Welcome back to the lectures on the quantum mechanics and the elementary or model systems in quantum mechanics. The last lecture was on the power series method to the harmonic oscillator problem and I stopped at the point where we arrived at two recurrence relations well essentially one, but recurrence relations for two independent coefficientsfor the solution of the harmonic oscillator differential equation. So, let me recap that in the first two minutes and then continue in this lecture with the solution and the solution to the wave function of for the harmonic oscillator ok. So, differential equation that we wanted to solve was d square h by d y square minus 2 y d h by d h by d y plus lambda by alpha minus 1 is equal to 0. This was the differential equation and we proposed to the solution that h of y is equal to sum over n 0 to infinity a n y to the n and if you remember the overall solution that we were looking at for the harmonic oscillator we hadpsi as exponential minus y squared by 2 h of y. This was the equation that this was the solution that we were looking at ok it was basically beta y square, but it does not matter it is minus y square ok. The wave function must go to 0 at the boundaries and here the boundary is that y isplus r minus infinite infinity. The nature of this function therefore, should be such that the whole thing goes to 0 for very large values of y. It looks like it does, but if h of y for example, grows faster than exponential of minus y square by 2 growing slower then psi of y may actually tend to increase. Therefore, it is important for us to see what is h of y. We have obtained a relation for a n we have obtained a relation for a 2 n in terms of a naught that was the last line of the last lecture and a 2 n plus 1 in terms of a 1 ok. Therefore, we know that the series that we have h of y n equal to 0 to a to the n a n y to the n. We know what the a n's are and we need to look at a n plus 2 by a n because you see it is either a naught or a 1. So, the series alternates with the coefficients. So, if we take the ratio of this and if this has a certain pattern of convergence slower than that of this then we have to relook at the h of y and the solution is that we will truncate h of y to finite number of terms and the justification for the truncation is that h of y otherwise will not allow the psi of y to converge to 0 ok. So, let us look at a n plus 2 by a n if you recall the coefficients will be minus lambda by alpha minus 1 minus 2 n by n plus 1 times n plus 2 which goes as minus 2 by n and goes to 0 as n goes to infinity. So, coefficients are will behaved, but if you look at e to the y square for example ok which we can write as 1 plus y square plus y to the 4 by 2 factorial plus etcetera y to the 2 n by n factorial and so on. And if you look at the coefficients a y of n plus 2 y of n if you take the ratio of the two terms coefficients coefficients of the power of y to the n plus 2 and coefficients to the multiplying the term y to the n if you take that ratio that also is 1 by n by 2 plus 1 and which goes as 2 by n for n going to infinity ok. So, there is a problem here that even though h of y is such that the terms as we increase more and more coefficients as we add more and more coefficients and we write this as a larger and larger series the convergence property of this is very similar or it is the same as the convergence of e to the y square. And you have seen that if that is a case this whole thing will actually go as e to the y square by 2 for very large values of y and that is a problem with this not satisfying the boundary conditions. Therefore, it is important for us not to have an infinite series h of y needs to be truncated at some finite value some finite number n ok. And to truncate that at some finite number n what it means is that the coefficient a n is not 0, but the coefficient a n plus 2 is equal to 0 is equal to a n plus 4 is equal to etcetera. Therefore, it is important for us to choose the power series in such a way that all terms beyond a certain value of n have 0 coefficients. How do we do that? We do that by looking at the structure of the coefficients please remember a 2 n was written earlier in the last lecture as minus 1 to the power n. If I remember it is lambda by alpha minus 1 minus let me see it is 2 a 2 n was yeah 2 into 2 n minus 2 I think we had this and lambda by alpha minus 1 minus 2 times 2 n minus 4 and so on till lambda by alpha minus 1 all of this divided by 2 n factorial times a 0. Therefore, what we want to do is to have a certain value of n such that perhaps a 2 n is not 0, but the a 2 n plus 2 will be 0 that will be 0 if one of this leading terms if this leading term goes to 0 or if we choose lambda by alpha minus 1 to be equal to whatever that follows ok. Here we are talking about a 2 n for a 2 n plus 2 this will be lambda by alpha minus 1 minus 2 times 2 n that will be the leading term. Therefore, if we set lambda by alpha minus 1 is equal to 2 times 2 n then you can see that a 2 n plus 2 will be 0 and likewise all the other terms which involve a 2 n plus 2 and so every term in the power series with n greater than this coefficient will be 0. So, this is a way of truncating the power series to finite values. What value of n? n equal to 0, n equal to 1, n equal to 2 each 1 will give you 1 hermite 1 h of y ok. If we truncate h of y at n equal to 0 which means that is we say a 2 is 0 a naught is 0 then you have only 1 coefficient constant a 0 ok. I have not yet said what is a 2 n plus 1 we will do that in a minute ok in terms of a 1. Let us assume that we are considering only the even terms in here ok. We are considering only the even terms then the even terms are such that if we let the a 2 to be 0 then only one term a naught then h of y is simply a constant and that will happen you see that a 2 will be 0 when n is 0. Therefore, lambda minus by alpha minus 1 is 0 that will give you what is known as a h naught of y which is a constant a naught. If we truncate this at n equal to 1 then lambda by alpha minus 1 is equal to 2 into 2 4 which means that we will have a naught a 2 but not a 4. Therefore, what you will have is h naught y with the leading term a naught you will have 1 and then you will have plus y square times some coefficient. So, it should not write this as a naught sorry it is a naught plus a 2 y square and that is it a 4 is 0 and all the others are 0. Therefore, this is h 2 h 2 of y ok. So, if we consider only the even terms and for the moment we do not worry about the r terms we consider only even terms then we have h naught of y h 1 of y each one is a finite has a finite number of powers of y and each one is obviously a polynomial in y the first one is of course, a constant the second one is a quadratic in y the next one h 4 of y will be a quartic one in y and so on. What about the odd coefficients? If we keep a 1 as the only term and what a 3 a 5 etcetera to be 0 then we have the polynomial or we have the h function 1 of y which will be a 1 of y. If we choose the terms here I have written a 2 n. So, let me write a 2 n plus 1 here and tell you what that condition is. So, if we write a 2 n plus 1 that is minus 1 to the power n you have lambda by alpha minus 1 minus 2 into 2 n minus 1 ok times lambda by alpha minus 1 minus 2 into 2 n minus 3 times. So, on till the last term lambda by alpha minus 1 minus 2 into 1 all of this by 2 n plus 1 factorial times a 1. Therefore, if we leave a 1 not 0, but a 3 we want it to be 0 a 3 has to be chosen by having lambda by alpha minus 1 to be equal to 2 that is that is the only term it will not the others will not be there. Once a 3 is 0 all the other terms are a 5 a 7 etcetera or all 0. So, you have the same thing that lambda by alpha minus 1 minus 2 n 2 into 2 n ok ensures that a 2 n is non 0, but a 2 n plus 2 is 0. So, therefore, the condition is the same whether you are with 2 n or with 2 n plus 1 the corresponding n value should determine this factor ok. Therefore, what we have is when we do that truncation this term the the way function that we wrote down as e to the minus y square by 2 h of y ok. Now, becomes psi 0 with h 0 of y as 1 possible solution psi 1 of y with e to the minus y square by 2 h 1 of y and so on. Therefore, what we are doing is that to ensure that the way functions are do not explode, but they become 0 at the boundaries we are providing solutions which are solutions obtained by truncating the power series to finite number of terms. The polynomials that you get by doing that are known as Hermite polynomials Hermite polynomials. Just to complete this part of it we should then give the successive terms namely a 2 a 4 a 6 etcetera in terms of a 0 which we already know here in here. Therefore, if we assume a naught to be a constant some suitably chosen constant we can immediately calculate a 2 by using that condition namely it is lambda by alpha minus 1 ok times that ok. After all lambda by alpha minus 1 is truncated at some value. So, you put that value here and you put get the numerical factors this will be substituted by whatever n that we chose and then obviously, this will fold beyond a certain point to 0 ok. So, we know the explicit expressions for a 2 a 4 a 6 etcetera in terms of a naught the moment we know where to truncate the series because by doing that we have chosen the value for this in terms of an integer ok two times an integer or whatever that may be two times twice n or whatever ok. Any integer where we choose to truncate it that integer get substituted here. Therefore, we have explicitly numerical expression algebraic, but with the numbers for each of the coefficients and without doing explicitly those things I will write down the solutions that we get as the final result which you can verify and it is also one of the background quiz that you can do to convince yourself that that is the answer ok. The answer when we do the truncation is the following ok H naught of y is 1 we were assumed a naught to be 1 ok H 1 of y is 2 y we have chosen a 1 to be 1 again I guess ok I will leave it leave a question mark there H 2 of y is minus 1 you can see that a 2 minus 1 lambda by alpha minus 1 is chosen already and therefore, what you have is 1 minus 2 y square ok which istimes 2 factorial times 2 factorial ok which gives you 4 y square minus 2 H 3 of y is given by minus 1 2 times 3 factorial into y minus 2 third y cube which gives you there is of course nothing else which gives you 8 y cube minus 12 y ok. So, you can obtain a whole series of them and what is interesting is that H naught H 2 let me write H 4 and also H 5 I will stop beyond H 5 H 4 is 12 minus 48 y square plus 16 y to the power 4 and H 5 of y is 120 y minus 160 y cube plus 32 y to the power 5 ok and so on. So, what we have therefore, iseven an odd in y H naught of y even in y plus or minus y is the same H 2 of y 4 y square minus 2. So, H 2 of minus y is the same as H 2 of y it is an even function H 4 of y 12 minus 48 y square plus 16 y to the power 4 H 4 of minus y is also the same thing therefore, all the even ends naught 2 4 6 etcetera are all even functions in y all the odd ones H 1 of y is 2 y therefore, H 1 of minus y is minus 2 y therefore, H of y is minus of H of minus y which is an odd function. So, this is an odd function this is an odd function 8 y cube minus 12 y 5 120 y 160 y cube 32 y 5 it is an odd function therefore, all the odd ends contain polynomials which are odd functions of y what about exponential of minus y square that is y square by 2 that is an even function. Therefore, you see that the Hermite polynomials give rise to wave function solutions for the harmonic oscillators with odd and even parity alternating between the ends corresponding to odd n or corresponding to the even n. So, what is the final result? The final result for the harmonic oscillator wave function is that psi naught of y is e to the minus y square by 2 psi 1 of y is e to the minus y square by 2 times 2 y psi 2 of y is e to the minus y square by 2 of whatever we had written already 4 y square by 2 now you can see so on ok. So, a table of these harmonic oscillator polynomials are given in the lecture set and I would request those of you who are not certain about the solution to substitute the solutions in the differential equation and see that the answer that you get is 0 by choosing the lambda by alpha minus 1 corresponding to that n value you will know that ok. So, this is the approach here has been if you recall the last lecture looking at the Schrodinger equation we looked at what is called an asymptotic solution or the solution for very large values of the argument the variable x, x was changed to a dimensionless variable y because you remember x was the position variable that is the amplitude of the oscillation. So, we removed the physical parameters the dimensions out of that by redefining the x in terms of y and then looking at what are called very large solution very large values of y solutions which gave us the exponential minus y square by 2 as the asymptotically applicable solution and then with that we wanted an arbitrary solution that is a solution valid for all arbitrary y values y small y large etcetera. Therefore, we multiplied the asymptotic solution with a functional form called h of y which was assumed to be an infinite series and then we use the convergence argument that this function cannot forever be an infinite series or ever increase for all values of y we had to truncate that in order to have a meaningful solution and the truncation led to us a whole series of solutions depending on when we truncate what n value what integer value we truncate and therefore, you see that the harmonic oscillator in principle provides an infinite number of solutions because there is nothing here which tells me that I can I need to stop at some point if I stop at that point that is the value, but there are depending on where I truncate the n I have that many different size solutions. So, the solution of the Schrodinger equation for the harmonic oscillator problem using the mathematical properties of the differential equations and convergence immediately gives us an infinite number of solutions, but you know that a harmonic oscillator approximation is not really a valid approximation for very large extensions of or very large values of amplitudes. So, these are theoretical, but in practice when we consider very large values of extensions we will have to worry about unharmonicity and so on otherwise these are exact solutions obtained for the half k x square potential energy problem or the harmonic oscillator energy problem in one dimension ok. Now, there are a few mathematical properties that I would like to write down here, but let us pass for a few seconds and then we will come back to writing some of these properties ok. So, I shall give the value of n in a minute, but we will also now see that each n each psi n corresponds to a given energy E. Remember when we set lambda by alpha minus 1 is equal to 2 n for any given value of n 2 into 2 n we put in, but that was for the coefficient a to the 2 n and therefore, for any Hermite polynomial of order n it was truncated at that ok. So, if we do that lambda please remember recall from the previous lecture lambda is 2 m e mass of the harmonic oscillator by h bar squared and alpha we have just now written that alpha is k alpha is equal to square root of k m by h bar square or square root k m by h bar. So, if we substitute this lambda by alpha is equal to 2 n plus 1 then what you have is 2 m e by h bar square times alpha is 1 by alpha is h bar by square root of k by m and that should be equal to 2 n plus 1 ok. So, let us cancel out these things and the m becomes square root m. So, the answer goes over to e is equal to h bar into square root of k by m times n plus a half taking the 2 to cancel out and this is h times 1 by 2 pi into square root of k by m times n plus a half and you know that that is the harmonic oscillator frequency nu and therefore, the energy of the harmonic oscillator is h nu times n plus a half where n is the index associated with the wave function psi n ok. So, we have an n plus a half that is very interesting because that is going to give us the idea of what is known as the 0 point energy later on, but this has to be kept in mind. Therefore, psi n is associated with a given energy E n also indexed by the same n as you have it here. Now, what about the normalization constant? Mathematically one can work this out, but I am only going to write the final answer it is easy to check these things and verify text books give you these things over and over again. So, what you have is n is pi by alpha 1 by 4 2 to the n by 2 n factorial 2. 1 half what exactly is this? This is the normalization constant such that the psi of n of x psi of n of x d x now is equal to 1 minus infinity 2. So, we have to write this psi n of x from whatever is given here this n square and we have write polynomial we have to write n by this expression and now we can write therefore, the wave functions psi naught of x is going to be alpha by pi because it is how do I define this yeah. So, I should define this as 1 by n here ok and if I do that then what do I get psi n 1 by n squared psi n of x psi n of x d x is 1 and then we can see that that is given by the corresponding expression. So, and this n is what I have here pi over alpha and so on. So, psi naught will be alpha by pi because it is 1 over and it is to the 1 by 4 e to the minus alpha x square by 2 ok psi 1 of x is given by 1 by root 2 alpha by pi to the 1 by 4 e to the minus alpha x square by 2 h 1 of root alpha x ok psi 2 psi 2 of x normalized is given by 1 by 2 root 2 alpha by pi to the 1 by 4 e to the minus alpha x square by 2 h 2 of root alpha x and so on. What is what is important is that 1 psi is an exponential of that is a Gaussian function to indexed by the same n by the harmonic oscillator and 3 that the function the argument of the harmonic oscillator is dimensionless and 4 if you remember the integral of psi star psi d x is equal to 1 tells you that the dimension of psi has to be 1 by square root of length because d x is length and you can see that it is alpha to the 1 by 4 alpha is l square dimension 1 by l square dimension alpha is 1 by l square dimension therefore, alpha to the 1 by 4 is 1 by root l. So, these pointers should be kept in mind that alpha is in the numerator and alpha x square come as a as a product or root alpha x come as a quantity so that we do not write functions which have difficulty I mean you cannot interpret those functions. So, those are things of course, you have to worry about these constants because you require the wave functions to be such that they satisfy the probability distribution, but other than that you can see that everywhere it is alpha to the 1 4th alpha to the 1 4th alpha to the 1 4th and so on. So, you can see that it is 1 by square root of the length which is a one dimensional problem because 1 by square root length 1 by square root length times length dimensionally it is a number it is no no dimensions ok. So, these are important these are things which one has to keep in mind when one is doing this for the first time. After some time of course, physicists have a very nice way of doing these things by removing all these dimensions from the process right in the beginning and writing what are known as reduced variables or dimensionless variables or redefined constants and so on, but you know we are not physicists and what we want to do is to understand the problem of molecular parameters to be interpreted properly. So, it is important to keep track of all these things. Now, in the given a given that I have another 10 to 12 minutes left let me summarize some of the properties of the Hermione polynomials I am just going to give you this for you to verify, I do not intend deriving these properties here ok. In the same way I did not tell you how we get the normalization concern there are details of calculations which we can always omit and then there are other things which we have to remember and keep in mind ok. So, let me just write down an extremely important relation that the Hermite polynomials satisfy it is called the Hermite polynomial recurrence relations recursion sorry it is not recurrence relation it is a recursion formula that is they satisfy this formula namely any Hermite polynomial n plus 1 order of y is connected to the Hermite polynomial of order n and the Hermite polynomial of order n minus 1 y is equal to 0 ok. This is very important it basically it is also a very it is it is worth remembering this relation even though I do not remember it now I just copied it from the paper, but it is worth remembering at least in the first few years and manipulate with them to know that all these polynomials the Hermite polynomials and the others that we would study soon like the log air polynomials or the spherical harmonics or the Legendre polynomial all of them have this beautiful what are called recursion relations and also they have very fundamental properties they are all called orthogonal polynomials in that the Hermite polynomials corresponding to different orders or orthogonal to each other with a weight function which we call as the exponential function and so on. So, this is worth remembering and all that you have to remember is this relation and the fact that H naught of y is equal to 1 and H 1 of y is equal to 2 y ok. If you remember these two and this in principle you can get H 2 n plus 1 ok n is 1 from n minus 1 which is 0 H 0 and n which is H 1. Therefore, if you want to get H 2 of y you are using n is equal to 1 1 here ok then minus 2 y H 1 of y plus since it is n is 1 it is 2 H 0 of y is equal to 0 and this we already know is 1 ok. Therefore, it is 2 and we know that H 1 of y is 2 y 2 y ok and therefore, this whole thing being 0 implies that H 2 of y is 4 y squared minus 2 which was written down a few minutes ago as rising from the solution of the differential equation yes and in the same way you can immediately write H 3 y also like n equal to 2. So, if you do that H 3 y is 2 y times H 2 y ok minus 2 into 2 H 1 y because n is 2 and you can see that immediately that it is 2 y into 4 y squared minus 2 minus 4 into 2 y. So, that gives you 8 y cube minus 12 y ok. So, this is also something that we wrote down ok. So, you can construct all these polynomials just from the first and the second one using this recursion formula is one of the things which is worth remembering ok. Another way of remembering the generation of Hermite polynomials is through what is known as a generating function formula ok which let me write down ok. The H n of y can be generated by this particular form minus 1 this is n minus 1 to the power n e to the y square times d n by d y n on e to the minus y square ok this is another generating function. So, if you want H 0 of y obviously, it is 0 there is no derivative and minus 1 raise to 0 is 1 e to the y square the derivative is since it is 0 it is 1 e to the y square times e to the minus y square is 1. H 1 of y is easy to write down again H 1 of y is minus 1 e to the y square d by d y of e to the minus y square which you know is minus 2 y times e to the minus y square and this minus and this minus go away and e to the minus y square and y square cancel you get 2 y ok. So, you can generate the whole Hermite polynomials also through successive differentiation of an exponential of a Gaussian function and then multiplying by the inverse of the Gaussian function and a sin factor ok. So, this is another interesting formula a lot of these things have been studied for several at least 250 years or more because the Hermites equation is a fairly old equation studied by Hermite and orthogonal polynomials are very well known in mathematics they are there are very rich discussions on the second order differential equations and so on. So, I would not elaborate this beyond this point our objective was to convince ourselves that we know at least with some degree of confidence we can write down the Hermite polynomials by solving the actual differential equation of the Hermite equation or the originally the Schrodinger equation for the harmonic oscillator with the help of the harmonic potential. And we have seen that the wave functions are ah given by these functional forms yes one last expression that I must write down which is also very very important is that these functions are orthogonal Hermite polynomials are orthogonal ok that is integral minus infinity to plus infinity psi n of x star psi m of x the star is actually a redundant quantity here because these are all real functions ok. But in quantum mechanics we always have to remember this because very often if we forget the star it comes out at the most innocuous place as something that we have forgotten and it gives you all kinds of nasty answers. So, keep the star always as star even if you do not use it psi n star of x psi m of x dx is delta n m the normalized for normalized ah harmonic oscillator wave functions. So, that is ah orthonormal and the corresponding expression that you will have is that the n n n m the normalization constants associated with the Hermite polynomials and minus infinity to plus infinity psi n star is e to the minus alpha x square by 2 and of course, there is this also gives you that. So, it is e to the minus alpha x square h n of root alpha x h m of root alpha x dx and this integral is delta n m. So, this is the orthogonality orthogonality of the Hermite polynomials justifying the term that these are orthogonal polynomials when the n and m are the same that is going to be 1 given these normalization constants and this is known as the weight factor in numerical calculations numerical integrals ok. The weight factor weights the Hermite polynomials for different values of x according to the e to the minus alpha x square ok. Alpha is a constant associated with the problem the moment you choose a harmonic oscillator alpha is fixed the x goes from minus infinity to plus infinity the exponential alpha minus alpha x square contributes different values to different Hermite value the the function at different points of x and therefore, if you have to do this integral numerically this ah function comes in as a weight function and a numerical method which ah calculates integrals using this kind of Hermite functions is also often referred to as a ah Hermite quadrature you will not do that here, but when you do numerical work involving these integrals ah it is important to remember that that is this quantity ok. The exponential minus alpha x square acts as providing the right amount of all it is all it does is that for very large values of x it contributes so little that the Hermite polynomials you can pretty much neglect for large values of x exponential of minus alpha x square is almost 0 almost close to 0 therefore, the product is not contributed so much this kills them. So, if you have to do this integral numerically for finite values you are very happy that you have something like this ah the only thing that you want to make sure is that the alpha is reasonably big and therefore, you do not have to calculate the numerical values of these integrals for very large ranges of x which is important when you do computer calculations ok. These are some things which you have to keep in mind and in the next lecture what we would do is to look at the functional form more carefully using graphics and also ah the consequences of the Hermite polynomial and the harmonic oscillator wave function being ah everywhere that is except for some finite values of x where the polynomials go to 0 ah the Hermite polynomial there are the roots of the polynomial we call it you know after all it is a it is a power series in x finite power series and therefore, it has for each value of n it has n roots and apart from these n roots the polynomial is never 0 and therefore, the wave function is never 0 in the real physical space all the way from minus infinity to plus infinity except for a finite number of points and that leads to a very interesting consequence known as the tunneling or things that we were not very familiar with things which do not exist in classical mechanics and the half ah factor in the energy is another interesting phenomenon which leads to what is known as the 0 point energy therefore, these are consequences that as ah chemists and as spectroscopies we will have to remember and these in the next lecture we will continue until then thank you very much.


We're going to drive 35 dead-hand miles, 15 miles, though that's a 50 miles all together for 175. It's time for the pull-up to the airport and pick up the prize. Let's go. And just like that, we are here at the airport, baby. I don't want to do this, but we're going to see what happens this time. Last time I came here was absolutely terrible. This is real warehouse. Okay. This is perfect for you. Okay. I'm good to go. Thank you very much, so you guys have a good one. And just like that, I got about the pull-up so we can run it up. This is how to get it right. This is how you get fit. It's called a low-box. Good. It's perfect. It's very much how you have a perfect one. I told you it's small and low-box. You know the way I see it, the smaller the better. It's like the easier.


All right, I wanted to thank all of you for waiting to eat lunch and join us today. I am Jonathan King, I lead cloud strategy for Ericsson, and I am joined by esteemed panel today. We'll talk for about 30 to 40 minutes and then adjourn. Maybe I can just have each of the panelists introduce themselves, starting with their Hesh there at the end. Hi there, Radesh Balakrishnan, general manager for OpenStack at Red Hat. I'm Doss Kamhout, senior principal engineer at Intel, working on software-defined infrastructure. I'm Roz Roseboro, senior analyst at Heavy Reading, covering the Telco data center. And Susan James heading up the product line for NFE infrastructure at Ericsson. So this is an open panel to talk about current market trends, challenges and opportunities.  And I'm curious where Hesh, start with you, get your perspective on the announcement and how it fits in with trends that you're seeing in the marketplace today. So the core thinking behind the partnership centers around the fact that in the Telco carrier space, there's a burning platform moment. There is a need to make sure that NFE or network function virtualization as a focus area needs to be made real and into production with truly upstream contribution. So the partnership centers around three areas within that context. One is making sure that there is a 100% open source based NFEI solution that's built on Red Hat OpenStack platform, made available by Ericsson. So this is an extension of the Ericsson strategy in this place to become a multi-wim solution. I'm sure Susan can add more context on that one. The second pillar of that is around SDN solution, given the fact that both Ericsson and Red Hat are partnering around Open Daylight as a way to drive networking innovation. Ericsson are bringing to the market a solution that's certified around Red Hat OpenStack platform. And last but not the least, the HDS 8000, which is a hyperscale solution which is available in the market, will certify Red Hat Enterprise Linux as well as Red Hat OpenStack platform. So all in all, an end to end comprehensive alignment of portfolio across Red Hat and Ericsson to make sure that we are fueling the communication revolution that's going on. And maybe Susan, building on that, you can similarly add. Yes, I think for us it's very much about providing operators choice. You know, we don't want to prescribe to them how they should take their journey, and we want to be able to support them in that journey. And as Ridesh said, you know, that's why we have said that we want to take a multi-wim strategy. I think one of the things we see happening in the operators is that, you know, there will be pockets of different parts of the operator taking the journey to cloud and to NFV. And they will make different choices. And we want to be able to then provide a partner that can harmonize those choices in the longer term. And of course, we also see that the opportunity of partnering with Red Hat beyond just the NFVI space. As Ridesh said, you know, we're doing certification on our hardware platforms. And I think also it's about being able to support onboarding of other applications, not just Ericsson applications. So particularly seeing, you know, Realm has such a great market penetration when it comes to applications, not just in the NFV space, but in the anti-space, that it becomes critical for us to be a good infrastructure provider. We need to have support for Realm going forward. So I think, you know, it's about being open and giving choices. And does Intel sits in a unique position where you partner with a lot of people and you're looking at the roadmap of the industry out there when it's coming. So maybe your perspective on this partnership and what you're seeing in the industry. Yeah, well, I mean, fundamentally NFV and everything is happening in the calm space is where we've been supporting for quite some time ever since the start of even Etsy. Red Hat, we've been partners since, you know, Linux, right? So it's been a little while. And we've also been, you know, massive supporters together of OpenStack and into the Kubernetes space. So naturally from a software perspective, focusing on a market that's growing heavily towards Intel architecture is pretty interesting for us. And obviously with Ericsson, you guys are one of the first adopters, or the first adopter of our rack-scale design.  We're always interested in things that, you know, make the industry move. Excellent. Ross, how do you see this announcement? I mean, do you think of this as big news? Well, I think it's big primarily because it's bringing two industry leaders together. Obviously Red Hat has a history of being, you know, being a leader in open source and cloud and IT technologies. And Ericsson clearly has the history of supporting the telcos. So I think, you know, combining those two assets together, I think makes for a really powerful combination. Awesome.  Do you see this as a change of Ericsson's strategy and evolution? I mean, I see it very much as an evolution of our strategy. I think, you know, when we started this journey some four, five years ago, we saw the market playing out in a different way than it actually has. So, of course, as we take, you know, steps further, we hold our strategy. And I think, as I said before, operators need to have solutions from rail-based workloads. And we also see, you know, these different islands coming forward. So we do see that most operators will have more than one of them in infrastructure. And we want to shift our focus then on how to then manage this multi-vim environment and how to make, you know, open stack easy to use and consume in a multi-vim context. And that comes from both a management and orchestration perspective and how you onboard VNFs and different applications. But also from a hardware infrastructure, and I think that that fits really very nicely with our HDS 8000 product, where we have the capability of creating virtual pods where we can then allocate dynamically the amount of resources required for running those different VMC fill-on. Maybe, Red Hatch, if you look at the landscape beyond NFE, we look at SDN, we look at, you know, beyond their business models that are coming, you know, how does Red Hat see the operator space beyond NFE? And what are things that you're thinking about in that space? So, if you pull back and look at what's happening in the carrier landscape, clearly on the IT side there's more maturing of adoption of virtualization that's been ongoing for a while. And then now with NFE, introducing the same sense of technologies with different workload focus, I think we are marching towards a unified fabric that's going to be there for both the IT side and the network side and the carrier from a carrier perspective, right? While the journeys might have started at different points in time. Given that our focus has been making sure that we're not creating a forked solution when it comes to the carrier side, but how make open stack carrier grade rather than have a carrier grade open stack, for example, right? So, I think that fits in with the philosophy or the approach that Susan outlined as well, which is the market dynamics have changed. There was at one point in time a felt need to have certain capabilities which are required for telco specifically, but now the community has come around to realize and innovate to make sure that those capabilities are in open stack itself, right? So, that's kind of the long way of saying that we believe 100% upstream first innovation is going to be the model that's going to prove itself out. And we're pretty excited about being in the position to drive that in partnership with Edison. That's great.  You've done recent surveys, I know, on adoption rates and timing.  We've been talking about it a few for a number of years now. What would you see as the stake today? Well, funny that you mentioned the research. I just completed the survey for Red Hat. And we found for the first time we asked this question quite a bit as you can imagine. And this was the first time where over half of the operators that we surveyed said they were currently executing on their NFV strategy, which I think is quite noteworthy. And similarly, we found that nobody said they didn't need an NFV strategy. And that has happened before. So I think that the question of should we do NFV, that's pretty well decided. I think where we're moving to is now how do we make this all happen? And so I think that's, you know, from an industry standpoint, the more people we have kind of getting their hands dirty, they're starting to expose some of the issues. And of course, the sooner we can expose them, the sooner we can get them fixed. So, like I said, I was quite encouraged to see that. And of course, you know, people that are trying to take advantage of this trend. That's also very exciting. That's great. And does I know you said earlier, you know, have been partnering with Red Hat and Erickson for a long time and will they see a big opportunity with carriers around NFV? Maybe just some more perspective from Intel on what you're seeing in the market in that space, in Intel's perspective. Yeah, so fortunately, you know, it all is moving forward. So that's fundamentally what we want to see. And also, as Redesh noted, we're really interested in having one code base that can work across multiple types of workloads.  But they can all actually run on the same type of fabric. If I go back a couple years, I think I sat in room with Redesh and we went over rolling upgrades, all these key elements that enterprise needed. And actually, if you look at comms in telcos, it's the same things.  And by the way, I was building OpenStack Clouds in Diablo Day. So, you know, a lot of all that work, I think, is really starting to pay off. And so now that the adoption is happening, I think enough of a groundwork has been there that it's not, you know, you need some special OpenStack. It's, you know, you have something that's actually good enough. It's working and it's just going to get better as we get more laser focused on, you know, NFV workloads plus additional workloads that have, you know, very similar characteristics. Thanks for dating yourself. Yeah, absolutely. I was going to add one thing. You know, you're mentioning, Redesh was talking about carrier greatness and part of that same survey, we asked people, you know, what was important as they're looking at an NFVI platform and for the first time ever, something besides security was number one and it was reliability. But what's interesting was that we also asked them how confident are you in the existing NFVI platforms to provide all those characteristics. And I'm sorry to say they're not particularly confident that the existing platforms can do it. And so that's another reason I think it's important. I think it's interesting that Erickson and Ryan are coming together because the telcos want to make sure that the people developing platforms to them really understand what it means to run a network. And I think Erickson, you know, clearly has that kind of heritage so I think that's going to be important. I think that's going to make some, a lot of them feel much better because, you know, you've walked in their shoes and you know what their issues are. Yeah, absolutely. And I think that sets us up for, you know, a good transition, you know, looking at, you know, we have a sense on the state of the industry and why this partnership has come together. And I told the panelists beforehand I was going to make a terrible pun but I couldn't contain myself. We have to talk about containers. And that seems to be like that is the next frontier. And we had, you know, Mirantis in the meeting before next door making some news with directions it's going and taking. And I'm curious to get just an open discussion across the panel. I don't know, maybe Rahesh, if you want to go first because we're looking to do more in the community space around containers. You know, we both are highly interested and see it relevant but I think there's interesting things for the panel to share and just an open perspective on where do we think the intersection between NFE and containers is and where is it headed? Containers? Never heard of them. No, I'm just kidding. So from Red Hat perspective, we are all in on containers. So if you look at Docker as the Docker format, next to Docker the company, Red Hat is the largest contributor. If you look at Kubernetes next to Google, Red Hat is the largest contributor. And we also have a design from ground up fully functional container platform in the form of OpenShift Container Platform that customers such as Prettybond earlier today, they were up on stage talking about their big data implementation. Prettybond is one of the largest deployers of our containers on top of OpenStack as well. So we believe that being in the cockpit, so to say, of driving innovation across OpenStack, KVM, Linux, Kubernetes and Docker gives us an amazing opportunity to present choice in terms of you can run physical, you can run virtual, you can run containers. Our job is to make sure that the experience is seamless. So that's the opportunity that's uniquely in front of Red Hat, and that's our product strategies evolving as well. Now when it comes to probably the carrier space, we see a little bit of maybe a lag in terms of readiness to embrace containers per se, more to do with the applications or the NFEs themselves not being ready to get there. That's a fundamental re-architecting decision, you know, lots of manners of work ahead and our opportunity ahead, if you will. But at the same time from an infrastructure and platform perspective, we are working to make sure that when that ISV momentum does happen, the intersection of OpenStack and containers is ready to operationalize and have a life cycle, supported life cycle around a product. That's great, Susan. I've got to give you the mic. Yes, I've got something to say. I think two weeks ago we were in the SDN OpenFlow World Congress in The Hague, and I think we had a really good demo there that we showed where we had a rabbit-in queue server running in OpenStack and then spinning up the client in containers. And I think, you know, there will be more and more of these sorts of examples where you'll actually want to use a combination of both OpenStack and containers. And the great thing about that is, of course, when you're using a container, the startup time of the container is much, much shorter than it is for OpenStack. So, you know, being able to provide networking via SDN and automating that network becomes really crucially, I would say, going forward. And how we then use containers to be able to complement, I would say, existing applications or existing VNS certainly become something that we see going forward. As Ridesh said, you know, if you look at the bulk of the applications in the NFV space, then very few of them have any containers included at all. But certainly we see that as something that's coming forward. And then when we're building in the infrastructure around both OpenStack and working with SDN, we're making sure that we can manage workloads, again, from a native perspective, a virtualized, and also a container-based perspective. Because applications will tend to dictate what they want to use rather than operators making a choice or vendors making a choice on this is how we should go forward. So, for us to be able to support a myriad of infrastructure becomes really key going forward. Very good. And, Daz, we've talked about containers beyond in other meetings and other settings. It's been something that Intel's been actively involved in, helping, at least stand up, CNCF, contribute early on. So, I know you have a lot to say on this topic. I'm curious to get your perspective, maybe not just on the BNF side, but the industry adoption rate of containers. Sure, yeah, totally. So, I mean, containers have hopefully all known that I've been around for a really long time, heavily in Linux in 2006 and Docker made it easy. So, basically, we've been sharing at least a vision that we'd like to see all data centers, the core of them being containers, which are basically performance isolated processes. And in order to, and the benefit of that is high levels of resource utilization, performance optimizations that you can't do natively in a traditional hypervisor-based environment. If you look at something like Google's Borg, it's built with this concept.  But that hypervisor runs in a container. So, it's just, it's a constant container world that it's nice to see. We actually thought it would take longer for the industry from a technology perspective to get to where we are right now, but it's super encouraging to see the advances in Kubernetes, how much movement's going on to it. We love red hats, all over it. And it's allowing us to do some things that haven't been done before. Now, on the application side, though, obviously there's hundreds of different types of apps. NFE is an interesting space because when they took their initial appliances and moved them to NFE, they actually didn't really re-architect them very much. So, the reason that they want this high reliability is they didn't take cloud native concepts, which is resilience, how to design your app in a fashion that allows for failure. Now, when they see the ability to re-architect containers, it brings a whole new interesting space because when you see what the Kubernetes API can do, it's pretty powerful when you think about how you run software. Resilience is built into the constructs of the container orchestrator. So, we're happy to see the pay sets moving. I think there's gonna be a widespread of applications, but I think with what both Red Hat and Ericsson are delivering together, you have that full breadth of bare metal. Give me a VM, give me a container orchestrated, and then I'll go up to you with OpenShift and run across clouds. It's a nice space we're in right now. Yeah, absolutely. And, you know, Roz, you've done a study on NFE, maybe a study in the future on containers. What are your thoughts? We actually did run a survey earlier this year and we asked the question to the telcos about containers. And essentially, I don't think any of them said they'd actually deployed containers. And when I spoke with them, it was more an issue of we're aware of containers.  We're not sure when, we're not sure why. So we're kind of keeping up with it because we know we have to be prepared for it eventually. I think they recognize that it really is gonna be the VNF owners having to do that rearchitecture. And they will be more the consumers of the containers as opposed to creating them. So we just have to know how to manage them. But it's certainly very top of mind for everybody. Susan's tapping my elbow if I'm going to say it. I know I was actually gonna turn it around and ask you the question. Uh... Whoa. It was like the rent that would do this, so, uh... She's called my pun. So I think a couple things to say, I guess, and then re-put my hat back on on the panel piece. I think containers is this next frontier and actually a lot of what does it set in terms of just the fundamental computer science benefits that come with it. But also mindful of the application challenges that you talk about. I think this is an inevitable future, but how we get there has to be really well thought out and staged. And I think that comes with, from an Erickson standpoint, we feel like we've already made investments and have started this journey in certain parts of our business. What we're very interested to do is have partnerships that can help inform where we go when we go. And it's really one of the things that has drawn us to Intel and to Red Hat is that we can partner across multiple areas of our portfolio and then we can better inform and make decisions on where we take investments. And we view that as part of our job for our customers is that, yes, we want them to work with Erickson and they want to work with Erickson, but part of what they expect when they work with Erickson is that they're gonna get this perspective on where things are and where they're going and increasingly in the interconnected world we are in. Part of that means that we have to form relationships like this so that we can start to work together on the lab work, the coding, the development and actually my next topic, which is how do we upstream this in the right way? We have so many different open source projects out there and sometimes there's even contention amongst some of them. So, and then there's also the risk downstream of things happening in Forks and how do we work upstream? So, hopefully that answers your question Susan. But I think we've talked about the Alliance, we've talked about NFE, we've talked about containers, maybe talking more broadly about just open source organizations and upstream activity and you're very active in the open NFE, open daylight and you've mentioned it's Red Hat so you're very active and Intel's active. Maybe you shift the topic to open source and what is Erickson doing and driving right now and what are some of the priority communities that we're focused on? So, at least from my perspective because Erickson as you know is driving lots of different things. So, from my perspective of course I have a high focus on open NFE, obviously open stack, open daylight, open V switch. We're also getting more heavily involved in FDIO. We also have then the open compute platform and ODCCP. So, I haven't been so focused on the harder ones being more of a software girl myself but really we have very much embraced the open source community as a development model. I would say that over the last few years we have very much learned what that means in transforming to be an open source development model and certainly what we've learned along the way with open stack we have then transferred directly into our open daylight engagements where we do take a upstream only approach. So, you know, very much similar to Red Hat. I would say we're in the process of getting there from an open stack perspective. As I said, you know, we've been doing this for a long time and open stack was definitely not ready from a characteristics perspective when we started this journey. So, we still have a legacy of capabilities that we've added to open stack and we're driving the upstream of that content through open NFE as well as directly into open stack with partners working with both Intel and Red Hat to really make sure that that capabilities are upstream because I want to move away from doing any work post-distribution. That has also been our experience around OVS where we took OVS and did improvements. We're now moving away from that model so that we just work directly in the upstream. So, I think we've been doing some very good work with Intel around OVS in the last month or so where really made significant improvements in performance around OVS. So, that's the direction that we will go. You know, we're then using open OPNV as a way of how to glue these different initiatives together and really make some of those choices. It becomes quite confusing. And I think, you know, the whole mano space right now is a good example of that where there is a proliferation of projects ongoing and we need to see that really come together. I don't think it's in anyone's interest to see, you know, too many projects going on. And I think that you will see some more harmonization going in across the networking space as well going forward. And excellent, and active time for this. Excellent, and does Intel has made substantial investments in open source, in carrier space and beyond? I mean, it's a core strategic imperative. It looks like maybe you can share your perspective on Intel open source. Yeah, so pretty much all those projects we're heavily involved with. Even one of my peers, Adrian Hoven, covers a lot of the mono work from the technical perspective. Our goal constantly is drive as much upstream as possible, as quickly as possible because it floats all boats, right? So how to make sure whether it's a cloud service provider that chooses to do everything themselves, whether it's somebody that's working closely with Red Hat, we want to make sure that everybody that is using this technology can move as quickly as possible. We're actually in a weird state at Intel where sometimes the software actually isn't keeping up with the hardware advances, which is, you know, not something that we think is beneficial for the world. We see some of the top players able to utilize those hardware benefits much faster than the rest of the world. And if we, our goal is democratizing how computing happens in the software space and really if only a couple can benefit from this tech because they have deep, deep Linux experience and have their own patches, it's not, we don't see it as necessarily fair for the rest of the world that's trying to push the envelope too. So as fast as we can go upstream as many core projects as possible is pretty beneficial, especially now that we have new tech coming like 3D Crosspoint, which is gonna be a game changer for how people deal with memory and storage. And then what's happening with Silicon Photonics. We want to see core projects move as quickly as possible, get organized around something. Right now there's probably too many container orchestrators out there. We'd like to see maybe people latch on to one, maybe two, but really drive those forward as quickly as possible. There's probably too much strife in the container runtime or formats today. So that's why we care about things like OCI and driving some standards there. So the more that we can lock into a piece of code base, drive it up shame quickly and keep up with hardware, that'd be a fantastic situation. Yeah, we talk so much about software's eating the world, but with 3D Crosspoint, with all the technologies coming at the hardware level, it really is a point where software does need to catch up. And you have to go to an advanced level because everyone knows it's Red Hat, it's open source. So, how do you get the benefits of this upstream first mentality but still maintain the velocity of development to try and catch up to what Daz is talking about? Right, too. First of all, plus one to whatever Susan said and Daz said, right? From a philosophy as well as engagement perspective. To your question about pace of innovation versus sort of the stability, that's what we kind of pride ourselves in being able to parse on a day-to-day basis. For us, upstream communities all are about how do we move the needle on the pace of technology innovation? But at the same time, we quickly turn around and then say, we know intimately what does it take to run in production a workload or an infrastructure and to live with it for a number of years. And if you're from Japan, that years might be in two digits if you will, right? So, that is the product part of it. So, by making sure that we're innovating fast and in an upstream aligned fashion, we can make sure that the pitfall that Daz was talking about can be awarded. In other words, no snowflakes. Everybody gets the benefits of democratized innovation that we are driving at a very fast pace. At the same time, from a product perspective, we make sure that we spend an ordinary amount of energy driving quality engineering and having a support life cycle to make sure that customers can't live with that, right? So, that's the duality that we kind of pride ourselves in being able to do that for the last two decades and we'll continue to do that. That's great. Well, we've had a far ranging number of topics. We're approaching our end here. I wanted to see if there were any burning questions from the audience. I know there's probably hunger pains because we're in the lunch hour. And I have a very important question for Roz if there aren't any questions for the audience. I don't see any questions. We'll be up here afterwards and sort of joining you all in the movement towards lunch. My question for Roz is, like, what hat am I wearing? For those who don't know, our Cubs are going to the World Series starting tonight. Yeah, so this is like actually one of the first times I think I've ever worn a baseball hat at an event. I mean, I've done t-shirts all the time, but so this is the Chicago Cubs baseball hat. So it's the United States thing, baseball, the World Series. And the Cubs have not been to the World Series in 70 years. My mom pointed out that she was three months old the last time they went. Mine too. And they haven't won the World Series in 108 years, which is by some reckoning the longest stretch of any sport in modern history. So hence, I'm missing the opening game tonight to be here with you, so this hat keeps me comfort. So with that, we are a wrap. I wanna thank you for joining us in the lunch hour and please, if you have questions or anything, come up at the end and give our panel a round of applause. Thank you. Thank you.


I'm Kathleen Diggree and we're very excited that we get to talk about migraine today, but we're going to talk about things that are not part of the headache, but actually the visual aspects of migraine. And the objectives here are to review the clinical aspects of migraine with aura and differentiate aura from stroke and talk about auras and unusual auras and other visual phenomenon that are associated with migraine. With all headache, you know, we do histories and one of the hardest things about aura is trying to figure out if the aura is in one eye or both eyes, because patients will frequently think that it is in one eye. And they'll say my right eye becomes blurred. And what really is going on is that their right visual field becomes blurred. And many times they don't cover each eye while they're looking at a page to even know whether it's one eye or both eyes. So that's kind of a key question. And you'll see when we talk about other kinds of aura, like retinal aura, how important it is to figure out whether it's one eye or both eyes. Then we want to really try to understand how it starts. Is it a slow onset? Is there a march to it? Or is it fast? And we'll see that if something happens bang right at the beginning, we're going to be thinking more of something vascular going on. And then some things that I really want you to remember are could light cause visual blurring in one eye. And there is a thing called light claudication in older people where light comes into their eye and then their retina can't handle that. Or because they've got some ischemic changes to their visual system that light could be causing trouble. Now light often will trigger migraines, aura, and migraine in individuals that are very susceptible. And then of course, positional changes, any kind of visual phenomenon when they move their eyes. I always want to know if it happened before. And then I want to know how long the aura lasted. Is it more than five minutes or is it less than five minutes? Are there negative phenomenon? And that would be a scatoma. That would be something like a blank spot or positive phenomenon, which means like scintillations. And this positive negative phenomenon is actually an important historical thing to be thinking about. And then I always ask about other things, weakness, numbness, speech, because you're going to see that those types of auras can also accompany visual auras. And then of course, do they have a headache?  So the one eye or two is extremely important. If they report that it's in both eyes, migraine is by far the most likely diagnosis. Less likely is something ischemic, seizure, or something like optic discadema, giving them visual obscurations. Now, if they have visual loss plus scintillations, of course this can be migraine, it can be seizure, but you have to be thinking about other things as well. And especially if the visual loss goes beyond the time of the headache, then you really are going to be looking for something like stroke. Now, let's just take an anatomy of migraine with aura.  But this is an individual whose father had migraine. This individual was karsic as a kid, stomach aches early on, then started having migraines in college. They got worse when they got married. They got worse when they had children. And then the migraines got better as they got older. This is sort of a life history of somebody with migraine with aura. And the attack, there's a prodrome phase, but the aura comes before the headache in most cases. And we're going to talk more about this. And then of course you get the headache associated with light and sound sensitivity, nausea and or vomiting, and then you have a post-drome. So this is the prodrome that can happen before the headache. The aura usually comes before the onset of the pain. Sometimes the pain will come on with the aura and then all the accompaniments, the dizziness, blurry vision, fuzzy thinking, light and sound sensitivity during the headache phase. And then the post-drome is sort of this fatigue phase, if you will. So this is Mike. He's a 30 year old teacher. He has a family history of migraines and his mother.  And so what I'm going to try to do is show you this video if I can make this work. So let me see if I can get this to work. I'm going to stop sharing that and start sharing this. Let me know if you, can you hear that? We can't hear it, but we can see it. It's a little laggy. Okay, let's see. Now we can hear it. The main thing here is you can see how the spot develops and then there's these scintillations that are occurring. Do you see that?  And now she goes, are you having another migraine? And then as kids are going, do you have a migraine again dad? Oh no, are you okay dad? You're sure acting weird. Okay, now let's go to back to the slides. So you can look at this video yourself if you weren't able to hear it. But I think that is a really nice demonstration of the aura. Oh dear, hold on here. I'm gonna get rid of this and go back to sharing my screen. There we go. Can you see my screen now? Yep. Okay, good. All right, so let's see if we can get this to advance. So the ICHD3, and I hope all of you download the ICHD3, it's a PDF that you can download onto your phone, your iPad, your computer. But it's kind of the Bible of migraine. And to make this diagnosis, you have to have one or more of the following fully reversible auras. And visual auras are the most common, followed by sensory auras, speech and language, motor, brainstem and retinal. And we'll talk about these as well. A typical aura is usually visual and it can be sensory or speech. And there's usually no motor, brainstem or retinal. But that's a typical migraine with aura. And then the aura develops over five minutes. And sometimes you can have two or more auras in succession. So many people will first have the visual aura and then maybe they can't speak right. The aura rarely lasts more than an hour. So it's usually five to 60 minutes. At least one symptom, the aura is usually unilateral or and positive. And you could see from that video that scintillation that was going on during the aura. And it's usually followed by a headache. So that's what the ICHD3 criteria for migraine with aura. It's present in about 20% of people with migraine, most are visual. We used to use the terms classic migraine to indicate migraine with aura and then common migraine to be migraine without aura. We don't use that terminology anymore. Another terminology you hear people using is ocular migraine. There's no such thing as an ocular migraine. Ophthalmic migraine, complicated migraine. These are terms that are not used. Auras can be triggered by light. They can be triggered by flickering. A complex pattern because a lot of these people are extremely visually sensitive. And it's very difficult to stop the aura itself. For example, studies have been done where people get Sumitriptan and it does not stop the aura where it does stop the headache. Now, most of the auras, as I said, are visual. They're often wavy lines. You could see how there was a waviness to it. And then fortification spectra. You could see the little zigzaggy lines that were colored. Rarely there are hallucinations and we'll talk about Alice in Wonderland effect. Aphasia can accompany these visual auras and so can sensory symptoms and occasionally motor symptoms. Brainstem aura is a kind of a different animal. It has numerous brainstem symptoms like vertigo, chiroaural numbness, diplopia, dysarthria, tinnitus, hyperacusis, ataxia, and decreased consciousness. That's a brainstem aura and I'm not really talking about that today. Now, there have been studies that have looked at what kind of phenomenon really occur with individuals by using diaries and things like that. Flashes of bright light are seen anywhere between 16 and 38% of the aura, time of the aura, foggy blurred vision. Blurring seems to be a very common symptom and blurring alone is not an aura. Zigzaggy, jagged lines are pathodynamic, usually of migraine with aura. Skatomas can occur from other things but skatomas are very common in migraine.  Very common symptom in a lot of people. Another common aura is like a heat wave if you've ever driven along a highway and you see kind of a shimmering of the highway in the light, that is somewhat what people describe in their auras. White spots occur in about half. Hemianopia is usually not a very common type of aura. Tunnel vision can occur and then colored dots can occur and then people can get this corona phenomenon where everything has a halo. So when we talk about fortification spectra, this is a medieval fort in Europe and before World War II but anyway, you can see these zigzaggy type lines and that's where fortification spectra actually came from. This aura was actually drawn by a family medicine resident that rotated through headache clinic many years ago but you can see it was just very like that aura I showed you of Mike where it was colored zigzaggy lines. Usually starts in the center, slowly moves out to the side along with a cortical spreading depression that we think is what is going on with aura. And then you can see by 25 minutes, it's way over to the right side. So this aura was in his left hemisphere. It was, he would have sworn and many of you who've ever had an aura will swear that it's in one eye but if you cover one eye or the other eye you'll still see it on a page so you know it's in both eyes. And I always tell people if you have trouble defining it, have a person look at a text and then cover each eye and see if they can read the text. In the center will be a blank spot where nothing is. Sometimes it's kind of dark but then you'll have this fortification spectra along it. If you can get somebody to draw out zigzaggy lines as part of the visual phenomenon they have, this is a typical really visual aura that comes in the occipital lobe. You can't get zigzaggy lines except in the occipital lobe. So you know that is going to be in the occipital lobe. Now, as I said, we think that aura is a cortical spreading depression phenomenon and I believe this week Dr. Brennan will be talking to you about CSD and pathophysiology and migraine. But the neurophysiology of people with migraine is different in the way they integrate sensory phenomenon. There's a wonderful video on Novel. I'm not gonna play it here because it takes too much time but Shirley Ray has this lovely video of a person with an aura, the beginning of an aura and then they did PET studies during the aura to see a change in blood flow. And I know Dr. Brennan will cover that when he speaks to you about pathophysiology of migraine. So what about this woman, a 41 year old woman who started having visual disturbances about age 33? Her, she has these gray waves in the vision. It's in both eyes. It lasts anywhere between five and 30 minutes. It moves off to the right and she has three, she could, these can occur up to three to five times each day and then she gets a very slight headache. And sometimes when she has the aura, she has a sweet speech disturbance with it along with the visual phenomenon. And this is migraine aura without headache. So this usually is a typical aura, but no headache follows. And it used to be called migraine accompaniments or asephelgic migraine, but we know the proper terminology is migraine aura without headache. These are tricky and the differential diagnosis, you have to be really careful is to be sure it's not a TIA. We'll talk about how to differentiate an aura from a TIA. A seizure, and these I'll show you how to differentiate a seizure, an occipital lobe seizure. They're usually stereotypic last seconds. They're a little bit more complicated. Often pinwheels, circles, balls, I'll show you a couple examples. And people who have a aura without headache, a lot of them can have underlying tumors. This can be a symptom of reversible cerebral vasoconstriction syndrome. Can be a symptom of amyloid, AVMs, dissection, vasculitis, autoimmune disease, and even severe preeclampsia and eclampsia. So aura without headache, most of the time this is migraine aura without headache and not due to a secondary cause, but these you have to be a little bit more careful about and especially someone who's having these disturbances several times a day. And then this is a lovely demonstration again of a typical aura with the progression of the aura going off to the left side. So let's talk about this one. This was an 84 year old physician, family history of migraine, migraine with aura since the 20s, always intermittent and never debilitating. In his 40s, he began having aura without headache and he has visual scintillations and sometimes with fortification, meaning the zigzaggy lines. And every once in a while, when the aura's off to the right side, he can't speak. He has word finding difficulty. He has occasionally a mild headache with it, but never a severe one. The speech problem started to last 30 minutes or so, but it was never, ever severe. But one day he was sitting in a board room. He had an aura off to the right. He couldn't understand the slides he was seeing. He got up to leave. He couldn't get his words out. And this aura lasted about three to four hours. He had no headache. About a week later, he had another one that went over three to four days. He was hospitalized and MR was negative for a stroke. He did have some slowing on his EEG and he does have some vascular risk factors. So the diagnosis on this one is again migraine aura without headache. And we put him on aspirin and verapamil and that combination usually stops the attacks and that really worked well for him. So typical aura without headache is a typical aura not followed by a headache. Sometimes it's a teeny weenie headache, but not a major headache. And it has to fulfill the criteria for migraine with typical aura and no headache following the aura. Now these migraine accompaniments, and I'll call them that even though they're auras, mostly are visual. Sometimes it can be blindness. This was a review of study of all these people who had aura without headache. Some had hamonomous hemianopia. Some had parasthesias with their visual phenomenon and some had speech disturbance with the visual phenomenon. And some had weakness and speech and parasthesia and vision changes. And then some people just had the parasthesias speech disturbance and parasthes. So these are these migraine accompaniments or these auras that came on without a headache. There is an entity and that's what this physician had was late onset migraine accompaniments or we sometimes call it Loma. These are usually after age 40 and typically it's people with aura and then as they get older, the headache piece goes away or it gets markedly, markedly better and they're left with the aura. And while visual aura is the most frequent sensory aura, speech auras, motor auras, auras can occur. And the big problem and look at the physician was a vascular path. We had to determine could this be a TIA where he had a march of one symptom followed by another one, but he had no evidence of any ischemia on his imaging whatsoever and it all went away with aspirin and verapimil. So let's just, this is really important for neurologists, okay? So migraine with aura is usually positive visual phenomenon whereas in TIA it's usually loss of vision, okay? Usually visual field is involved. It can be unilateral, it can be both visual fields. In TIA it's gonna be a homonymous hemianopia. This to me is the most important one. It starts in the center, slowly moves across the visual field and in TIA it's usually pretty fast and onset. It comes on and stays and then it leaves. And the duration for a typical aura for migraine is 15 to 60 minutes whereas in a TIA it's usually three to 10 minutes. And this buildup, I can't stress that enough is so critical because everything else in TIA is usually unilateral, abrupt onset, et cetera. And usually there's a vascular territory that's involved. Now, as I said, you really can't treat the aura itself but you can prevent migraine with aura. And I do like baby aspirin. I use it a lot in people with aura as long as they don't have any contraindication and I love calcium channel blockers. However, there's great evidence for to pyramid, amitriptyline, CGRP monoclonal antibodies and many other preventatives such as other anticonvulsants have been used. The acute treatment of the headache portion can be with triptans, midren, ergatomines, G-pans, dytans and of course treat the nausea if a person has nausea. Now, here's a 43-year-old woman who has no previous migraine and she begins to have a visual disturbance of pinwheels off to the left side of her vision. She'd have these 10 to 12 per day, they're short, 10 seconds to four minutes and she never got a headache afterwards. And she was diagnosed with aura without headache. But unfortunately, this was a presentation of her metastatic colon cancer. So, you know, migraine with aura, especially when it's new in somebody 40 years old, I would image these people and pinwheels, if you start hearing pinwheels in the vision, start thinking seizures, occipital load seizures. And these are some lovely colorful drawings of people's visual auras that are associated with seizures. They're usually multicolored, circular, spherical and in seizures, they'll last seconds, maybe up to one to three minutes and then they're really frequent versus a typical migraine aura, they're rarely daily. And they're not the zigzaggy lines, mostly the circular types of things. And so that's how to differentiate a seizure from an aura.  She has a history of migraine with aura. So she has eight weeks of squiggles in her left visual field. And when she closes her eyes, she has kaleidoscopic letters with her eyes closed. These symptoms are constant. She's had an MR and MRA negative. So what do you think about a diagnosis for this woman? Well, she has persistent aura without infarction. Now, this is not a common diagnosis, but neurologists should know about this. It's a typical migraine with aura except that it's gonna go on for more than a week. If it's less than a week, we just call it prolonged aura and probable migraine with aura. Amazingly, people can have these symptoms for months or years. Now, the ones I've seen have not been this dramatic. Mostly they are like a little rice kernel that just stays there and they see it forever or for many months or years. There have been studies, however, with people who had persistent aura without infarction of the auras lasting 11 days to 28 years. And the age of people that present with this can be young to older. And it's very hard to treat. People have tried Divell Pro-X, Ferrosimide, Vrapamil, Lomotrogene, Gabapen, Teperamid, Acetazolamide, Magnesium, and Aspirin and various other things. And this aura is very, very difficult to treat. But you should be aware of persistent aura without infarction. It absolutely requires an MR scan. And sometimes you may even need to repeat it again because the MR may be negative at the beginning. And then there is migraine aura status. So this is not in the regular part of the ICHD3. It's in what we call the appendix. And these are headache types and migraine types that are waiting to be put into the ICHD, the regular ICHD. These are people who have migraines fulfilling, migraine with aura. And these are people who have three auras occurring over a period of three days. Now that woman that I talked about at the beginning of this aura without headache, having three to five in a day, she would qualify for migraine aura status. Now these also are not common. They're very rare. And you've absolutely got to think about other conditions that could be causing it like RCVS, press, dissection, some structural lesion. And you really do need to image these people who have migraine aura status. Well, a very interesting phenomenon is Allison Wonderland syndrome. I think Dr. Pasodin did a grand rounds on this. This is a perceptual disorder. And it causes people to see things in different shapes and sizes. So you can have macro-semato-agnosia or micro-semato-agnosia. That means that your body looks, it has places that are bigger than normal or smaller than normal, or that you feel like you're bigger than you should be or smaller than you should be, or things are far away. So that's teleopsia or pelliopsia. Let's see, there's some chat here. Metamorphopsia. So metamorphopsia is where things are gonna look wavy. So if you were to take an Amzler grid and cover each eye individually, things could look wavy or the page could look wavy. And there are many causes of metamorphopsia. For example, edema in the macula. So metamorphopsia is a symptom that is not typical of migraine, but it can be associated with Alice in Wonderland syndrome. Is migraine aura status differentiated from persistent aura without infarction based on three discrete events or one prolonged event? So that's a good question, but persistent aura means that it's going on continuously, okay? Whereas migraine aura status is episodes of aura occurring multiple times a day or multiple times within a week, but persistent aura is continuous. It's all the time. Thank you for your questions. Anytime you have questions, it's fine. Try to raise your hand so I, or shout at me or something, so if I don't see it in the chat. Anyway, back to Alice in Wonderland. Dr. Jigri, can I interject with a question? Sure. Can you hear me? I can. So if somebody has a history of migraine with aura, can they go on to develop different auras through time? Is that something that's expected or is it always going to be the same? You know, don't ever expect migraine to be the same always, okay? So here was that physician who started out with just typical migraine visual aura. Then he developed aura with speech things, okay? Then he developed aura with speech and paracetias. So do you see what I mean? And people's auras can change over time.  Like they get visual aura and that's all they ever get, okay? So it's a very variable, which makes migraine so interesting that I can't imagine, I mean, isn't it cool that we as neurologists get to deal with this condition? Because nobody's the same and everybody's is a little bit different. So they can change over time, they can stay the same. It really is an individual phenomenon. For sure it can change as you get older. And typically I see people who had migraine with aura, meaning they had terrible headache and migraine with their auras and then as they got older, they had a kind of piece went away and the aura persisted. Seamiller Fisher really popularized this late onset migraine accompaniments and actually wrote about his own auras throughout his life. If you want some really good bedtime reading, I won't put you to sleep because it's really interesting. You can read Seamiller Fisher's articles on this. I've got them, if anybody's interested, send me an email and I can send them to you. So any other question about migraine with aura before we go into these more complex types of things? I have one question, one more question. Sometimes people ascribe like a stereotypic something that always happens with their migraine that aren't the actual like migranist characteristics and they aren't actually what would fit is what we consider an aura. Is there a specific way that we should call these sort of things or just describe what happens? Okay, so now you said stereotypic before their headache. That? Well, that happens with their headache, maybe not before it, and it may last longer. Okay, like blurred vision with a migraine. So blurring a vision is, I mean, very, very common with migraines and often it occurs during the whole migraine. Where is that coming from? It's probably not the occipital lobe. I'm not, nobody, I mean, neuro-ophthalmologists that like headache and migraine, we talk about this all the time. Is this something in the midbrain going on, affecting focusing? Is it just, is it something on the occipital lobe? It's just a non-specific finding. It is not an aura. Okay, because it's going on with the headache, but they get the blurring. I don't call that an aura. An aura is a discrete neurologic event and it's usually stereotypic, meaning it occurs the same each time they have a migraine with the aura. It's the same, or mostly the same, okay? And that is an aura. It has to be kind of a discrete neurologic thing that happens usually before. Sometimes it can go into the headache phase a little bit, but it usually happens before, sometimes with it. And I guess my question isn't differentiating those two as what do we call this other non-specific findings? Is there an actual term that we should be calling them or should we just be describing that that's part of what happens while they have their migraine? I would describe it as part of what's happening with their migraine, that they have visual blurring during the migraine phase, the headache phase, yeah. Okay. These are hard. It's splitting hairs a little bit, but I think it's important that we kind of, for neurologists to kind of understand this a little bit more because we're the ones that are dealing with the brain function that's going along with migraine. Any other questions about migraine with aura or aura without headache? Okay, so this Alice in Wonderland syndrome is not common, but it's really interesting. And it's been, it's actually, it's been a diagnosis over the last 60, 70 years. It comes from Lewis Carroll, Lewis Carroll had migraine and he did have auras and many people believe that some of the things that happened to Alice were part of what he had with an aura and nobody really understands the pathophysiology of this and it is not specific to migraine. It can happen with seizure, it can happen with autoimmune disorders and even infections. It's been associated even with Jacob Kreitzfeld disease. So this is where she feels like she's too big for the situation. Here is her distorted neck and elongation and then this third one is when she looks like she's too small. So mycropsy and macropsy and then this body distortion. Any questions about Alice in Wonderland? Okay, I wanna talk about retinal migraine and I wanna talk about this because it's important to differentiate retinal migraine from transient, monocular blindness associated with carotid artery disease, okay? Retinal migraine, first of all, is rare. It is repeated, monocular visual attacks, usually scintillations, blindness in one eye. And it's usually associated with the headache and you can have positive phenomenon, you can have negative phenomenon during the attack either or both and patients need, they really need to draw out their defect after instruction. Most people who have an aura, a typical aura will feel like it's in one eye and that's where it really becomes important for people to draw out their field and really test their vision each eye individually. And then it's so hard to make this diagnosis because you have to have a clinical visual field exam or the patient has to draw this out. And the spread is usually over five minutes and the symptoms last five to 60 minutes and it usually comes with a headache and it's very rare and I haven't seen this very frequently, if at all. Maybe I've seen it. Now what I want you to notice is that these field defects, altitudinal and hemianopic are usually what, or this sort of gray to black vision, this is more likely to be vascular transient monocular blindness. Occasionally it can be a constricting blindness, but rarely and spots and all these little dots and things are more likely to be sort of this migranous phenomenon. And monocular visual loss can be from dry eyes and blurriness in one eye or both eyes. This is a benign condition. Migraine, of course, we've been talking about that. I'm gonna show you vasospasm, that's usually benign and many people believe, neuro-ophthalmologists in particular believe that most of the retinal migraine that's in the literature is actually this vasospasm. The one I really don't want you to miss is transient monocular blindness in the elderly because that can be deadly or lead to blindness. And of course, we're always looking for anabolic phenomenon. And then the only other things that can cause this monocular blindness are intermittent glaucoma and intermittent red cells or white cells in the anterior chamber. Now, for many years, people thought, well, people thought that this vasospasm was retinal migraine, but we think retinal migraine may actually be CSD that's occurring in the retina. So it has a very slow progression. It's not fast, whereas vasospasm is usually pretty fast. Vasospasm will result in a pale nerve and then afterwards you'll see kind of a hyperemia that's occurring and it can respond to a calcium channel blocker. Now, I do have a vasospasm. Let's see if I can see. Tell me if you can see my video coming up here. Can you see the video? Yes. Okay, good. So this is a person who has intermittent vasospasm and one eye, it's a right eye and it's just intermittent. But I want you to notice how fast this occurs. We're photographing him because he got several episodes in a day of transient monocular blindness and boom, this occurs. This is not a slow, gradual phenomenon. This was a boom, sudden vasospasm. And this went on for quite some time and you can see that his red cells are starting to go flow the opposite direction. If you want to look at this yourself, it's on novel, Neuroophthalmology, virtual educational library, novel.utah.edu. And you can watch this. I've got it in the Moran Eye Center. And here again, you can kind of see the red cells actually going into the disc, not out. You can also notice that he's got some silioratinal vessels that are still supplying parts of the retina, whereas the rest of the retina, see how pale it's getting and the vitreous is getting a little milky looking. So this guy needs to work up obviously, but he had vasospasm and it was not a retinal artery occlusion, but it was a vasospasm. He had a mass in his orbit that was intermittently causing an occlusion, kind of an occlusion of his central retinal artery. We took out the mass and the vasospastic episodes completely went away. So, but he did not have any emboli coming from the crottids. He had a big crotted workup multiple times. He had echocardiogram, all kinds of stuff until we diagnosed this vasospasm. But this is what a lot of people think of when they think of retinal migraine, it's more likely to be vasospasm and not retinal migraine. Now, any questions about retinal migraine that's not common if you think you've diagnosed it, send the patient to us so we can take a look at them, because it's really rare and very uncommon. But it's important to know about it because not only is it in the ICHD3, but it's also important to note it because it's in the differential diagnosis of transient monocular blindness. Any other questions on that? All right, next I wanna talk about other migraine phenomenon that can occur and these are not auras, okay? So, well, they could be auras if they occur stereotypically before a headache, but most of the time these are not. So, some people can get persistent positive phenomenon and I'm gonna talk about what these persistent positive phenomenon are. And these can just occur with or without a headache and some people are more visually sensitive who have migraine than other people. They see millions of dots, they see crack lines, blobs of white and gray, blue squares, bubbles, carpet patterns, circles, clouds, comets, greeny vision, heat waves, light flashing, flickering, lines of ants, photopsias. Photopsias are little white spots, rain-like patterns, snows, squiggles, TV static. So, these phenomenon can occur in people and they can see through these, okay? So, they're not an aura because it's not a discreet neurologic event usually before a headache, but these are visual symptoms that people who have migraine can have. So, persistent positive phenomenon. It's, they're not common either but it's not rare. You're gonna hear people talk about this. Oh, I get migraine with aura but in between I can see little spots and dots or I look at carpet and it looks like it's moving or I look at bathroom tile squares and it gives me the sense it's moving. Other people have what they call stripe-induced discomfort. They can't look at Venetian blinds without closing their eyes. Remember I talked about this flickering and their periphery of their vision that can be occurring. That can occur with their eyes closed and then this palenopsia can occur too as some people can get palenopsia just because they've got sensitive brains and palenopsia is two kinds of palenopsia. One is where an object moves across space like your hand moves across and you can see the hand moving. You can see the hand kind of making a movement along the way. And another one is looking at something and then looking away and still seeing that object. That's another form of palenopsia. Palenopsia can come from migraine. It can come from medications like people who get put on clomaphen for trying to induce pregnancy. That drug and many others can give you palenopsia. Even some of the anticonvulsants can give people palenopsia. This isn't migraine per se but it can't accompany it. It's just these migraine phenomenon that can occur in some people. So now I'm gonna take you through somebody who's got something like that and then we'll make their diagnosis. This is a 17 year old. He's a high school student and he got sent with the question from the neurologist is this persistent migraine aura? Is this persistent migraine aura? He has a family history of migraine. He's had typical migraine without aura and he's had a migraine with aura maybe every three to six months. He's a good student. And of course, the phenomenon that's going on his mother's worried about him driving and he insists that he can still drive. But he has these silvery lines that are present when he concentrates on them. Then he gets kind of floaters or squiggly lines especially if he looks at the sky or at snow when he goes skiing. And he's had grainy vision all the time as long as he can remember. And these symptoms go on all the time without or with a headache. And he sees through him. He says, mom, I can drive because I can see perfectly normally. I'm 2015. And so this is somewhat of what he's describing. Here's this grainy vision. And then these are the floaters that he can see in the blue sky. This is one form of palinopsia where you see the trailing image of the hand.  And this is another form of palinopsia where you look at an object, then look away and you still see the same object. And he endorsed these three, the grainy vision, the floaters and then the little dots in the blue sky. And so this is actually visual snow. This is not rare, but it's not common either. I see a lot of kids come in with this and they have these continuous dots in their visual field for at least the last three months. And then you have to have two other phenomenon, either palinopsia or the enhanced and topic phenomenon meaning excessive floaters or self-light of the eye. So self-light of the eye is when you close your eyes and many people with migraine may see waves of purple or light and their vision with their eyes closed in the complete darkness or photopsias which are these little bright spots, photophobia or nictalobia meaning night vision problems. And it's not consistent with typical migraine aura and these symptoms are not explained by any other disorder. It's seen in both men and women, many people have migraine but some people have headaches as well. And there may be a continuous from the beginning and there's a high prevalence of tinnitus or ringing in the ears and there's altered signals that occur in the parietal occipital region and also in the cerebellum, interestingly enough. Okay, Shay says sounds like, almost like Van Gogh. Do you know Van Gogh had migraine? He had migraine with aura. So many, some people believe that a lot of his paintings are somewhat of the kinds of visual phenomenon he had. And he had migraine and he had frequent migraine and he had terrible migraine. So interesting people that have migraine. So treatment of visual snow, I think the most important thing is that if you hear this story, reassure the person that they aren't crazy and then medications don't always work, people try different medicines all the time but they don't always work. And sometimes we try FL 41 tint. I wanna say a caveat about visual snow. Visual snow should be typical and it should be typically starting at a young age. When you start hearing visual snow in an older person for the first time, you've gotta work it up. We had a patient who got misdiagnosed with visual snow. She was in her 60s and she actually had multifocal coreiditis. So a retinal disorder that can cause similar phenomenon with sparkles and flashes in the vision and different things like that. She had night vision trouble, but it was a retinal disorder. So Jacob Kreuzfeld can sometimes be, have people think that visual snow. So please be careful in anybody older that gets this first diagnosis. You might wanna send them to neuro ophthalmology and have a good retinal exam and consider other diagnoses. I do wanna just mention photophobia. We did a big grand rounds on eye pain and photophobia so I'm not gonna talk about that but it's an extremely common symptom in migraine. 80 to 90% of everybody with migraine has ectophotophobia, meaning photophobia during their headache. And some people get migraine with and without aura with continuous photophobia. And these people can get very disabled. Don't forget that there are many causes of photophobia and many of these are neurologic like meningitis, pituitary tumors. The most common ones are usually migraine, however, and post-traumatic headaches. So individuals often report photophobia as the most bothersome symptom in migraine. In fact, many of the migraine trials now ask for what is your most bothersome symptom to treat and photophobia is right up there. If an individual has constant photophobia and you've ruled out other things, it could be, it is most likely migraine. And if you see continuous photophobia, always think about depression and anxiety because those things do come together. And the pathway for photophobia is in the posterior thalamus connecting to the trigeminal pathway. So I hope that I wanted to save a few minutes for questions. I hope you understand that migraine is more than a headache that visual symptoms are frequent. I really want a neurologist to always be able to recognize aura versus other visual phenomenon and differentiate aura from a TIA or a stroke. You can direct your patients to the American Migraine Foundation. Lots of great information. There's information about migraine with auras and aura in general. And then I don't know if anybody knows who the patron saint of migraine is, but this is St. Dimfna, the patron saint of migraine. And she's applying this very old sage rabbit on the side of this lady's head. She's taking vapors to try to treat the migraine. So with that, I'm gonna stop sharing my screen, but I wanna open it up. We've got about three minutes here for questions. So anybody with questions? No questions. Well, I hope that