back to this location. In between you were in some other places. Those places all contributed to what the learner knows in this trial. So the change that took place from trial 50 to 59 are a sum of all these generalizations in between. That's one equation with nine unknowns. In trial 51 you were over here. And at trial 73 you come back to that location again. In between you have all those generalizations that took place. You have another equation with a bunch of unknowns. So we end up with many equations and far fewer unknowns as long as we have a space that can be quantized in this way so that we come back to that location over and over. And by keeping track of that we end up with a set of equations that we can solve. And we end up with our estimates of these B's. So it looks like this. So on trial K of n you have the same thing at trial K n plus m. So in trial K I'm at some location and then m trials later I come back to the same location. I'm asking you again what do you know at this particular location. So my y hat sub i of n is K of n y hat of n. Ith element of this vector is chosen by this selector vector K. My error is y of n minus y hat of n sub i. Then what I learned y i is equal to b i comma x of n times my error. And then similarly y i of n plus 2 minus y i of n plus 1 is equal to b i x of n plus 1. And if I continue with this I end up with y i of n plus m minus. So if I sum these equations up what you will see is that these things cancel. What I end up with is this minus this y i of n plus m minus is going to be a sum b of this is one equation with n plus m minus one unknowns. The change from the estimate after m trials before you had learned it the change from n plus m to n is the sum of all these elements of the generalization matrix times the errors at those locations. So you just keep track of the errors. You keep track of the elements of the matrix that are describing how you generalize and that should be equal to the change in your estimate at those locations. So our representation of y is a vector. So at any particular trial I can ask you tell me what you know about this location. But in fact what you know is a whole vector. You don't just know one location. You know it everywhere right. So y i means at that particular location associated with x the element y i. It's one of these guys here. So basically you're treating y as a function that you now discretize. Yes exactly. Exactly. That's what that means. M is arbitrary. That has come back to some initial location. I guess that's what I'm used to. The key assumption here is this. That at n and n plus m, k is the same. Which means that whatever discrete space you have if you're here to begin with at some point you've returned to it. Because the reason is because you don't know any of these intermediate elements. You only know the beginning and the last one. So why is it that you don't know the intermediate elements? Because I've asked you and in trial n I asked you about this location. In trial n plus 1 I asked you about this location but my equations are all written about this equation. This location. So in trial n plus 1 I ask you about here. But I'm keeping track of what you know about here. I can't measure it. Until I come back to it I measure it again. Yes. Does that make sense? Because then they learn from that equation. I'm assuming that you can't do that. A real biological system, as soon as they make a guess the environment gives them the truth. We're making the assumption that the learner will learn everywhere even though you gave an input to one location. Anything about what he's learned except at the location where you've asked them to give you a guess. M can change. It's arbitrary. It doesn't matter. But as long as you come back to it once. It's just a random sequence of guesses that you're asking them to do. Why was this cool? In 1991 or something like that one of my professors, his name was Tommy Poggio. He used this idea, not this idea the way I've written it for you, but the idea of generalization to make a guess about a specific kind of learning. And here was the experiment. So what they did is I'm going to erase this. So what they did is that they had people look at what are called vernias. And what that means is that you look at the trading that this is something like I think the distance between these is something like I think two or twenty second arc. So it's tiny. And you're looking at this tiny difference between these two lines that are like two and a half meters away. And you ask the person, is the top line to the left or right of the bottom line? And they will make a guess. And these lines are so close to each other that they're in the position of the size of the photoreceptors in your eyes. So it's like impossible to be able to tell it. But the person is learning from every time you give him a feedback. So you ask him, is it to the left or right? And they say whatever. And you say, this actually to the left. So they say, okay, to the left. And then they do it again. Okay? And what happens is that trial after trial the performance actually gets better. So you know correct, percent correct. And it's always these vertical lines. And then what they did is that they said, all right, after some period of learning so this is vertical lines. We're going to stop the learning. We're going to now ask you, can you do it now if I do it to you this way? Horizontal Bernieres. And what they found was that they could not do it. They were back to being naive. So they could not generalize. Okay? So Poggio suggested that the way the learning was taking place was with these basis sets that had receptive fields that were basically quite small. So he wrote up this problem that said I have some basis functions and my basis functions have receptive fields that are about this size that I'm drawing here. Which are about the size of photoreceptors. And he said that if I had basis sets like this I could learn how to do this using you know that kind of a function up there. This is just some basis functions, W transpose times g of x. Each one of these is my g of x. And after I learned it if you now ask me to do this task I'm no better than naive at it. Because my receptive fields could not generalize to this horizontal. And you know from this in that paper they postulated that what was happening was that the receptive fields were very small close to what one might find in the primary visual cortex. This is in comparison to large receptive fields that one finds in higher visual areas like you know more closer to the frontal lobe. So in that paper they said look by looking at the way people learned this task we can have a sense that the fact that they don't generalize is telling us something about the shape of these basis functions. And they thought that the basis functions must be quite small. The receptive fields must be quite tiny and that would be consistent with what you might find in the primary visual cortex. So this was about 1990. Now what happened later in my own work was that we were looking at generalization of movements. And we sort of developed these equations to estimate the shape of the generalization function. And we moved from this visual domain to a different domain which had to do with reaching movements. And so in the case of the reaching movements what we began to study is how people learned when they made a movement and they had an error in their movement. So here was the error. Some force perturbed their arm. If you look at the next time that they moved they got a little bit better. The force that they estimated was smaller and then with training they got better at this. And what was interesting is to ask now what did they generalize to these other directions of movement? So if they acquired some model of these forces and learned to estimate those forces we could estimate how much they learned and how much they generalized to these other directions. And using a similar scenario as you see there we estimated that the basis functions were like this. They had a shape that had a two-dimensional basis set and if I were to draw them the shape of the basis function it seemed to have some peak here and then a smaller secondary peak here. So it was bimodal. It has a small peak like this and a large peak like this. So it seemed to learn a lot in one direction but also generalized a little bit to the opposite side. This was a two-dimensional basis set like the one that you see over there. And based on this we said that look it seems to us that the basis set that people are learning from in this task has a shape that looks like this. And then a few years later people looking in the cerebellum of monkeys found that the coating of the receptive field of the Purkinje cells for reaching movements had this bimodal shape to them. So perhaps kind of interesting. And we know the task depends on this particular task. Depends critically on the cerebellum. Patients that have cerebellum damage can't learn the task. And the generalization function that we drive through this process here had this bimodal shape to it that seemed to be consistent with what they found in the cerebellum. Okay. I'll stop for now. Do you have any questions? All right. So the basic idea is that we're keeping track of the errors and the inputs and the guesses that the learner makes on every trial and fitting it to basically a linear set of equations in which you have a set of unknowns that estimate how you generalize from any location to any other location you'll end up with a set of equations that should be able to estimate the generalization function. That won't tell you the basis set but will give you something pretty close. So you have a homework that's like that. Thank you very much.


Oh, nice shot, man. Oh, OK, OK, all this is going to be the third attempt out. And conditions are calming down. It's warmed up a little bit. And we're just looking for the right ball that we can get close to, get in bow range, you know? It is rifle season, and I do have my 308 with me. But I don't want to use it unless I absolutely have to. The ultimate thrill for me is to get in bow range with these guys. Colin was working a little bit this morning. Is the least getting them to, you know, come out. But we just couldn't get in bow range.  We got out of there after we saw how thick it was. And just didn't want to bump anymore elk and spook anymore. So now we're going to go back out, try to get on that big, and y'all moved like 300 yards. It is time to get down to business. Morning three. I am breaking out the rifle. Got to have it just in case. This bull last night, so awesome. Got close, called him in three times. You just would not get close enough when you step out of some cover. Tricky. I like that ridge. I like the possibility of being able to get on that bull and be able to take him as the rifle if I need to. Got to get it done. And it is rifle season. Ultimate goal, get him with the bow, but I'm taking an elk out of here. Okay. So I got the brace built 308 with me. I'm taking my bow and we're about to hop in the mule, head up to the mountaintop, probably do some glassing again, see if we can get them either bugling or spotted and then make a game plan from there. But we're taking both things. We're slinging arrows or slinging lead. An elk is going down, my friends. To where are we spotted? This big shooter bull. And this is where he's settling in. I've already heard him bugle once this morning. He has a very distinct bugle. It's very raspy and he's the biggest bull that's living down here in this canyon. The whole ultimate goal is to get one of these big bulls to come in with a bow. But so far, you know, just calling last night, just couldn't get him to fully commit. And I'm trying to get better at calling. I feel like I'm just like, I'm not closing the gap fully, but I'm getting better, learning every time I go. All right guys, it is go time. We're gonna get it done either way. Let's have some fun. Animals like this really glass them. So this is, this is cool. This is different and we've wasted a lot of time living some shooter bulls. We just, we just spook them, you know, we scare them.  So that's what I'm thinking. Definitely need to keep the rifle handy. I've had him come out like, you know, 80 yards, 100 yards, 150 yards, kind of check things out, distance where they are just ready to fight you. That's him. Again, same spot. Wait. Good shot. Load one more just in case. Good shot, he's going over. Nice shot, nice shot. Can stop whispering now here guys. Looks like he's down to his last breath right now. This is gonna be a tricky little back out. We're down here in this ravine. We have some buggies, but there are long ways from us at the top of this ridge when we chase this guy down here. So gonna be a workout getting him out, but that's part of the fun. That's what we came up here for Brad. Look at this bull. This is my first time actually holding the horns of a bull on my own bull. I got to see one other go down on this trip. These things are massive. You can't even really tell until you actually hold a real one. Beautiful shot too. Thanks. What a beautiful bull. Good old mature bull. Long fronts. So this is the part that YouTube really doesn't like these days. I think it's important to show the processing and everything, but I know YouTube's just gonna kill this video if I show it.  So we're gonna have to make multiple trips. Trying to get ahold of Jared Outlaw and some of the other guys. Mulletman is literally, he's hunting like half a mile from here right now. So he's still in the middle of his hunt, but definitely need some help. We're gonna quarter the elk and then put them in these game bags and then carry them back to camp where we can process them further. So exciting. I can finally tell Stephanie, babe, I got an elk. We're gonna have meat for a long time. So that's perfect. So I'm gonna put all my camera equipment and all of my extra stuff inside of the main compartment of the bag. And then we'll detach this frame, fill up the game bags, put them in here and then pack them out. Smoked a giant. Big boy. Got it all quartered. Heading back. Mission accomplished. If you listen closely right now, you can hear some bugles in the morning sunlight. Oh my goodness, y'all. Last night was an epic end to this trip. Me and Mike actually ended up shooting giant bulls, bulls of a lifetime. That was not the bull that we were chasing down. I originally saw this bull in this canyon that was a great bull, but he just ghosted us. We tried to catch up to him three times. He disappeared and then I just saw this little spike that ran through the woods as we were trekking to go call for the other bull. And then right behind him was a giant, giant bull. And then they just get lost in those cedars, but we just got down in there. We were about to start calling and then heard that spike up again and the other giant bull was behind him, guys. It was crazy. I will most likely never shoot a bull that size ever again. If we're hunting public land for the last couple of years, I really wanted to see what the private land was all about, because I heard just hunting with other guys, like you gotta do this, you gotta experience this as well. And I did. I feel like what we experienced out here this week is how hunters would see elk 100 years ago. I heard more bugles in that first evening than I did in two weeks hunting public land in the woods. And it's still my ultimate goal to get an archery elk on public lands in the future. I'm gonna strive for that, but I'm glad I got to experience this and really learn a lot too. I did all my own calling this week is my first time doing that. And I just felt a lot more comfortable getting those interactions. I wasn't able to fully close the gap with the bow. I got many close encounters where they kinda step out, you know, 100 yards. But I did get a few really awesome interactions where I'd get them to come in, you know, 70, 80, up to 40 yards. There's really no reason to bugle out here. These babies are screaming at each other constantly. There's one right there. It's beautiful and it's eerie. They literally have been haunting my dreams, these bugles. So I'm just so thrilled that we got to hunt up here and experience what we did. And we're going home with a ton of meat. The only downside is I literally don't have a place to do a shoulder mount for this elk. So I guess I'm going to have to keep it at the Guggen Squad HQ for a while. Well guys, I'm going to grab me a cup of coffee.  But thank you guys for tuning in to another awesome experience in the great outdoors. You got to smash that like button for big old elks bugling up here in the mountains and Godspeed in all of your outdoor adventures. I will see you guys on the next one.


Calcaneal osteomyelitis, OM, is a difficult condition to treat due to the risk of infection spreading to other parts of the body. This study examined five cases of calcaneal OM who underwent a two-stage procedure involving radical sequestration, antibiotics, and fixation of the foot in a favorable position with an eliziroth fixator. After the initial treatment, the foot was then reconstructed using transausteous osteosynthesis and arthritis. All five patients experienced complete resolution of the infection and no recurrences were observed over the follow-up period of one to six years. This study suggests that eliziroth distraction osteogenesis and transausteous osteosynthesis can be used to successfully treat calcaneal OM. This article was authored by Basim Hamad Harasha, Asim Al-Mijali, Radal Zaban, and others.


Have a nice summer day. With finance, Ukraine, he added. He stressed that Russia's aggressive war continues to affect our lives and worry us all very much. Germany provides Ukraine with the second most support after the US, also in military aid, Schultz said. It should be noted on the 11th of July, Germany confirmed the transfer of a new assistance package to Ukraine worth about 600 million euros. According to the Ministry of Defence, Kyiv will receive two launchers for the Patriot air defence system, 40 Mada infantry fighting vehicles, 25 Leopard 1 tanks and one Luna unmanned aerial vehicle system. Thus, we make an important contribution to strengthening Ukraine's ability to survive in the war with Russia. Boris Pistorius, German Minister of Defence said.


Not a bad movie. Hey Hey guys, this is my review for bon cop back cop the first film Which is actually if I'm correct the highest grossing Canadian film ever made in Canada Now while you American viewers may not give a crap This is one of our best movies that we've made in a long time. This movie came out in 2006 If any of you have Canadian Netflix, you will have noticed that it disappeared. It actually was quite funny There was a lot of Canadian jokes in it. It had two very good performances from Colin Farrell and Patrick Howard The film is about two cops one from Ontario and one from Quebec and for anyone who knows Any Canadian and our American who may know those two provinces don't really have a good reputation to each other if not just with hockey with anything in general so a murdered body is found on top of a A Stateline sign or a province line sign his ass is in Ontario and his head is in Quebec and The first scene where the two cops meet and they argue about who owns the body is hysterical It is one of the funniest scenes in the movie and everything just gets better from there It turns out that the perp the villain of this film is getting revenge on high level hockey executives Who were responsible for the trade of the great one and you will notice that they go to great strides to? Barely just not say Wayne Gretzky's name all the hockey teams in this movie are fake names But boy, do you know what they're talking about right off the bat? The guy is going after high-level hockey people who traded Canadian great hockey players to American teams purely for money and Ruin the chances of big Canadian hockey teams and this guy's got a grudge against all of them and What's funny is right off the bat Canadians can't relate to that because the trade of Wayne Gretzky was an awful trade He was the best player We've ever had in all of history and the Edmonton Oilers have never ever seen that limelight since even after this really good Playoff run was the first time they've done in like ten years that trade is still a black mark on Canadian history So what transpires is this investigation into finding out where this guy is and how he's operating and trying to stop him from killing off other executives including a midget and The relationship between column for all and Patrick Howard is fantastic Patrick Howard is the bad cop He's the renegade cop who doesn't really play by the rules whereas column for all is a Federal very by the book guy. It's their own version of lethal weapon The chemistry between the two is absolutely great.  It is a really fun really well shot The editing is very sporadic. There's a lot of up-close Dutch angles, which you would think is kind of annoying, but it actually works It's the most dynamic film you could ever think of that be made by a Canadian But either way bon cop backup is a fun time. It is one of my favorite Canadian films ever made I absolutely Adored watching this movie when I was a kid and when I saw I was on Netflix I instantly picked it up again.   So in the end I will give bon cop backup a Five out of seven. It is an enjoyable movie is one of Canada's Best films and it's our highest-grossing film apparently I'm doing this review mainly because the second one has just come out and I plan to see that very very soon So I hope you guys enjoy and also showing you that even Canadians can make really out of nowhere sequels to movies That are over ten years old. Anyways, see you guys later


Internal Revenue Service IRS tax news reminder to Ira IRA owners age 70 and a half or over Qualified charitable distributions are great options for making tax-free gifts to charity Honestly, isn't it funny how even the IRS is like yeah, if you want your money to actually help people for goodness sake Don't give it to us unless we make you And it's like but wait a second IRS aren't you a charity too I mean the government deals with like social security medicare and all kinds of social programs If you're like a charity helping people out. Why aren't you advising us to give our charitable contributions to you? And the IRS is like yeah, but we're so inefficient. It's ridiculous. I mean For example just last year. We've spent five trillion dollars Ain't only probing a rare species of bat to find the cure to kovat Only to later find out the bats were actually just rats with wings stapled to their backs Apparently part of some guys halloween decorations Yeah, I mean seriously best to give the money to charity if you can I mean honestly like given the money to us is basically equivalent to stuffing the money directly up hunter biden's nose Which while entertaining is not actually charity really any case First to joke the IRS auditor actually told me cleanliness is next to godliness Remember cleanliness is next to godliness. So make it kind of clean, but not too much Amanda more ambiguous on the dusting and I was like well, yeah, maybe But I'd rather try to emulate god himself rather than some super clean dude that just happened to be sitting next to him Look at you guys.  Come on.  So the super clean murderer dude just happened to be next to god Just before god spotted the snooper clean murderer dude casting him into the fiery pits of hell I'm gonna regret this the rest of your life both seconds The rubbing alcohol hand sanitizer the clean freak bathed in every 15 minutes firsting into a ball of flames on the way down Like I I don't want to emulate that guy IR 2022-201 November 17 2022 Washington the internal revenue service today reminded ira ira Owners age 70 and a half or over of their option to transfer up to $100,000 to charity tax free Each year these transfers known as qualified charitable distributions or qcd's Offer eligible older americans a great way to easily give to charity before the end of the year Moreover for those who are at least 72 qcd's count toward the ira Owners required minimum distribution the rmd for the year So let's first take a step back with this ira and think about the ira in general The required minimum distributions and how the charitable contributions might fit into this So usually when we're putting money into an ira note that the ira is not like the only Investment tool you can put money in in order to save for retirement We could put money just into stocks and bonds for example We usually put money under some kind of an umbrella of a retirement type of account Because uh, we're going to get a tax benefit at the point in time that we put the money in to something like an ira We're usually going to be paying less taxes at that point In time and then the earnings are going to be deferred in terms of the taxes as well That's why we do it and so then the ira is is so now our money's been restricted to us But we also got that tax benefit side of things. So there's a pro and con to it then at some point Towards retirement and retirement age Maybe we don't even need the money that's in the ira and we know that if I pull the money out of the ira It's going to cause me tax problems possibly because I'm going to have to pay taxes on it when I pull the money out Because it's a deferral. I didn't pay taxes when I put the money in So then at some point in time the government's going to actually force us to take the money out Those are the required minimum distributions They do so in order to Get their piece of the money because it's been deferred up until that point in time Now they want to be collecting the tax on it So they want to require people to pull it out at some point So then the question is well if I'm going to if I'm going to pull the money out Is there some way that I can get a tax benefit? By giving the money to charity or something like that and that's one place where you can think of The charitable contributions the qcd's The qualified charitable distributions that could come into play in kind of conjunction With your ira. So that's the general idea. Okay. So how to set up a qcd So any ira owner who wishes to make a qcd for 2022 should contact their ira trustee soon So that the trustee will have time to complete the transaction before the end of the year Now we're talking about cashed based transactions typically here So if you want to do this kind of activity You've got to plan for it and do it now because we're rolling up, of course on the end of the year So normally distributions from a traditional individual retirement arrangement an ira are taxable when received With a qcd. However, these distributions become tax-free So long as they're paid directly from the ira to an eligible charitable organization qcd's can be can be made electronically directly to the charity or by check payable to the charity An ira distribution such as an electronic payment made directly to the ira owner does not count as a qcd Likewise a check made payable to the ira owner is not a qcd Each year an ira Owner age 70 and a half or over can exclude from gross income up to $100,000 of these qcds Right. So obviously for taxes income is bad If you've got to pull money out of the ira and if you have to include it in income That would not be good if you cannot include it in income possibly by having a contribution to an ira That would of course, uh, generally be good notice that if you had if If you were to just count it as income and then deduct it as you normally get a deduction for the ira It would be on a schedule a which you get a lot less of a benefit from possibly Due to the fact that you might not be standardizing Uh, and you might not even have access really to the to the deduction there. So So it's a little bit different, but anyways you could I won't get into the detail So for a married couple If both spouses are age 70 and a half or over and both have iras each spouse can exclude up to 100,000 for a total of Up to $200,000 per year the qcd option is available regardless of whether an eligible ira owner itemizes deductions on schedule a So schedule a again is the normal place where you would take, uh charitable contributions Although there's like a 300 dollar amount, uh, if you're not Schedule a transfer amounts are not taxable and no deduction is available for the transfer Uh report currently a 2022 qcd must be reported on the 2022 federal income tax return Normally filed during the 2023 tax year filing season. So clearly 2022 is coming to an end We've got to do the reporting generally by april 15 2023 for the 2022 tax year So in early 2023 the ira owner will receive form 1099 r There's a link to that here from the ira trustee. So usually a 1099 r would show the distribution You want to make sure that if you have a distribution that's not going to be subject to tax That you have set it up properly so that they have the proper code in the 1099 r to indicate You know the type of transfer it was so trustee that shows an ira distribution made during the calendar year for 2022 including both regular distributions and qcds the total distribution is in box one on that form There's no special code for a qcd So like other ira distribution qcds are shown online form line for a form 1040 or form 1040 s r There's links to that here if part or all of an ira distribution is a qcd Enter the total amount of the ira distribution in line for a this is the amount shown in box one on form 1099 r Then if the full amount of the distribution is a qcd enter zero online for b So in essence, you're still going to be reporting what was showing on the 1099 But i believe for b is going to be the taxable amount So if it wasn't taxable because it was a qualified qcd Then you would have zero on that line and again you want to make sure that you're talking to That the issuer of the 1099 to make sure that everything Is on board in the event that the iras has questions about about it or audits it in some way So if only part of the qcd the remaining taxable portion is normally entered online for b either way Be sure to enter a qcd Next to line for b our further details will be in the final instructions to the 2022 form 1040 So get a receipt qcds are not deductible as charitable contributions on schedule a but but as with deductible contributions The donor must get a written acknowledgement for contribution from the charitable organization before filing their tax return So notice what's happening here Is if the money comes out of the ira which you would have had to record as income But instead you're giving it directly to the charity Instead of getting a deduction for the contributions. You're getting a reduction of the income So what you cannot do is get a reduction of the income and Record it on schedule a that would be double dipping right then you'd be doing to you know, that'd be double dipping Uh, but so even though you've reduced you're kind of doing a similar thing Although it's probably a bigger benefit to reduce the income oftentimes because again the schedule a could have issues It could be phasing out if you're high income. You might not have a schedule in a if you're low income and so And so but you still need to back up and support the amount that's going to the charity With the information in the event that you get audited for that So in general the acknowledgement must state the date and amount of the contribution And indicate whether the donor received anything of value in return For details see the acknowledgement section in publication 526 available on irs.gov There's a link to that here for more information about ira distributions and qcd's see publication 590 b Also available on irs.gov. There's a link to that here. There's links to all the stuff I said there was a link to here. There'll be a link to this in the description


Jiren's just kind of cheap overall if we could be honest. Go ahead. I want to see you mash mash for me. Oh Oh, the dammit How's he going everybody? Dahtonoi here back with some more Dragon Ball Fighters ranked matches this time since we got so many requests to do it We are going back to the Jiren team of Jiren Krillin and Yamcha And it's a good thing too because we are going up against a great priest rank or the second highest rank in the game Oh, I was not ready for the B assist. Baby's B assist is really good. Oh, I just played Jiren. Yo, that is sick Oh, let me counter that though. Let me go ahead try something real quick. We had to start it off good the rock assist Oh, I'm missing everything. All right, at least we stopped the beat. I made a mistake there made a huge mistake I like that. He's also playing Jiren, but that didn't scare me. I thought I was getting countered, dude But yeah, I actually during super baby two week. I got a lot of comments telling me to play Jiren anyway I was like guys, it's the DLC week But hey, if you guys like see a Jiren, I I like playing Jiren Nice that was clean into the corner, but I didn't even superdash my thumbs didn't even think to do that Really early counter nice almost confirmation. I Think we should switch out here. Now. We just countered the key blast coming back. Why not? Okay? Now we can switch out Now we can switch out Krillin bend it back. Let's get some let's get some knockdown pressure I'm going in low. He blocked out. He blocked that at least we got a bar. I Don't want I don't want to be in this corner to be honest Oh, oh, if we could have I don't know how we would have been able to do it But keeping Jiren in that combo would have been the cherry on top Jiren assist is really good as well mix-up time. Never mind After image is met with immediate superdash, and I think Krillin might be leaving Krillin actually might be leaving soon Unless we see a drop but these cell combos are looking clean. It doesn't get much cleaner, but we do see a drop Maybe be assist is good. Did I mention that I? Look, I know a lot of people don't want to see it get nerfed I think I genuinely think they made a mistake with baby be they can they had to write cuz they keep nerfing assist that track I'm just getting destroyed right now. They keep nerfing assist that track That was a really clean superdash answer and then they do another one I the thing is I don't know if they meant to do that. I really can't tell That was honestly that assist it's not like it's crazy busted right like it's not broken I wouldn't say oh man. It's bird. That's must nerf. It's just that they've nerfed stuff like it before in the past And then they did it again. I was very confused when I saw that. I was like, oh, okay I thought I thought y'all didn't like when you did that Sit down Okay, oh That is not even a sea assist. Oh That assist gets me hyped up though hyped up the place of a super baby, too I counter that I counter that every day of the week bro. Come on. Let's not be childish about it Let's not be childish about it. Let's just admit Jiren's built a little differently than the rest knocking them up Falling them down. I hope I don't miss that should be right on the money nice All right, now we have a very decent lead if we keep the character lead Jiren is like one touch away from dying Even as an assistant. Oh my be assist hits like a sea assist That is just diet sea assist and not even that diet Level three I'm dead. I've been dead.  Can we kill here if I'm a good player? We win here. I mean not win, but I'm a bad player. I'm a bad player. I'm a really bad player I got him. I I put him way too high with the spirit ball and that's what I started panicking nice dive. I Don't know why I reflected. That's such a far away Jiren call. I Really should have let that hit me. I should have let that hit me Nice nice beautiful needed that all right now It's anchor Jiren. I actually believe Jiren's one of the best final characters to have the limit break is crazy The assist wow, did you see the Jiren assist actually hit him? That was crazy Jiren come out here and finish it. You deserve the win. You deserve it Jiren hit this man. Oh Let's go that was sick that assist was insane Wow, we traded with him and that was all I needed it really I wouldn't be shocked if it just surprised by a Pote he looked like he got caught off guard there game one goes really well going into game two with confidence That said we did have a really good. I'm just try some I keep forgetting I keep forgetting I gotta keep reminding myself that that does that that is so good All right, we got pretty lucky there. Oh Jiren assist. Oh He tested me there's Jiren dead. We didn't lose Jiren all game last game. Did we already lose him three bars? I think this man's well. Nope. We're alive. I Actually don't mind getting hit by the B assist there Although I do mind this we are in a bad way right now. This is not a great start cell just going to town Cell is just clocked in Making it look like a job. He takes no enjoyment in this. This is all business That's why I got to file some paperwork real quick Can't really work out. Oh, I should deserve to get punished for that. Okay. Remember remember we're not safe up there It's like a it's like a physical Vegeta assist a Super Saiyan Vegeta assist instead of Key Blast He's throwing hands. Oh my good They're definitely nerf. It's getting nerfed. It has to be it's not it again not even because it's broken I just can't believe the tracking on that. There's no way they meant to do that. I'm knocked down That assist has to be a mistake.  I went in full confidence. I am now at zero Cheap assist. Oh, there was it. There was the that was the punishment all game I said I was gonna get punished for that. Oh No tech to boot that was time. Was that a world record Guinness? Can you clock that in? I think I might have just did the speed run for game two. I think can't believe it. Is that a world record? Did I get WR? No I got mixed Guinness mark that down Mark that down Guinness. That was a good one. All right He's wearing I should have known he was matching colors dude game to green team's gonna take that every day of the week That was a really bad round. All right, if I could just get a better start I think I got a dragon rush. I'm gonna be show a little confidence Okay, finally we take that's a good sign All right. All right already. I don't know if this is a good thing or a bad thing to say But already better than the first round. I mean second round, but I thought I got punished for that. Oh my god, man so good I'm actually so happy babies out right now that assist was destroying me Yeah, yeah, yeah, we take that every day of the week. Hurry. Nice. I'm just gonna try to kill this time here All right, most of it. Yeah sparking's gone This is bad. Oh my goodness. I mean he he actually misplayed there. So we got lucky, but oh He's fast. I don't know why I try to do that. Yonkha's nerf. You can't really play like that anymore. Oh My lock down. Oh Whoa, this intense. I'm not even talking anymore this third round. I think people can tell I think people can tell I've tried to bring this home A big luck factor there. Ah, why why did I do that? Get in the corner reflect Yeah, dude get Jiren out here so we can take the lead. Yep. Yep. Yep. Just like we drew it up punch him really hard Call that a lot of Jiren really has a level one. That's just him punching somebody. That is crazy But now we have a decent character lead rock assist. I'm just gonna 2h. I'm gonna start 2h'ing that now Beautiful beautiful. I could not have drawn that up any better myself nice Let's go. I'm gonna punch him really hard That is so sick Jiren's cheat to let's talk about cheap Jiren is that you could call the sister in that counter I wouldn't be surprised if I nerfed that one day. I wouldn't be surprised I mean, I hope they don't because nobody's still playing Jiren, but man It is really good Jiren just kind of cheap overall if we could be honest go ahead I want to see you mash mash for me. Oh My god Wow Well, that was our first game great game to our opponent really sick and now we're moving on to the next one. Wow That was intense. All right, we are back and ready to return. I gotta play Oh, yeah, I gotta play baby B after tech that all right. Good tech. Good tech This is just what a cheap couple of matches. We've had I'm going again. I'm going again this time I to web Yeah, dude, I am feeling it right now, dude fighters. I'm at my my peak for fighters right now This is peak enjoyment now. Oh I needed to counter that I needed to do a physical counter on that. Oh right there. Oh No, I missed I missed I missed. Yep. Just unfortunate.  Don't let him at us Keep him keep him far away a Good distance is always preferred baby B assist. Don't run Don't run. I'll take that beautiful movement. We just want to try to keep this going All right, let's hear an atom. Let's hear and get back in there Let the beast back in let the fighters King play some fighters Jiren, of course, not me. What do I do? Do I just grab? I'm built different Jiren Well, just be all right. He's gonna change the future. I'm gonna counter it. I see the future. I wasn't changed the future That was changed. Oh now. He's nervous I love jeered because of his just to do it just that jeered That's my oh, that's my favorite part about the character. You can tell when people are like, all right I'm I'm so done getting countered And not like it's not like something like oh, yeah, dude, they're playing wrong No, you have to be afraid of the jeered counter. It's just um when that state kicks in that's when he becomes the most fun Counter that counter that I'll take a level three there. Oh Man One of my favorite characters in the game for sure. Oh dude, it just keeps getting better. Oh Gee, it's so cheap. It just doesn't get any cheap. I don't know why I didn't win the game right there Got him. Oh man. Oh Oh, I think I blacked out that guy. I can't believe it's over. I definitely just passed. I Was just so focused on the game Or just not even the game, but just jeered like the moment. All right rematch. We got to go again, dude We got to go again Game to All right, bit of a break here. That's fine. Oh, we're hopping right back in though the breaks over I'm gonna get bar docked. Oh Oh The reeds have been the reeds have been good today, dude This is the most jeered right match. I've played in a while and we're tech who is playing right now It's not it could it can't be me. I take two dragon rushes. Oh dude. We are just it's a good day Nice rock assist going to go ahead and finish that off if it didn't I think we genuinely would have had enough time to Do a dragon rush, but that's more than good enough Rock assist coming back Oh beautiful. I gotta give it up. That was a great reaction time Beautiful darkness spring shot to make sure I can't get him. I wish I could space that just a tad better Oh Jiren is actually a pretty hard counter to baby I love this match, dude. This matchup is sick baby versus jeering Or take a might as well right might as well spend the meter while I have it. I don't see anything wrong with that uh Okay, beautiful. Let me go ahead and take another one. Let me go ahead and take a piece Yes Oh, oh nice two s actually works there. I took a bit of a risk But I will take that. I thought it'd be fine because if he blocked it I think the key blast would have went away, but I could have been wrong on that change the future You didn't want to do it again. I'm looking for that uh that uh two eb again Counter that all right vanish. Don't let it happen. Wow the rocks actually I could have not even vanished that I think I think I would have been fine. I think Krillin would have held it down Instead we're going to take a bit of damage. I might be getting erased. I might be leaving this timeline I need to be stopped. Oh, no Goodbye. Oh, this is bad. Oh the timeline. Okay. No, I'm still in it. You know what no no No, I'm supposed to spark. Okay good. Oh, that didn't work Oh, but that will I am just bad at the game. Oh, he actually did it. I didn't think he would I thought he was baiting me. Okay. That was sick. I thought I really did think he was just uh Trying to look like he would do that Oh, no, we kicked him try something. Let's it was a very jeering ruffle of matches But I think that's where I'm going to call it for this. That was so much fun Man, if you enjoyed this one, definitely let me know down below if you guys want to see more jeering. Let me know No, but for real, let me know your favorite moments down below the comment section And let me know who your favorite character in dragon ball fighters is to play right now Other than that while you're down there, make sure to like button and subscribe to the channel If you like these videos and want to see more of them And you can also check out some more of these videos that should be on your screen right now Other than that, I have been dr doya and I will see you in the next video


A new pan-sharpening method is proposed using convolutional neural networks that adapts a simple three-layer architecture for super-resolution and includes several maps of nonlinear radiometric indices to improve performance without increasing complexity. Experiments on three representative datasets show the method to provide very promising results, largely competitive with the current state of the art in terms of both full-reference and no-reference metrics, and also at a visual inspection. This article was authored by Giuseppe Massi, Davide Cotzilino, Luisa Verdeliva, and others.