besides the fact that you can see your kind of grades and what I have logged for basically the grades. I also put a, I enabled a way to upload an M file so next to your homework I should be able to, I'm not sure from your view but that's not what I wanted. So in, when you go to grade, let's see how do you upload actually? I should be in Dropbox, okay? In Dropbox you can upload, yeah that's what it is. So you can upload the M file for the code, for the code that you know, you know for the homework. The reason for that is if something like, if your code didn't publish, right, right? But there was just one, one thing, one typo that caused all the errors, you know, to appear then I can figure that out but I need the code. I cannot just look at the, at your published version, okay? So just as a matter of routine I would say when you hand this in which is still the way to do it, just upload that the latest version. And a warning is you cannot upload an M file as it, like by itself, you need to zip it first. So it doesn't recognize dot M files. You need to zip, so if you have three files for three problems zip them in a folder and upload the folder, okay? Yeah. Yeah, so do it, do it like today, tomorrow, just do it for homework one, homework two, just so, this way you also have a record, you know, like a record of the latest code, okay? Let's see the grad students, I think there are only two. So if I could meet, let's see, so who else? Okay, there's a second grad student. So rather than me talking here about the projects, maybe we can just meet and chat about that. So, all right, so let's see, I think we can, I guess, start it. Any questions on this homework? I have, I have the solutions here, well my solutions, at least the version of the solutions. So, have you turned it in? Okay, so I can, oh, oh, thank you. Okay, so let's see, we're already in chapter three talking about, you know, what are the issues that come about in trying to, you know, design them, I mean, build a model and then try to solve it, but when you don't have luxury of, you know, capable, like symbolic, everything done symbolically. Last time we talked about, I think one of the, one of the such situations, so, and we talked about, you know, again, one variable optimization, revisited, and we talked about the nonlinear pig.m, so the problem was we changed the assumptions from linear growth or from whatever, so we picked some assumptions that initially were very simplistic and then we kind of tweak them a little bit and we got to a situation where solving an equation, asking the computer to solve, in fact, I think it was maximizing or minimizing a function, so, but you had to, even if you had the function explicitly given, you know, by some elementary functions, so you can type it in the computer as an expression, so you can take a derivative, symbolically if you want, right, but then solving this, so solving an equation of one variable becomes difficult, sometimes impossible, right, exactly, so what was our, well, the method that we display was a Newton's method for approximating roots, right, of equations of one equation, right, so one, I have a function, maybe it comes from a derivative of another function, but we have an equation set equal to zero, and Newton's method approximates that, so this was in one dimension, and the code was written based on, you know, it was kind of iteration, right, so what was the code was saying start with some x0 and then iterate xn plus 1 equals xn minus f of xn divided by f prime of xn for n equals 0, 1, 2, and so forth, okay, and if they have a stopping criterion, the simplest one was, you know, fixed number of iterations, right, or if the value, oops, sorry, I should use capital F, as I'm talking about that, so there are several stopping criterion you can, you can code, you can put in, now how about if you have a multivariable optimization, so how about is there a Newton's method for a multivariable optimization, well, let me not even say optimization, for multivariable problems or functions, so what do I mean by that, well, let's imagine we don't have just one equation, but we have, you know, more than one, we have a system of equations, so let's start with two equations and two unknowns, make sure I'm staying with the notation, did we use capital or small little, we use capital, okay, so let's say we have two functions, f and g, and what we'd like to do is we'd like to find approximately a solution, of course, would be two components, x1, x2 star, so let's just use this notation, kind of vector notation, capital X, so by capital X I will mean, you know, depending on kind of notation we could use a row or a column, but it's just a pair of x1, x2, okay, so let's kind of see where this can come from, so there is a problem, there's a situation described by a so-called long-chair problem, so example, I think it's called 3.3 long-chair, but again it's just one of those pet examples that we just use, you know, to develop the method and see how it gets implemented on the column, okay, so it's still a manufacturing problem, so you have a manufacturer makes two types of long-tares, one has wood frames and one has aluminum frames, there's a cost for the wood frame per unit, and there's a cost for the other for aluminum frame per unit, and the market conditions are so that the number of units sold depends on the price per scrap, so if you set a price you may sell a certain number of units, if that price changes, you know, the number of units will likely change as well, okay, and the selling price has a certain expression which is kind of odd looking, right, so there are some fractional powers of those numbers of units, okay, so as you can see very quickly it's, we distilled kind of the situations, we went through that step one, step two and almost step three very quickly, so right now all that matters to us is I have, I have this, let me try to use x1 and x2, x1, I think that's what the code uses, so okay, so I have a function of x1, x2, so x1 is the number of wood frame chairs, x2 is the number of wood of aluminum chairs, okay, and we're building this production, excuse me, we're building this profit function, right, that we want to maximize, so this function ends up being the number of units of one type of chairs times the price, market price per unit, so the price per unit is kind of, has a kind of a strange model, right, so it's not a linear dependence on, excuse me, so let me put x1, x2 here, x2 has this price, so 15x2 to the minus 0.4 plus 0.8 times x1 to the minus 0.08, okay, so this would be kind of the revenue minus the cost, the cost is I think $18 for the first type and $10 for the second type, so it's another looking function and we're tasked to find the maximum or the minimum, right, well the maximum in this case, we don't have constraints other than saying that the two quantities have to be positive, right, so we can think about it as unconstrained, you know, if we choose this approach of unconstrained then we know what we need to do, right, we need to, so theoretically in theory very simple, right, simply find where the gradient vanishes, right, and solve, now you see when you compute a gradient you can, you can imagine what system you're going to get, you're going to get two equations, right, so you're going to get partial of f with respect to x1, so let me call that to be capital F and partial of f with respect, little f with respect to x2 and let's call it capital G, so that's what you need to do, and let's see, I'm going to flash the code here in front of you just to see how it's set up, sorry about the size, let me make it a little bit bigger, I think 16 is better, okay, so all right, so the usual stuff you can just start symbolically, because symbolically you can type in that function, you can plot it, so you can see that indeed, you know, it has a maximum where the size of the domain is problematic, right, when you plot it the first time, so the way I came up with that is, again, you kind of run through the code first and kind of get an idea where the maximum might occur, also notice that I didn't start at zero, because those powers are negative powers, so you would have some undefined expressions, right, but it's close to zero, 0.1 to 10, and what is that in units, does it say, and it says units per day, so I guess that would be, 10 would be the units per day, but again, this window kind of captures the maximum, all right, so so far you see what we did is just set up the gradient, right, and we can take derivatives symbolically, so why not do that, but now when it comes to, so let me run this once, okay, and nothing, oh yeah, you need to see the graph, so that's, here's a graph, okay, so clearly it's, it's not clear, there might be other, maximum, some other place, right, so unless we do some analysis of the function, we may never know, right, but there is another maximum, some other place, but what kind of analysis would tell us that this would be sort of the only maximum, or the absolute maximum, right, but it will look ugly, so if you take the derivative, you might not be able to see that there are no other solutions, so in fact, in fact, you could have like a, like a local mountain here, right, and then you could have something that kind of keeps going up and up as you move away from, you know, with larger x1 and x2, so to avoid, I mean to kind of rule out such a situation where you did find a local maximum, but then the maximum can, you know, it might not be the global maximum because the function may take higher values farther away, what do you need to do? You have to look at kind of the highest powers of the variables, x1, x2, and decide whether those coefficients are positive or negative, right, what is the highest power of x1 in this expression, x to the 1, right, because this is x to the 1 half, and this is x to some negative value, right, so this, this is kind of the, as x1 gets bigger, this one is dominating, right, and being negative says that you're going to go to zero, I mean, you're actually going to go to negative infinity, you're going, your profit is going to sink, right, below zero, same with x2, right, if that wasn't the case, you couldn't actually tell, you had to do some other things, other sort of analysis of the function to decide that you had, what you found is an, is an actual maximum value, you know, just by the graph it's impossible to do, right, because you don't know what the window size to, to pick to, to plot these things, does it make sense, of course you just have to try it on your own, and see, of course if you, if you allow something like huge x1, I mean a bigger window size, and you will see a, you know, something that you cannot tell much of it, except that things are going negative very quickly, right, so again it's, it's kind of a, not an art, but it's, it's not immediate how to, to, to, to display things, okay, so, so how does this method work, Newton's method in two variables, and two or more variables, well, so there's an algorithm, but you know, before I, we talk about the algorithm, I'm going to, unfortunately have to change a little bit of the notation, so let me imagine we have n, a system of n equations with n unknowns, and let me call h to be the set of these functions, f1, fn, okay, and x to be x1, xn, okay, so the system can be written as just h of x equals 0, and when we write this we mean, we have a system, x is a variable, right, x has n components, and we need, we seek x star, such that h at x, h at x star is 0, okay, so now let's remember the Newton's method comes from writing the Taylor series of the function that you're trying to set it equal to 0 around this, around this solution, right, so I think, I think we do that, well, maybe we didn't do that that way, so let me, let me say the following is that if we think about the linear approximation of h around or near x star, so think about one variable, at this point, imagine what you see is one variable, h is a function and x is a one variable, but what I write is also valid for systems, so what is the linear approximation? The linear approximation says h of x minus h of x, or actually is approximately equal to h of x star plus, this will be a derivative, right, that's I think what you learn and given in Calc 1, is that to approximate a function around near a point, you evaluate the function at that point, then you add the derivative times the difference between that and the point, visually if it's one variable, so this is a one variable, and then we see what it looks, so if this is h and this is x and this is, it doesn't necessarily have to be where h star is zero, but let's just do it like this, so if this is x star, okay, and this is an x here, the linear approximation means what? Although, actually that's not exactly how the, we should make the linear approximation not around x star, but around x, so let me turn that around and say I want to make around x, so I want to, the reason I want to make around x is I know x, during my iterations I know x and I want to compute the next value for x, so I'm going to do x star, I'm going to switch the roles of x and x star, okay, so the picture now looks what? You don't do the linear approximation at the point where you are, that you want to find, because you don't know that point, but you do the approximation around this point, right, the current location, okay, so now it looks okay, and what you want, the desire is that, so I want h of x star to be zero, so why not set up, you know, these are approximate values, but why not set this expression equal to zero and solve for x, excuse me, solve for x star, right, so zero equals h of x minus h prime of x, x star minus x, and then solve for x, okay, so what you get here is x minus h of x over h prime of x, okay, so this, I just skipped the steps, but so now this actually tells you that I now have this value for x, I'm going to use this formula to compute the new value for x, now it's not going to be exact, well you have to be very lucky to get the exact solution, right, so that's the idea of Newton's method in 1D, how about if it's more than one variable, well there is a similar, well there's an exact analogous way of writing the linear approximation, of course you don't have the luxury of visualizing anything anymore, but the exact same formula stays the same, so h of x star is, if you want to call this, it's a Taylor series of the function h, which has two components around the point x, so this is plus, now the problem is what is the derivative of h if it's not just a function of one variable, right, it's actually now a function of two variables and h itself has two components or more, several components, n of them, right, so what plays the role of the derivative, well that's what's called a Jacobian matrix, so let's see what is the Jacobian, so where this is actually an n by n matrix in which you put partial derivatives of the first component of the function h, so that's, I think we call it a little f1 with respect to the variables, each variable, that makes the first row, right, and you keep doing this until the last function, last component of h with respect to all variables, okay, so not only, so now we know what this is and this is evaluated at x by the way, so all these partial derivatives are evaluated at x, x being the point in that, in the region where you're doing the, you know, search for the solution, but now I have a matrix and what about this multiplication, what is this multiplication, just simply matrix multiplication, so that's where it's useful to think about x as being a column, okay, because this is now a matrix and now it's multiplied by a column and the result is a column, right, so also h is a column, right, so this now makes sense as far as matrix multiplication is concerned, and again this is just Taylor series expansion, so it comes from the Taylor series expansion of h around x, now a Taylor, what's a Taylor, Taylor series would actually have additional terms, right, so if you had to kind of look at the second term, what do you think you'd have to write, hmm, second derivatives, right, well, okay, if it's just n equals 1 and you put second derivative evaluated divided by 2, right, 2 factorial, when it gets to multivariable that's not that easy anymore, so for instance the second, second, second term would look like, we'll look at this follows, h of x, so that's, we've seen this, dh of x, x minus x naught, and now it's the second derivative at x, right, but now this thing is no longer a matrix multiplication, but it's what's called a bilinear form, so second, right, so it's no longer, so you have to define what this term is, it's no longer a matrix multiplication, because let's see, let's let's remember what it is, if I write just f1, okay, so I just take one of those components of h, okay, now it's a scalar, so what is this, this is f of f1 of x plus, this is the gradient of f1 at x, that's a, that's a row times x minus x naught, what am I saying x naught, I think it should be x, x star here, we use x naught above, no, okay, so does anybody know what's the next term, when it's just a scalar, so that basically means it's partial of f1 with respect to x1 times x1 star minus x1 plus partial of f with respect to f1 with respect to xn, x 1 minus x, sorry xn minus xn star, so this is this term, right, what's the next term in the expansion, it would be second derivatives, right, and the easiest way to write this is x star x transposed the second derivative of f1 as a matrix, this is n by n now and is x star minus x transpose, excuse me, x star minus x, so this is, if x star minus x is a column then this transpose is going to be a row, right, so it's going to be a row times a square matrix times a column, what's the output of this, it's going to be a scalar, right, 1 times n, this is n times 1, of course this was 1 times n and this was n times 1 and what is this, this is the so called the Hessian, right, so it's the second derivatives, maybe I'll just write it like this, x, second partial derivative of x i x j, yeah, so that makes it n by n matrix, so you can imagine if you need additional terms in that territory it's going to get more and more complicated even if you have just a scalar function, right, but now you have, so that h is actually a stack of several such functions, right, so that's why that second term in the Taylor series is going to be rather complicated, it's called bilinear form and so forth, okay, but the first one all we need to know is really the first, the linear approximation, the first term in the Taylor series, so I want everybody to be able to write the linear approximation of a function of n variables with n components, so a function of n components, each component depending on n variables, right, it's simply the derivative as a matrix multiplied by the column vector, so that's the key that we want, whatever, I just wanted to display this Taylor series so you know where it's coming from, okay, so now we're going to do exactly the same thing, we're going to say, well, we'd like the x star to be the solution, so we'd like to make this equal to zero, so what we'll do is we'll take these two terms, 7 equal to zero, right, and solve for x star, okay, so we want h of x star equals zero, now this zero means, right, it's an n component zero, we want this solution, a system to be zero, I'm not going to put errors but that's what we need to keep in mind, so that's what we want, and now we need to solve for x star, now keep in mind everything's a vector, a matrix, so we cannot longer just divide by, like we did before, but it's not too different, so here's how you solve that, and then we'll see how it gets implemented, but we solve it by setting, we just move this on the other side, so it becomes minus h, and now what do we have, we have a matrix times a column, and that's the unknown, with the unknown as x star, right, equals another column, so how can we solve for x star minus x, take the inverse, assuming that this inverse exists, and I have a minus somewhere here, minus, okay, and now the rest is, as I say history, because it looks just like the Newton's method in one variable, with the only difference that here we don't divide by h prime because it doesn't make sense to divide, I mean there's no h prime, instead is this matrix evaluated at the current x, take the inverse, multiply by h of x, subtract from x, and again, this won't give us the x star, but it will give us a new value for x, hopefully getting closer and closer to the solution. Now, is this always foolproof? No, I mean there's, just like in 1D, you can imagine much worse things happen in multi-dimensions, that this algorithm may never converge and so forth, but the point is that if it does converge, then the limit will be a solution, so let's see. So again, Newton's method has a start with some guess, initial guess, x naught, and that already has two, whatever components you need, how many n components, and then iterate xn plus 1 equals xn, and now this is a vector, minus the matrix, the Jacobian matrix, evaluated at xn, inverse of it actually times h of xn. Okay, that's all. I mean that's, we haven't done really any analysis that this thing converges, you know, goes to the right, okay? But at least we kind of described how this should look on a computer, and here's how it does in this example of the launch here. Now, you will find ourselves sort of at having difficulty with the notation, of course. It's one thing when you write on paper and another thing when you start writing in the computer. So, so far, I really should have called this h, right? Maybe we should do that, but I'm afraid to change codes here on the fly. So, just think about this h, but this h comes from the gradient of your objective function, right? And then on this line, what do we do? We compute the Jacobian matrix of that. So, it's a two-by-two matrix with just derivatives, partial derivatives of each component. And again, it should be f1, f2, okay? Little f1, little f2. And then I just assemble this matrix which should be dh, right? So maybe we should do that. I mean, do you want me to do that or can we follow this the way it is? Just type, yeah, just type then. Well, let's see. It's not too difficult to... Because in the end, it's just a notation, right? Okay. So, of course, if I have to change this to little f1, little f2, then I have to do it here. This is h. f2. Oops, nope, yep. Okay. And this is f1. This is f2. I mean, it's good if you can do it on your own. So, whoops. Okay, f2. Okay. I think this should be it. And now, let's look in the code. In the code, what we do is we start with an initial guess, and I start it with 5 and 5. Well, even that can be tricky, right, to determine where to start. Because remember, I don't know how to plot exactly... You know, the window size, so it may be... I may be actually off by a lot. But anyway, so... And here, again, I do a finite number of iterations, prescribed number of iterations. So, let's see. The way it is is going to give me error because I have changed things around, right? So, our h was the one where I have to substitute, right? So, I have to substitute in hx, the current x, right? So, let's give it a name h... I have to give it some name h0, right? And also, I have to do this in... That matrix, 2 by 2 matrix, I have to evaluate it at the current... At the current point, right? So, the first time this goes around, it evaluates at this point. So, you see, I substitute those two values for x1, x2 into h, and I store that as a column, right? This is going to get stored as a... As a matrix, but I need to give a dh0 or something, right? And the last step is to apply that operation, right? And then the next time to do the iteration with a new value, I just rename these things. But again, these things are going to be columns. Remember, in Matlab, you need a semicolon to create a column. Okay, so I think that's pretty much it. So, let's just run it again. Hopefully, there's no errors. Okay, so you see, when I start changing things, it tells me there's somewhere capital F left around. What is it? Yep, thank you. So, this should be f1, f2. It's never good to make the code in a notation that you want. It's usually the other way around. You have to be very flexible to be able to change a notation on the fly. Whatever is more convenient. Okay, so that's... Basically, it has found a... Well, it hasn't found an exact minimum or maximum, but after a few iterations, which I didn't display, by the way, I should have displayed, so you see that actually converges. Okay? But it ends up having this coordinates, and then the values... How do you know it's maximum? Right, we don't even know it's a critical point, but it's close to a critical point, right? And the next thing we would have to do is we would have to do some sort of second derivative test, right? For the original objective function, so it would have to look at the metrics of the second derivatives of that original function, right? Z. So in the launcher problem, N was 2, and we found x1, x2 star equals 4.68, 5.85. Now, you may say, well, how can you have a number of... decimal number for units? Depends, right?  So again, it depends on the modeling sort of the situation, but theoretically, that's where kind of we found it to be a critical point, and once again, to decide if it's a max to decide whether it is max or min, we would need some sort of second derivative test on... of the function, right? Just to... What is the metrics or determinant that we have to look at? Is the second derivative of this one, right? So it's second partial of f with respect to x1, squared, right? Second partial of f with respect to x1, x2, x2, x2, and the second partial of f with respect to x2, x1, and also we have to look at the sign of the pure second partial derivatives, right? So sign of, right? But keep in mind what is this? This is when we take the derivative, so going back here, what would give us the first term, the second derivative of f with respect to x1? That's the derivative of... Excuse me, the derivative of f1 with respect to x1, right? Because f1 is already the derivative with respect to x1 of... Okay? And then we have to evaluate this at that point, right? And remember that that point is not actually the exact critical point, right? So you'd have to look at the sign of this expression and see if it's, you know, far from zero because if it's, I mean the sign, the value. If the value is very close to zero, it would be impossible to tell, right? Whether the true maximum, I mean the true critical point is, you know, is a positive or negative, right? So you have to substitute x0 is the one, right? You have to substitute in the derivative ff1x1 x1x2 with x1 x0 of 1 and x0 of 2. All right, and you get it to be negative. And it's negative enough that you can be, well, you can never be 100% sure, right? None of this is actually improved, but it's an indication that you have a max or a minimum. Assuming that the determinant that you still have to compute is positive. You have a max, right? When the, on the diagonal entries are negative, the second partial derivatives pure ones are negative and the determinant is positive, you have a local max, okay? So again, I didn't do the code, but you'd have to do this also for the other metrics. And again, the other metrics is not, I think it's just dh. H is already the gradient of little f, okay? You just have to be careful. So this is just dh at x star, right? And this is just f1. I'm sorry, it's partial of f1 with respect to x1, okay? Or maybe let's call cap left. Maybe it's less confusing, okay? So anyway, so when you do the code with Newton's method, the important thing to realize is you're just solving the gradient equal to zero. You're just solving this system of equations that's coming from setting the gradient equal to zero, right? And you solve that numerically. I think if you tried symbolically, I think I'd try that. Would you get anything good? So this was f1 is a mass, right? F2 is a mass. And if you have to solve f1, f2, who knows how long it will take, it's going to give you no explicit solutions, okay? Anyway, so that's just how you can approximate a solution. So that's conclusion is, you know, of this problem is you know, you should plan that many per day, or you should adjust the price, actually, based on this optimal values, okay? So I don't know what's going to take forever. You should adjust, you should kind of set the prices so that, you know, based on that model, you're going to get optimal maximum profit. It's kind of frustrating. You don't know if it's actually running, or if it just froze, or what, yeah. But it's very clear that you don't want to try this symbolically. Any questions on this? We haven't done any sensitivity on any of the quantities, yeah. Yeah, that's a good point. I mean, no, I mean, the truth is that there are, you need methods of actually initial guessing. Even those can be complicated methods. So if you are, if you don't have a visual aid like in 2D, then you need to know something about the possible, maximum possible minima so you can start close to it, okay? Again, from a modeling perspective. Now, if you're just giving me a function of seven variables, right, and asking, you know, how do I know where to start? Well, it's impossible to tell because that function might have a lot of minima, local, and you may get trapped into a, you know, you may start somewhere and get trapped in like a local minima when the global minima is right next to it, but you cannot escape that. So the algorithm can get very, very complicated. Newton's method is really kind of baby method. I mean, that's kind of the first, if you've never seen any method for minimizing or solving systems, what do you start with, right? There are some very powerful one, if I have time to talk about some very powerful one that are, you know, built in Mala, for instance, you can do F, I'll just say this, and you can read about it, F min search, but of course you need to input something in it. And this is like extremely robust way of finding minima, okay? So, I just want to say one thing about another example in the book, which is about finding minima or maxima, it's a totally different problem and I don't want to spend too much time on it, but this the, this method is called random search method, and example is 0.2, and I'm just going to show you the code for that and I'll let you read it's kind of an interesting practical way of deciding where to place a fire station in a sort of in a city where you have some sort of constraints, you have to be within I don't know, two minutes from every point in that city so if you look at the objective function which is some sort of a distance or time actually is probably better to think about it as every response time, okay? It looks terrible, right? So you don't even want to look at it, let alone to differentiate it by hand or find it's minima or maxima okay? So if you have the code which I posted on our course website you know, it takes a while to type it in but if I run this one thing that I say here is again don't do it symbolically because it will never I mean definitely will never get anything out of it but if I run this and takes a little bit of time what this random search actually does it's the word the title says it it starts with some initial so this is how the function looks like in a contour plot, okay? So in a contour plot it's clearly there's a kind of a minimum point here so that's the you want the minimum average response time okay? but you want to pinpoint it so what happens is I have some sort of a movie which is um probably illustrates this a little bit better what you do is you start with the initial guess which is this point, right? and then you randomly pick I mean it's kind of the craziest idea, right? you just randomly pick points in that region, right? and you do it with a certain distribution I think here is just uniform distribution so every point is equally likely or every region right? if a certain size is equally likely to be hit and what happens is you only record things where the value of the function is actually lowered from the previous one, right? so this movie kind of illustrates um if I could run it again there's some flickering I don't know why the smallest are the one that are picked at random time the red dot every time I found so it's evaluating the value of the function at this point and if it's lower than what it was before it puts a red dot otherwise it doesn't, right? so you see that they're only like 1, 2, 3, 4 I don't know why it's um okay? 1, 2, 3, 4 5 maybe points that actually got lower, right? and again you have some stopping criteria which says okay it's enough, right? I mean you have all kinds of limitations, right? when you can only I mean your region search region can only be like as small as I don't know, one block, right? 100 meters by 100 meters or something so you don't need a accuracy, right? that's the reason why this random search is working well because it just says well if I'm doing a random pick of points and I do like 1,000 points what's the probability that I'm going to be actually heating a region of size 100 by 100 meters, right? um well it's going to be you just have to divide the area the total area by the area of the small thing and figure out the probability, right? so it is likely you're going to actually get that region, right? and that's good enough, you see I found a value here which you know has this coordinates and has this minimum whatever is the average time, if I run it again is it going to give me the exact same point? no, because the random search picks other but is it going to be still in that region? yeah, now is this the best method to use for for minimizing in no way for certain kind of rough modeling problems that's the first thing to try for instance, right? so you see it's finding smaller and smaller and this code actually elicits the iteration so for instance in this run of the code there's been first iteration was picked pretty close to being minimum, right? and then only the 87th so all of the other ones were higher, right? only close to the end it kind of got lower a little bit lower in other runs it might take several iterations okay? but that's pretty much random search see, so the second, the seventh, the fifteenth iteration it got lower, right? the other ones didn't get lower okay, 37, so anyway just look at that problem and see the code I think one of the homework by the way, I signed the homework for next week on the web from chapter three I think you will have one of the problems that you have to do this again, there's really nothing to do I would say to look at the code and see how to implement choosing random points next homework is due Monday, yeah, so week from today and let's see, so Wednesday we're going to start talking about linear programming in case you have seen anything before it's probably a good idea to refresh we'll talk a little bit about the theory, but we'll quickly get to the application so the more familiar you are the better okay and tell your friends to show up here


What is Indigenous education? Tisa, that's a, that's a wide area, you know? Yeah.  And the importance of knowing what the tobacco is and how it relates to, you know, the relationship with the land, for example, because you always have to, it's a reciprocal relationship that we have. So if we're going to take anything from the land, we have to make sure we give, we give back, you know? And I think when we talk about Indigenous education, that is one of the most important components is that reciprocal relationship that we have because anything that we do regarding Indigenous education, this tobacco always has to come first. Because we were the last ones to come here upon the earth, according to some of our prophecies and teachings, you know? And we're the most pitiful-est ones. So when we think about it from that aspect, then we know that, you know, if we're going to take a plant from the ground or if we're going to kill an animal or, you know, like we need them to survive, so this here is what really helps with that, you know? And then the other thing, too, I think when we think about Indigenous education is all the different stages of life that you go through, you know, like, because our way of life is exactly that, you know? It's a way of life, it's not a religion. So when we walk our path, there are certain things that we always have to be mindful of and we have to be aware of. For example, when we know that the baby is coming, we know that we know by that water, when that water breaks the birth, and then when that baby travels through the canal, the birth canal, it's already telling the baby that you have to work on this side. So that, you know, that knowledge is already there, it's already embedded, it's in the blood of us as Nishnabe people, and so we have these different things that tell us about that. So the baby, you know, when the baby is working through, traveling through that birth canal, that, you know, the baby is kind of saying, you know, or the spirit or whoever is saying that you have to work on this side. So then when the baby comes, you know, after making it through the birth canal, you know, and then when you watch that baby take its first breath, you know, and they begin their journey on this side. So then all through their life, all through their life there's things there that help to guide them, to give them that grounding, you know, like all these different teachings and all these different ceremonies. So, for example, like, you know, when the baby first walks upon the earth, you know, they start walking up the ceremony, you know, because it gives that child an opportunity to offer him or her to explore the earth, to develop that relationship with the earth.  So, you know, all these different ceremonies, that's what helps them to understand their relationship. And that's where that reciprocal comes in, because all creation is giving to them, so they, the child or the human beings or Mishnabek have to, they have to give back, you know. I'm big on giveaways, you know, I really truly believe that we need to give away every time there's something that's given to us, whether it's a naming ceremony, fasting ceremony, you know. Puberty writes fast, you know, like all those ceremonies we need to give back because something very special and very sacred happened. So, you know, it's important to give back because of that reciprocal relationship.  So we have to always respect the child creation, and this is one way, it's by the tobacco. So we're giving, you know, and even we give back to when we have those giveaways, you know. So to me, that's what I look at in indigenous education.  And you have to, I guess the question that needs to be asked is, did I leave good tracks to follow? Because then you become that knowledge keeper. So you, and again, you're giving back. See, there's that reciprocal relationship. So you're giving back to those ones coming behind you, all the knowledge that you've attained in your life. So it's not just, like people say that the elders have a lot of knowledge and they have a lot of those experiences and whatnot, you know, and it's true, I agree. But there's also those young ones like yourself who has knowledge, you know. But when you look at the relationship you and I have, like we had a good conversation here. But yet at the same time, I'm giving back to you, you know, based on the experience that I had and the knowledge that I've gained. And that's how it should be with a lot of our elders and the young people, they should be giving back. Again, that's that reciprocal relationship. So when I look at indigenous knowledge or indigenous education, I guess that's part of it, you know. And it could be so much, there's so much here that's such a big question, you know.  And all that goes on in those seven stages, you know, the ceremonies, the feasting that you need to do and, you know, how to walk a good path and to walk it with kindness, those values, those Mishnabe values we need to really focus on as well. I don't know. What are they? Like some say the seven grandfather teachings, yes. There's those values in the four direction teachings. And then of course we have like the values that we've learned, you know, just in our own home environment. So there's so much there, that's such a big question. Yeah. So I guess too, just with this question, like you talked a little bit about what you, like the tracks you wanna leave and is there anything, like anything specific in terms of knowledge that you feel that you want, you know, future generations to know, like, is there like a number one thing that? Well, my gift that I have, I guess, is that right surpass such a, and you know, to me, to me that's important because, you know, we hear that the women are the teachers. They're the teachers of the knowledge, teachers of the language, you know, teachers of all the different ceremonies that they need to be aware of, you know. So if there was any one thing, it would be the role of woman, you know, the role and the responsibility that a woman has in regards to her children and her partner, or even creation in general.  And so, you know, her role is to be able to give life.  So to me, the woman is a very important, important component when we talk about indigenous knowledge or education, you know. Cause when you look at the woman, you know, like she has to be, she's in tune with her children. You know, she's in tune with what is happening with them. She can pick up on it right away. Like I have a daughter that lives in Texas. I know when something's up, you know.   Your child is still connected to your umbilical cord, you know, but we don't really see it, you know. But that's how I see that.  And even though like, you know, the father's there, but it's her that's actually teaching the child mostly about values, like respect, for example, and stuff like that, you know. And children will do what you do.  And so they're, the mother is, the woman is really a part of that. That would go on and on. So, okay. So the next question is, are there any stories or kind of talk to this actually, are there any particular stories that you'd want your grandchildren or grandchildren to be able to hear you talk about in terms of indigenous knowledge? I think one, it's funny because when I was down in Texas visiting my granddaughter, I took out the Michelle's book and I read some stories to her in that book. And I think one of the most important ones is that that should be passed on from generation to generation is the creation story.  We hear that often, you know. And it does, it does make sense. And, you know, like we have to kind of see our path from back then in order to move forward. And even like our history, Nishinama history, like what has happened to us as a people, you know. And so as long as we know what is happening there and where we're going, our generations need to know our history. I think that's so important, they need to learn their history. But the creation story is one, just one aspect of that. And the language is another component. I think, like when we're talking about 10 years, like goodness, our language is, if we don't start speaking our language and using our language, like I don't cut my little granddaughter, she, I mean, she's just learning Navajo. And to me, that's fine. As long as it's an indigenous language. And for me, not knowing my language, you know, like as strong as some of the elders my age, like I feel like I'm really missing out on something. And when we go, when I go to places and I hear that language, you know, it's just, it just, it just really moves me, you know. So I think the language needs to be really promoted. And it really needs to be brought in the forefront.  And because it's, it's so important that language. And I think too, the other, like my other granddaughter, she just recently fasted her very first one in the fall. And to me, like when she did that, what that was telling me is that, connecting to the spiritual aspect of life.  But we also know that there's spirits that are, you know, that are around our ancestors and so on. But when she did that, that's what she connected to, was the spiritual aspect of life. So I think, you know, when we look at, you know, the next 10 years or over something like that, children need to be taught about the spiritual aspect of life. So yes, yes, we know that a tree outside has life. There's a spirit there. There's winds, you know, there's a spirit in there. But how in depth do they want to learn about that?  She said, you know, she said, I miss it. She said, because I could smell, it was a different kind of smell. And she said, I just, you know, she hugged her, she took her own pillow out there. So she just hugged her pillow and she just said, well, I could just smell it being out there. But that's that connection, you know, to her spirituality and her spirit connecting to what was out there. And, you know, to have that experience, I think that's really important. Like all children should go through something like that.  There's always going to be those spirits there, you know? And those spirits are those ones that are going to give them that guidance and direction. And, you know, I see children today that they don't really have that, you know? And it's kind of sad in a way because they don't have that connection. Like when I look at this little girl, and even my own girls, you know, how they connect and how they feel about that. And I look at that little girl, you know, and how she is now. You know, just the way she conducts herself and what she says, you know? And she usually tells her mom, sometimes we need as much. Because for whatever is happening, you know?  More of our people need to learn more about that. Yes, it's starting. There's a lot of our people that are starting to go to ceremonies and whatnot, you know? So it's starting, but we really need to maintain that. And probably bring it more. Like bring it out more. Like sometimes, you know, we talk about that, like we know that the spirits do exist, you know? And those are the ones that help us sometimes. Sometimes those are the ones that could scare us too. Okay? But yeah, it's important to know that, to understand that thought. And that you yourself as a spirit in this vessel of the body that's walking. That's walking this realm. You know, one time I was up in a bush and, well, I guess like I was fasting. And anyways, when I was sitting there, it just got really, all of a sudden, it just got really quiet. And this was in the spring. And it just was really, all of a sudden, and then I could sense something coming, you know? And I was just, you know, I, well, I couldn't run because I was, you know, but I just sense something was coming and I didn't know what it was. And then as it was moving this way towards me, I kind of braced myself. I hung out to my tobacco, you know? And I just kind of waited because as it was moving, the birds were, they were quiet, you know? They were quiet when that was coming because there was just no sound out there, nothing. Even no wind, total quiet. And that's what I noticed because the birds weren't singing. And I thought, you know, like I have to follow them, you know? So I kept quiet and I just sat there and I held my tobacco in my hand and I could feel that coming, you know? And then I was just getting so close and I just went, and I could just feel it. It went right through me and then it passed. And then I kind of sat up there, you know? And I was sitting there and then opened my eyes and then I started to hear the birds, you know? They started to sing again. Anyway, what I found was that it was the changing of the season from spring to summer. And that's a spiritual connection, you know? Just to feel that, you know, that season change like that, that to me, you know, it was really, it was such a like scary but awesome feeling. And it kind of relates to, to my name, you know? So that spiritual connection to creation and to one another is so, it's important. When we talk about the 10 years, learn more about that. Children need to learn more about that. Whether it's through fasting or whether it's through, you know, storytelling, like even storytelling, when we do, when we say tell stories, there's meanings behind them. And when you hear those stories, because it's like, it's like, if there was, say, a group of people sitting around the circle of my age, exactly my age, you know? And we hear a story. Somebody might get that story different compared to my interpretation for me because we're at a different level of growth and development, you know, what, you know, spirituality, whatever, you know? So that story has a different meaning for that different person who's still yet the same age as me.  When you're telling the story, child may have a different interpretation of it. So when we talk about storytelling, then it's actually a way to bring meaning to life, our life, you know? Because going back to parenting, going back to being a mother, when the child is growing, we have no right to have control over the child. But we can give them decisions or choices rather, you know? Well, do you want to do this or do you want to do that? Because in our whole life, we're always going to make choices. There's always going to be two for sure. So we have to, you know, so by doing that with the child, then we're allowing that child to make the decisions for himself, you know, himself. And then that way, it still maintains that power that the Creator gave them, you know? And we have no right to control our children in that way. Yes, sometimes we have to say, and be stern and say, no, you can't do that, you know? But sometimes, so a majority of the time, you're going to give them options, you know? Because it's not our place to have that control over them.  So you always teach them that about giving them choices and options, you know?  And sometimes they were based on life experience. And sometimes they were stories from teachings or like ceremonies.   So when you give them storytelling, it's up to them to decide, well, what does that mean for me? You get it? You know? So, so storytelling is really important. And yes, they say storytelling is not, could only be done in the wintertime, but sometimes when you're talking or trying to discipline your child, you're going to give them a story related to that action or behavior, you know? And then they make the decision on how they see that in relation to the mistake that they made. So I can't even think of an example right now. Well, you know, like just for example, I'm going to try it. If a child was caught stealing, yeah.  Because a story that's related to that anyways, you know? And so then that gives the child, you know, the child is made to think about her actions or her behavior in relation to what he or she did, what's stealing. That's not a very good one. Or hurting somebody, you know? Because you could use the story of respect, something around respect, you know, if a child is hurting somebody. So storytelling is really, I don't even think many of us do that anymore, you know? I don't think too many of us do storytelling in relation to a child's behavior and actions.  The reason I say that is that I remember, I met this old man a long time, and people probably know of him already, like P. O. Cheese, you know? But he used to tell stories, you know? And one story I remember he was sharing because he talked about it, but he based it on his personal life.  And he said, my wife died. He was already up in age, you know? And he said, my wife died. And then somebody came over and, you know, I was grieving so much. And he gave me a pack of smokes and told me to smoke these cigarettes. And he said, that's how I got to smoking. And so I was sitting there. And I asked, I asked other people who were there, what did you get out of that story? Just said he picked up smoking. Yeah, he did, but what else? But to me, the story that I got out of it, like I didn't say they were wrong or anything, you know? I nice shared with him, the story I got out of that is because of the grief of his, the loss of his wife. He needed something there to help him. And so he picked up smoking. So, you know, there's reasons why I reduce them. And even myself, like I used to smoke. And I remember having my own cigarette. And I share this story. Story.  And I said to them, you know what I did?  So I mentioned to her, you know, we should quit smoking. And she said, yeah, you know? So anyway, then she calls me the night before, you know? Well, are you ready? For what, I said. They quit smoking. Oh, yes, I said, we did say that. And she said, yeah. So anyway, I went outside here, was probably close to midnight. I went out here and I took, I had that, my last cigarette. And this what made me think about Pito Chispa story. And then I said to her, I said, well, I was holding that cigarette, you know? I says, well, you've been with me all these years.  And I said, but now, you know what? I need to do it on my own. I need to walk by myself now. And I was talking to that cigarette. I said, I have to do this on my own. You've been a good friend, but I need to do this on my own. I never had no cravings. And I just stopped just like that. Wow. Yeah. And if you want to look at it from a psychological perspective, you know, like I had to tell myself internally that, you know, I don't need it. But I share that story every once in a while. And then people kind of laugh at me and, you know. But in reality, it's a story based on a life experience. So that story, and even funny stories, it's how it's the mind is developing on those stories. So going back to that, if all people were sitting in that, in a circle of my age, people would tell, get an interpretation different from what I got out of it, you know. Because we're all growing at a different level. So those stories are really important to tell. Whether it's a life experience, whether it's a Nanapush story, or, you know, we tell stories in the winter, like they're important. And we're losing that. We're losing that. That's why that's part of that. That's so important when we talk about storytelling, you know. And going back to my little granddaughter in the States from reading those stories, you know. And the one that she really liked the most was the flood. And she really enjoyed that story about the flood, you know. So, you know, like we really need to, we really need to focus on that. But getting back to spirituality, going back to my little granddaughter again.  So she's never been really exposed to the bush. So when she came home here, they were spending a couple of weeks here. And I went to do a ceremony back at the power grounds here. So I asked her if she wanted to come with me. So we went and, you know, sitting around the fire there, you know. And then afterwards, the feast food, we have to take it out of the bushy. So anyway, I took that feast food and I said, come on. So she walked with me and then as we were getting closer to the bush, she said that I'm scared. I don't want to go in the bush, you know.  And I said, it's okay. You know, you're going to be just fine in there. I said, huh? So she held my hand as we were walking in, you know. But as soon as she got in there, further in, you know, she realized what I was sharing with her that it was safe. You know, she was okay. Like, so she was just running around over the place, you know. But that's what I'm saying. Like those, you know, that spirituality.  And she didn't get afraid anymore. And so she knew, again, it goes back to being in the blood. Like our ancestors are there in our blood. Oh, when we do stuff, you know. Yeah, that's spirituality, you know. So I think I already did that. What stories are teachings, can you share? Yeah, you did that one. You did the, did you want to add anything to your vision of education the next 10 years? Well, number one, it needs to be taught by Nishnabe. You know, and I think that's the only way we're ever going to learn is by our own people teaching us.  Because that connection we have, you know, it's right there. As soon as somebody says something or we do something silly, we don't, like, we have, we know, though, you know. So I think to me, that has to be, it has to be taught by an, you know, an indigenous person. And even the writing of curculums, anything like that, it should be done by indigenous people. Like, I truly believe that it has to be done by our people. Anything that has to do with education down the road, it needs to be done by our people. Because we have a unique way of viewing the world, and we have a relationship that's in our blood, you know, and so to have anybody else teach that, they wouldn't grasp that, you know, they wouldn't understand it. So I really believe that that needs to happen. Anything that it has to do with education in regards to native people, it has to be done by an Nishnabe people. I don't believe either that we should, you know, record our teachings, you know, or write our teachings down. But if there's anything that's going to be done, it should be very generic, you know, not in depth, you know.  So I don't think I'd like to see that written down I mean, you can talk about it very gentle, but not the story, you know which one I'm talking about. Like that, there shouldn't be written down. So there's oral stories that relates to the ceremonies. So that's where I would say anyways, you know. Yeah.


I think you guys can just wrap up and send me what you have if you didn't get to the end of it. Just send it to me. I think it'll be more productive to also like discuss what we think. So um I guess you know we've been doing retina or doing mole for I don't know how many years now maybe five or so. I think it's a good time to kind of like assess like how effective the curriculum is in meeting your needs. You know that's the only point of like mostly the only point of the curriculum is to help you guys. So I think this is like uh maybe sometimes as faculty like we feel like we don't have that much like so now this is like a dedicated time for you guys to just you know discuss like what you would like to see differently like what would help you more. And I just say this is like my first time doing like the team-based learning thing and I've never actually experienced it in real life. I just went by what the med students told me and what I YouTubeed so definitely curious for feedback on that at the end too. So logistically it can be like a little challenging with all the different documents and things. So um so what I was envisioning was that we would split up into three groups and we would discuss um a couple different aspects of the retinal mole curriculum. So one could be discussing FA conference and other could be discussing the lecturers and then the other could be discussing you know learning on rotation. So I'm going to ask you guys for the case-based learning to like split up my year. One, two, three, four, five, six. So maybe like try to sort yourself into three groups where there's approximately like junior and senior people and the three different groups physically organize yourself together. So let's do three groups and there's going to be like some senior and junior people in each group so. All three groups. Not this one side of the room. We'll let you know but if you take them and all the you know the right side of the stuff, it's me, it's us three. All right, these three, these three, George.  So three more members? We're both good people. This is a problem. We can't help very hard. That's a problem. All right, so let's group over here. You can discuss FA conference. What are you, how do you like that to be different? Let's group over here. And then you can discuss like you know on rotation. And then nominate one of you guys to be the scribe to write down your comments. Okay. I'll look for that. I better put on that. Okay, so you need to look at the current curriculum. I posted it here. It's also in the box, in the peds written on 2023 under written a whole curriculum. In case you need to look at our current curriculum, it's on box in the peds written on 2023 folder called written a whole curriculum. I'm going to do it several times. Yeah, but I know what's interesting is going on. I was actually thinking it's really easy. It's like, you know, but more than once I wanted to do it, it's like I don't know what I was saying. So what was actually Well, so that's what I'm asking you. Yeah. So much. Like you're saying this is the area. Yeah. Yeah. Like my sounds like we're not all boys. You know, what is it? Yeah. Yeah. Yeah. Yeah. Nice. So so and then to so I mean, the Red Bulls are just like, yeah, they have that shirt, like I can't think of any better way to give it a more good gift than to give it to the Red Bulls. I've seen the pictures of the Red Bulls and I haven't recognized them in a while. I cut these three big dolls in a row. That's a Red Bull, right?  I've seen it a lot. Do you go to the Blue? I've been to the Blue so many years. Yeah, I've been to the Blue. Yeah, I've been to the Blue so many years. I've been to the Blue so many years. Do you guys feel like if we wrap up in like five more minutes of your time, are you ready now to discuss in a big group what your primary is? Okay. Like we're ready. You're on the ground. So it's almost like, it's getting like too creative. Yes. And you're like, just give me a lecture. I think it's on the ground. Yeah. It's basically just like that. You guys, do you have an anti-vegetarian lecture? No, wait, I don't. I was just curious because like I saw that on here. I was like, is there a specific anti-vegetarian lecture that's separate from diabetes and AMBs? No, that's true. You guys could also talk about like whether the topics of the didactic sessions are good. Like would you like different topics? Would you like to cut any of them out? Do you feel like there's something that's like really critical that's missing? Yes. Thanks for calling. Yeah, no problem. All right. So maybe we can just like, feel free to... Okay. Yes. Okay. So what do you guys, what is your, George, what did your group say about FAA conference? I can't go, I mean, should we go for it? Okay, we'll wait. Let's just get out. You're always... I guess since we showed up together, we've been together every day. I don't think she didn't realize that like a lot of siblings and like... I'm just going to get in. Now we'll hear what Abigail has to say about her group. FAA conference. Conferences tend to go over time. So having it less often or having only like a max of 2% each time. Okay, that would probably be great. Because I find myself, I couldn't focus in the first two presentations and then I just... And I think that's really good to think about because I think, I don't know if the... Like the, what is it called? The AUPO has some sort of requirement for how many like FAA conferences each fellow has to present at. So I don't know if that's like the driving factor. And then I don't know if residencies have a requirement for the number of FAA conferences you have to go to or present at. I think we should, maybe if you could make a note that we should look into that and I don't think we should be trying to go exceed the requirements. I've talked to Bernstein in the past about doing FAA conference and I asked him, what are the requirements? He's like, well, it's only required to have it once a month. So I was like, why are we having it twice a month? But he said it's because it often gets canceled. But I was like, I don't know. So it may be that if you guys unanimously would love to have it less often that we could, you know, bring that to the like PC and be like, hey, you know, we have a lot of burdens on our time already. Like we are not required to have this twice a month. Like, you know, I was not able to make a change, but I spilled that way. We can do it. Okay. So maybe the timing of it should be different too. Those are just ideas. I guess in terms of Tuesday and Wednesday, I assume Mondays are Orbit conference still. Is Tuesday or Wednesday preferred? Wednesday is also preferred. Yeah, definitely. I will be more strongly for the months of the month than the change day per day. But we can do both. That would be great. How they just like apply their words to just raise their solicits to see if they're going to have it easily preferred. Yeah. Do you guys have like a good resource that anyone found one that you like? There's a super basic one. I grew up in a medicine resource. I guess one thing I do, I personally as a resident looked back on is I got the slides from one of the fellows that they gave at the beginning of the year. So that could be something that we could share. Maybe that's the best resource to share. Like more systematic. Okay. And it is great to like be able to, if you're wondering, oh, what does this look like? Like be able to go back to that case. So it sounds good. And then the last thing is to focus more on book reps in the morning. And then at the end of the summer, I think that that sounds like a really good, like let's make that they like more resident focused. I do say that sometimes it going really long is like you're guys fault.  You know, you can also focus on what's necessary for. Okay. But the fellows are also too late. I don't really remember, but we did not have it as often. That's for sure. I barely remember it. Okay. So any other comments on FA take homes is having it less often and making sure the things get uploaded. And it's more like O caps resident focused. Okay. Thank you for not just trashing everything. Should we discuss the didactics first? I just want to point out that, you know, when I asked Elaine like, okay, how many hours of lecture are we required to have? It was substantially less than we were having. So just thought to keep in mind that apparently, although right in the lecture hours have been reduced, you know, whether you want to reduce that further or not. So yeah. Like there's not like a systematic framework for your brain to like stick the information in. That sounds really good. Yeah. So, and I guess maybe the, so I guess the pre-work is a very quality in terms of providing you that framework, maybe like some of us might have assumed that it like provides that. And that's why they're like jumping into the quiz. But maybe it's helpful to like, because people learn in different ways and develop that framework in different ways, that it is helpful for people to like share. Yeah, so I mean I think that the first thing to allow that to have been about two hours was having the fellow or the entire session of like first pass going through material, foundational knowledge. Wait, are you raising this in style? This is all just me. Since we're not really recording our lectures anymore, to update content and things like that, that's available. So if people did, are you recording? Yeah. She taught us lectures. So as you're making the chapter, you have like questions to answer or fill in the blank. I think we're just going through it. And then we're like, oh, I just come back to it. So it's rock, paper, scissors. Yeah. All right. So, and then I think you guys, if you have a specific, deep back for specific Brettnell lectures, if you, as long as Sean's written them down, I think we could maybe, anything else we should discuss. Yeah. I guess what kind of questions come up on about the empty, like the trials. Is there anything else? Okay. It's not so much about what we're trying to do. Right. Anything else? Do you guys feel like we have like the good topics? Like, I don't know. We have the intro to retina, which I don't know. I'm happy to ask any of my lectures. Pete's retina. I feel like Pete's retina, like, I don't understand. I still have been trying to find useful ways to occupy your time. Because I feel like you get a two hour Pete's retina thing from the theater service. And I'm happy to quit. So I don't know. I'm thinking of axing that. And then, but I do feel like the inherited retinal degenerations that are associated with systemic diseases are really critical for OCAPs and boards. And I know I've been to Bernstein's lecture about four times. So, but just, I don't know. And I created, you know, there's some videos out there from me on that, but I don't know. Just any thoughts about the overall topics? Yeah. But I think having your lectures that you gave last year that's pre-York, those are really good. And I believe like the way that you organized into a pre-York. So having that as pre-York and then focusing on that. Because those type of information, but those details are things that are constantly asked. So I think it's good to coach this. So if you want me to continue to occupy your time, I'm happy to. If you don't want me to. Like I'm happy. I, you know, can make horror videos for you or update them or whatever. Try to improve upon them. There's so many questions. Do you feel like the intro to retinal like scleral depression is okay or you want to have more like, this is basics you need to know what to call instead of like this and see it's on? Okay. Okay. Okay. All right. Yeah. Yeah. It's good. It's going to be relevant like how to see this and even down to specifics like that. Yeah. I'm going to get way faster. Right. Assuming that you see it. Yeah. And our, I don't understand. Yeah. Sounds good. Okay. So that's maybe enough discussion of the didactic sessions. Sounds like the anti-veget. Like Jeff lectures not happening. So I'll just remove that from the curriculum. Yes. Just one thought. Yeah. Yeah. There are so many times. Yeah.  And I'm like, I've seen you and I don't know. I was like, don't look at this what's happening. I don't know is there a room for this. Yeah. And so that's been like a source of stress a lot of the balls. That's true. And I think that's really nice to go for like the really basic random moments. Yeah. I could. Yeah. Maybe I can incorporate that into the indirect. Yeah. Yeah. Yeah. Yeah. Do we have a copy of that? Yeah. Okay. No. It's also great. When you said that, I thought of that. It's also great. It's also great. Oh, really? You know me in the video. Yeah. Yeah.  Well, I said so much time. No, I mean, it goes through all different random pathologies. Yeah. Thank you. Thank you. Okay. All right, shot. You took good notes. You'll send that to me. Yeah. Okay, Ashley. Are you subscribed for your group? Yeah. Oh, shoot. Okay. We'll have Nicole. It's What I'm having to call is, are there multiple retina rotations? What is to this type of tissue, why is there retina rotation? Okay, so it's pre-charting. What other scutwork are you guys doing? I don't think it's like, I think it's a lot of scutwork compared to the rest of our rotations, but in general I don't think it's, like it's, you're seeing a lot of the patients, you see a lot of patients who are self-imaging. It does talk, when you're not used to it, like when you're coming off of a pee, it's in your eye. That's true. I feel pretty lost. Yeah, pretty used to it. So it helps, you know, the patient and thank you, when I do next, and then it's close and it protects really. I don't know what to do with you, but thank you. Other feedback on the retina rotation? Yeah, I don't think we're going to get, Tally has, we're not going to get away from taking, I think that I agree with you that it's not that educational, but there's, I can't change that. Okay, I have a question, so. Yes. I'm not sure, I'm not sure where this is, because it was definitely going to give you a certain direction when I was thinking about how I had to explain it, but what is happening to retina rotation? I don't know. I was just going to be my feedback. I think whatever happens in the future, that takes a change. There's so many OR days in my skin right now. So, what was bad about it? There's no direction. Yeah, there's no direction, so ORs, there's typically like, like it wasn't clear what you needed to be, or what. Yeah, but even if you were scheduled to hurt, like there'd be days where there's like zero cases. Can you write that down? Well anyway, there's not going to be a clinic with her. I see, it's not like as clearly defined, like this is what you do, and if, like for example, if HeartNet has no cases, like can you just like relax? You know, that would be nice. I look at this good blood room. It's still awesome. Again, a lot of them are results from that. I think part of it is it seems like there's a lot of chaos among the fellows, like constantly they're like showing themselves around to make sure everyone's meeting the needy people's needs. Yeah. And I'm like, well, I'm happy to operate by myself, but I feel bad because you guys should be doing these things. That's why I'm like, yeah. I was thinking a bunch. There was often a day where I think Dr. Parks didn't have a fellow, and I was able to help in with you, which is BASCA. Yeah. Well, I think it would be really good when the Retina fellows remake their schedule for a resident representative to be like heavily involved with that. Any volunteers? Cole? Abigail? Okay, maybe I'll ask them to kind of schedule a meeting and maybe I'll attend the meeting too so I can help to advocate for you. And if you have another call. Yeah. She's been small converse personal fellows, so I'm not sure how I see it. It's helpful. All right. Other comments sounds good. I think hopefully we'll get some residents to attend the new schedule. I think that would be something. So, okay, so you might let that to me, Ashley. Let's see what time it is. It's eight o'clock. So we have until nine o'clock. Is that right? Yeah. So we might have to skip the Pete's Retina post year little chorea part, but I feel like that's the least important. That's just my... Okay, so next little mini lecture song, this Rob. So she requested it. So, by the way, I think I also probably have like a fakeomatosis lecture on their YouTube or the more I'm core somewhere. So, yeah, what does a fakeomatosis have in common? I try to, I'm not really good at memorizing things. So I try to like start from like a really basic level. Like what can I like find that's similar between like most of these things? And what can I find as like an explanation for why things are the way they are? I find that helps me memorize things more, but different people are different. So, but, so most of them are autosomal dominant, autosomal dominant inheritance. What's the reason for that? Why does that make sense?  Those are autosomal recessive because like their mutations and enzymes. And if you have one bad copy of the enzyme gene and one good copy, you still probably have enough enzyme to do the job because like, you know, enzymes like catalyzed reactions, you know, we only need a few of them to catalyze a lot of reactions. So half is plain enough. So what's the explanation for fakeomatosis being dominant? The way I think of it is it's because many of them are mutations in tumor suppressor genes. So basically, if you have one bad copy of the tumor suppressor gene, you know, the other copy is still suppressive tumors everywhere in your body until something happens to that one copy. Then you start sprouting a tumor. So I don't know if that makes sense to you guys or questions, thoughts on that. So the lesions that people get are tumors. They tend to be hammertomas. They call them, you know, neurocutaneous syndromes because many of them affect the brain and skin. Not all of them have pain or skin findings. And then why are they called fakeomatosis? So fake, as you know, means lens. And the connection is not to like the lens of the eye and fake omulsification, but it's to the various, you know, birthmarks. They kind of look like lentils or lenses to the Greeks.   Some of those might knock out the good copy, the only good copy you have of the tumor suppressor gene. So a couple of definitions, hammeredoma, malformation, that's an excess of elements normally present at the site, chorostoma, it's a tumorous growth that has things that are not normally present there. Most of the neurofibromatosis or, sorry, fakeomatosis have hammeredomas, not chorostomas. And then some of the fakeomatosis, they're not really from tumorous growth, they're really some sort of malformation. So something didn't grow, right? Something wasn't developed correctly. So, you know, there's the mutations in tumor suppressor genes, which lead to tumors or hammeredomas, and then there's mutations in genes that affect development and that might lead to more like malformations, especially vascular malformations. So what's the angioma? There's a lot of words and then there's like variations on the words and they're all like used, it's really drives me crazy. The way I kind of approach it is I just pick one that I like the best and then I try to like just use that one, but then, you know, once I feel like I have a better grasp on the whole overall situation, then I link those other words back to that same word. So otherwise, I find like I just get overwhelmed and can't like, you know, memorize things. So a capillary hemangioma is a proliferation of capillaries. There's not very much like cells in between and it's a hammeredoma. So that's like a lid capillary hemangioma versus a hemangioblastoma. The word blast sounds bad, right? Like those are, so that's when you have like more stromal cells and these stromal cells have a lot of like vacuoles in them and that tends, so you see it's not a lot of blood vessels like in the tumor. The tumor is actually mostly the stromal cells and it's got some blood vessels and that can be more aggressive. That's why the word blast is in there. So what condition gets retinal hemangioblastomas? VHL. So those tumors tend to be kind of more aggressive than a lot of the other hematomas that you get in the fecomatoses.  It's actually an arteriovenous malformation. So I would try to like think of it as an arteriovenous malformation then later connect in the word racemos, you know, hemangioma there. So unfortunately, people came up with a lot of names and some of them make more sense than others. So I think of the, so most of them, you know, being autosomal dominant, a couple are sporadic. So that always like confused me, but they yet they have a gene associated with them. Do you guys know why that's the case? Like how can you be sporadic if it also be caused by mutations in a gene? Actually, I think usually it's when there's a sporadic or a new mutation. So it still kind of has some effects. So you can have like a de novo mutation that's everywhere in your body. And that's one way that I still would call that autosomal dominant, but you can also get a de novo mutation when you're like kind of like a blastocyst. And then that mutation will just be present in certain parts of your body. So for example, like in Sturgeweber, maybe the mutation is just present like here, like on one side, you know, because you're, I don't know, was it your poriola is like symmetric, but you know, this cell is not going to, mutation of this cell is not going to like affect the other side. So that's why, you know, they found that when they tested like the tissue of people that have like Sturgeweber, they have this GNAQ mutation, but the rest of their body doesn't have the GNAQ mutation. And so the Clipel, Trinae, I don't know how to pronounce that, it's also like that. Fiber basin, I don't think anyone's found if there's genetic thing, but it's also sporadic. So yeah, that's an overview of the genetics. What was over here? Oh, so I just wanted to say that in general, you can have a characteristic tumor that's a characteristic of this syndrome without having the syndrome. So for example, you could have like a retinal capillary hemangioblastoma, single isolated one, without having VHL. You could have like a retinal arterial venous malformation without having Fiber basin. So that's just something to, you know, keep in mind that although like maybe we most commonly see retinal capillary hemangioblastomas in the context of someone who has VHL at multiple tumors, both eyes and tumors also are in their body, that it can be by itself. Okay, questions? Thoughts? The ones with W's in them are sporadic. Oh, thank you. Sporadic. Sporadic. Okay, so next we'll go on to the quiz. So there's a, should be in the box a fecometosis quiz blank. So you can like download that to your device and start pulling it out. And then what you're going to do is you're going to like have a partner check your answers. Or maybe BK and Lydia could be partners. Abigail and George could be partners. Nana and Tony could be partners. Sean and Mubarak and Cole and Ashley. Just to kind of split up the seniority. Wait, you're silently working on this. This is not an open look test. And then you'll grade each other. Sean, could you send me your feedback on those? Is there still an intern reading list? The politics book is not here. Cause I feel like that could be a good place to put the like an MA, like imaging basics. He told me he has like five copies. Cause not everyone gives it back.  Shhh. They will ask. Oh. They don't, they don't. Silas, you're right. Silas is in the eye. Wipe her nose. Oh. Did you do? I don't know if there's anything else. Is there another name for him? Oh, that's right. I think it is. Oh, yeah. Does it actually? I'll just like comment that I've definitely been gotten by this on OCAPS where they like used the first third lever and I guess they do like do it in real life like in real years. I don't know if this is going to happen. One is, and that IP is actually not in it right now. So if you just remember those three... It's a con. Oh. They have the refuse cruddle. I guess I'd be like... Yeah, what's the difference? So this one is just like... It's just like... You know, at the end of this beat, it's sort of like... It's like a sped-up moment, right? It's like a response. It's just like... It's a foul, a criminal, whatever. It's sort of like... Like that's a bad guy. That's a good syrup. I'd got a little bit of a triangle on it. What I was talking about was... What I was talking about was syrup. What I was talking about was still martial arts. What I thought was... What I thought of a HL on that. What I thought was like... Yeah, I don't know. I definitely had a u-world portion at some point that only showed this, and asked what it was, and it was, like, these are all heads of Thomas, and they're right next to him. It was, um, this was straight out of the house. Straight out of the house. Straight out of the house. Straight out of the house. And then you'd be able to tell. Yeah, that's right. That's a stick. We'll find out. Yeah. I feel like NF1 is the one that can do a bunch of random things. What are you guys about done going over your quizzes? Any questions that came up, or? I did have a question. Uh, is that supposed to be, those are supposed to be portable tumors. No, those are supposed to be subendymal nodules. The cortical tubers, I think, are just, like, triangular white things in the cortex. They don't really, like, I don't think they stick out. Maybe they, maybe when they get really big. Look like a potato, I don't know. Like they only call the potato because they're triangular. Oh, really? Yeah, that's two birds. Potatoes are triangular? I don't know. I don't know. In the description it was like, yeah, the two birds. Oh, maybe it's a bird. Oh, that makes so much more sense. Really bad character. Thank you. Two birds. Okay, so now we're going to do groups or two groups for our split it this way. And then this guy. Okay, so next we're going to give K-Space learning a try. So you can, each of you should have a scribe. Each group should have a scribe. Sir Bella. Oh my God, I don't know what this is. Sir Bella Pro. You can start going through this case together and come up with the answers together. And then we'll kind of, like, have periodic, which we, like, meet, discuss things. Yeah, you just come up with answers as a group. Like, so the first, you know, so you review this case. Then you come up with a differential. And then come up with, you know, what are the blood vessel abnormalities, names that go with those items on the differential. Just pick a couple of top items. Don't list every single fake hypothesis. Is this something you, is that a crap? Just be a non-spiric. So act like this vessel's a little dilated and tortuous compared to a dilated and tortuous. It's hard to examine so you can't see it. He's on the left. Wait, are you two on the left or are you two on the right? Are we on the right? It's a lot of follow. How is it? I'm trying to look at everything. Hey, Chow, how are you? I'm on the right. I'm supposed to do this one, see how I'm going to do it. You're supposed to do this one. You're supposed to do this one, see how I'm going to do it. You're supposed to do this one. He'll probably do it. And he'll have to do it. I didn't realize, I forget, it was like really small, it was like what color did you see? Yeah, what's your favorite color? I always guess the birthday, I'm looking at the chart and I'm like, oh, it's your birthday and I'm like, do you know what it is? Oh, I guess it's my mom.  I don't know, you gotta be really good.  I guess that's one of the favorite colors. It's always green. And I'm like, you know what you're gonna see green? And they see green. Is it blue? More questions. Go to the next slide. I can bring it up. Yeah, you're gonna break it up and drive yourself. Oh, this is a self-driving exercise. Yes. That's what my question is. That's what my question is. That's what my question is.  Yeah, we only came up with that. You put like IVT. Oh, sorry. Coherence. I can't hear you. Doesn't he have a skill or what? IVT does. I'm just like IVT up. Okay, so you put it in? Oh, that is something. It's like an other, yeah. And I put also, uh, make a mitosis treatment for vascularis. Yeah? I don't care about that. What do you guys do to work together on this? Okay. We're key questions asked in parents. Family issues. Family history. I was like, you're expecting this? I don't think it's necessary. Oh, what? I know it. Yeah, that's like what they'll ask of you. Check their blood pressure. They have feel, I think. See if they have curative or anti-aging. It's rare though. Okay, do we do the break? Are you guys up to the break for group discussion? Okay. So I guess, oh wait, you guys are past that. Okay. Okay. Where are you guys at? The first break. Okay, they kept charging on, but I accidentally left the answers in the next question. Anyway. All right. So, what did your group advocate want to do for examining the kid? Take a clinic in a U.A. Consider fluorescent mu-teography and examine the periphery. Awesome, that sounds pretty good. My soul throw PMA on there. He left us for PMA. Okay. So, the one thing that might not have come up when you guys were discussing the differential is a congenital retinal macro vessel. You were going to tell. I did overhear something. That's good. Actually, when you have a congenital retinal macro vessel, you can get a brain rupture. What's a congenital macro vessel? It'll be pictured if we ever get to the end of this. Which we probably won't. All right. Let's just discuss. I'll just tell you that it's really awkward sometimes telling the parents talking to them about the U.A. when you have not that good of a clue what's going on. If I have a really good clue, I try to get as best of a clue as I can before I schedule the U.A. First, I can be prepared in a second so I can talk to the parents about giving them some idea. Because if it is like VHL and the tumor is pretty small, we should just cry over it while we're there. They'll come out and tell the parents that they've got a tumor in their eye and then you're trying to set them in five minutes so you can rub back to the OR and laser them. That's not good. I think if I saw something like that I would tell them that maybe VHL is on the differential and that we have tumors but they're not like cancers, they don't spread elsewhere in the body but just tell them we're going to take a really good look and that's going to help give us something generic like that. This is VHL. There's some subretinal fluid leaking from that tumor that's affecting the vision. Did I leave the answers on the next question or today? Maybe we could just discuss this one as a group. No, you can discuss them in small groups. Okay. You can enter small groups and start going over that. Is that an OCTO subretinal fluid? I can see it right now. Can you adjust a little subretinal fluid in that? So what kind of treatments do you recommend? I'll just see it about myself. What are the risks of treatments? What are the risks of treatments? What are the risks of treatments? What are the risks of treatments? These are... This one is you can't always ask them what happens if you get a treatment for as far as... If we can take the... Yeah. So these tumors can be really, really bad. If you let them go to the forearm that's like a total endometrial retinal deterachment in that way. doesn't that happen? So yeah, and they probably, it's exadata, but they're just scars together. As long as it's not like, they're growing for 10 colleges. Okay, say that you want to do genetic testing. So I think genetic testing is good. Like, it's really sensitive. So, you know, you could consider whether you want to get all the other tests, or if you want to get the genetic testing first, and then if that's positive, then do all the other tests. So, because it's a single isolated Cavalier-Humangeoblastoma, it could have just been a random occurrence and not associated with BHL. So, then you can go on to the next question. Discuss in your groups. A test back. Oh, like, let's say you have a variant in BHL. How do they quarter the classifications? There's like a variant of uncertain significance, of the nine variant. Likely pathogenic and pathogenic. Pathogenic means like, probably, there's better evidence that it causes the disease, but nine means like, lots of people, you don't. Okay, let's have her. So, I think, let's, any questions, you guys on like, the treatment and like, effects and stuff? Or you don't feel like you have a reasonable understanding of that? It should. I saw some, a lot of us preparing for the lecture, I didn't see some people ejected anti-vegeta, as well. Like, I don't think it was like, you know, if you crowd lesion and like, it stops growing and stops exuding, that's the end of the summer. I don't think it'll be gone forever, but. So, yeah, what tests? I guess I have the answers somewhere here. What do you think? So, I thought, you know, if someone had like a VHL, so, okay, so you would expect it to be a pathogenic variant. So, variants, when you get a clinical genetic test back, if someone has a variant, it means like, you know, 99% of people have this and I don't have this, this, you know, variant in the gene.  Then, you know, these are classified as benign variant of uncertain significance, likely pathogenic or pathogenic, based on the existing evidence in the literature. Like, for example, if someone did a pedigree, you know, another family has this exact variant that everyone who hasn't had a VHL in their room doesn't have that, that's probably gonna be a pathogenic one. But, this is a variant that's present in like, in one in 1,000 of the general population and that is considered healthy, then it's gonna be probably a benign variant. So, you know, the genetic testing of the tumor, they would likely be compound heterosigus or homozygus or pathogenic variants. And if someone had, were homozygous and they had basically, they'd have no tumor suppressor in their whole body and it has to be one big cancer, so that's why people aren't born with that. What's compound, what's compound heterosigus? Well compound heterosigus, sorry, compound heterosigus means like you have like one variant that's bad and another variant that's bad, but they're different. It's like, it's on the same gene. Different, like the locations on the same gene? Yeah, like different locations or one could be dilation, the other one could be like a, a sense mutation, you know, those are the same gene, Okay, so you can move on to the alternate reality slide. For a hundred steps in the race, we'll look at it. So, what's that mean? It's called fixed, what's it called? Toid. Toid. Toid, toid. Toid. Toid. Toid. Toid. Toid. Toid. Toid. Toid. Toid. Toid. Toid. Toid. Toid. Toid. Toid. Toid. Toid. Toid. Toid. Toid. Toid. Toid. Toid. Toid. Toid. Toid. Toid. Toid. Toid. Toid. Toid. A lot less, or was probably more. So the next vertex, ok. I know what happens. You tell a joke. And they can have like a brain, I think brain vascular abnormalities too, so it's a scan of time for you to change. Is there like fat problems with that or? I don't think so, but I'd have to google it. It's general problems. So you think of almost like, you know, like, transplants, weird vessels, and other miscellaneous. It's a dying brain. Yeah, I know, I missed it last year. I won't just see her. I'm lucky no one's there. It's the 13th of June. I put 11. Yeah, that's cool. Yeah, I love it now. They moved much more, so I won't miss it again. There's an extra survey. Ask, they're just like right now. Is it asking for a survey of toasties or something? I've never made red-hot cameras. You know, it's a great deal of clifferative tumors. Or too often, maybe. It's like the elevated risk of mutation associated with a cause of reaction. It's 70 years old.  Especially with a cause of reaction. Yeah, I did almost disease. It's a cause of reaction. It doesn't matter. You get cause of reactions and not cause of disease. It's like R.P. I thought something that was interesting was why they're releasing it is like they can have like skin things. I heard someone mention orbit, or whatever, vascular malformations. That was really good. Yeah. That's what I heard. Oh, gosh, that's the term. That's the term. The thing with a macro vessel is that there's like a blood vessel going through the central macula where there normally is one. It might not necessarily be bigger than normal, or that it's just out of place. Do I see your approach? No. I don't see it. I never thought to ask. I have seen people's visual acuity be decreased from there to normal, but without any fluid or anything like that. Okay, so retinal blastomas is what I wanted you guys to think of. Maybe that was a leading question. I came up with carotidol hemangiomas, retinal cavernous hemangiomas and basal proliferative tumors. Do you guys come up with anything else? Yes. And the basal proliferative tumors, apparently the most common causes are retinas, pigmentosa, and coaxies. So... All right.  I have a lot more stuff, but I don't think we should necessarily go through it all. Well, I don't have any more science. We can keep going. Or we can just call it quits. You can work on your own and let me know if you have any questions. Let's call it quits. Thank you. So if you guys could, you know, I guess let me know, tell me more about this format thing, with the case space and how that's going. What are your thoughts on that? I'm looking for your feedback now on the case-based format and talking and discussing. I do like the little pre-lectures. That was nice. You read our minds. I think, Ashley, we can talk to Strav and then Strav now. Any other feedback on how this thing is today? Wow. Thank you. Thank you guys for participating and for doing your pre-work. Yeah. Comment, Janssen syndrome. Okay. So speaking of off-the-questions, does Janssen syndrome affect the eyes? Wow. No. He has told me that it did and the off-the-questions is like it's not the correct answer, but it is the answer. So I think it does not affect the eyes. I've searched the literature as thoroughly as possible. Don't think about it. But if I'm wrong, let me know. Is that a different Wagner syndrome? Yeah. It does affect the eyes with high myopia of right-wing attachment and it's a mutation in versicam. That's like a skeletal dysplasia. Yeah. It's a metacondro dysplasia, but I don't think it affects the eyes. I just want to clarify that. Yeah. This thing, I don't know. I just want to clarify that.