Thank you very much for the invitation.   But I still have trouble making, I mean distinguishing between the Mibu's function and an Amiibo something like this. But this talk actually is about, is a talk in number theory proper, I think. And this is kind of the main message that I would like to pass. So this is a talk about the sun product problem which is one of sort of, which everybody presumably knows. And it has been treated and studied usually as a question of arithmetic or adjective combinatorics or maybe geometric combinatorics. So everything I've seen done about this problem was done using these methods. But this is, I think, the first time when we fetch number theory proper. And now the after this work has been done, I do think about it as an open problem in number theory rather than anything else. So this is, this is a recent paper, I mean, reasonably recent, in the summer it came out in maybe in late spring or summer. And it with Brandon Hansen, Ilya Ashkredov and Dima Dmitry Zhelezov. I mean against the rule, I know this against the common practice, but I emphasize Brandon because he was really the brain behind this project. And I, this could, this work could have easily been done without me, but it definitely wouldn't have been done without him. Okay, now I press my cursor and it doesn't work. Oh, okay. So this is, this is the Ender-Stimeredi. So I'm just, I'm going to quote from, from the 1983 Ender-Stimeredi paper.  So I'll just read it in English. So suppose we have an integers. And let's consider integers in the form, which are either pairwise sums or pairwise products. And then they write it as tempting to conjecture that for every epsilon greater than zero, there is a threshold value n zero. So that for every n, which is bigger than n zero, the number of distinct sums or products is n to the two minus epsilon. So almost n squared, almost as many as, as, as, as one can possibly get. And since that's paper, this is known as the sum product conjecture. Furthermore, they say moreover, the conjecture that you can take a longer word, that for every k and again, and big enough, there are more than n to the k minus epsilon. That is almost as many as you can possibly get distinct integers in the form, which are k-fold sums or k-fold products. And even more so, even more carefully, they say, perhaps our conjectures remain true if the a's are real or complex numbers. I will say just a few words about these multiple, many-fold sums or products, because the product, the problem is still wide open for this case as well. Yes, by the way, if anyone has questions, it would be really good if you just stop me and ask. Right, so what is best known, first of all, since most of the studies, or pretty much all of the studies that I'm aware of has been done over fields and over reels, or perhaps finite fields, I'm not going to talk about finite fields in this talk, but the best, the world record over the reels is that the number of distinct sums or sums or products is a to the power, which is a little bit bigger than four thirds. So in other words, one can take epsilon bigger, slightly smaller than two thirds. So epsilon is how far away from the holy grail exponent two. And for multiple sums or products, the known result is much weaker and actually known only over integers. So we don't know much about all over multiple sums or products for fields. And basically, this rather convoluted looking estimate just says that if you want, so you have n, if you have n elements in the set A, and you want to reach the cardinality n to the B, this is how many roughly two to the B squared times that you need to add or multiply the set A with itself. And this is a 2020 result by Brandon Hansen, Oly Rosh Newton and Dimar Zhoff. This result follows. And let me ask, as opposed n here is the cardinality of A, right? Yeah, n is the cardinality of A. Thank you. So this estimate, it follows from a more specific estimate, which is really the essence of a lot of previous study. It's an asymptotic case of the conjecture, which some people call few products imply many sums or F, B, M, S. And the specific result which is behind this estimate is this, that in the asymptotic case, when the product case is reasonably small, so A is M times A, and you can think of M as the size of A to a very, very small power. So not a log, but a very small power. Then the size of the K-fold sum set is, well, A to the K, this is as much as you would want to get, but, well, there is a little correction, and there is an epsilon sitting here. So if you want an epsilon to be small, well, you're welcome to have epsilon very small versus, say, K. So this correction can be made pretty small. However, the price you pay is that M, the multiplicative doubling constant comes in this huge power, well, you will have to divide by the huge power of M by the power M to the power 2 over epsilon. So this is the best few product many sums estimate, and we are only going to be talking about the case K equals 2. So we're only going to be talking about just some set and product set proper. So from now on K equals 2, and so I'll just rewrite this estimate for K equals 2. So this estimate in this form was obtained by Dima Zhelezov and Dormator Palveldi in about 2016, maybe, maybe 19 actually. Well, I mean, yeah, in the, yeah, in the, so maybe it was, yeah, it was 2000, I think it came out in 2016. And this was what I call a demystification of a famous paper by Burgan and Chang from 2004. So Burgan and Chang had qualitatively the same type of estimate, maybe with a slightly weaker numerology, but that paper was, I mean, that paper is still inaccessible for myself, for a lay reader, I like myself. On top of this, I should add that just recently, so this Zhelezov Palveldi proof, I really like this proof. So it's, I mean, there are two papers, it's based on a paper with more authors, there was also on that other paper, Dormator wasn't on that paper, but it was Imli Ruzha and Zhelezov Shakan, and goodness, Matolci Jr., the son of Mati Matolci, what's his first name, I don't remember. So, yes, so they kind of wrote what I call the demystification of Burgan and Chang, however, just recently in 2003, in 2023, this summer, there is this paper of the trio, I mean, Ben Green, Freddie Manners and Terry Tao, where they reproof this estimate, even, I mean, they reproof all this estimate, even slicker using entropy. So the proof is even shorter now, does, I mean, it's quite mysterious as far as I'm concerned, but so now there is also an entropy proof of this estimate. Right, so a few sort of technical things that we can probably, everyone knows. So first of all, we're going to be talking about energy, mostly additive energy, so energy or the second moment of convolution, so we just roughly, so in other words, this is just the, we take every sum in the sum set and take and add up, so r is the number of realizations of the sum, so we take with some of the squares of the number of realizations. And since we're talking about this equation, this equation can be rearranged, so the terms can be moved around, so the energy is either this, the realizations of sums, or the realizations of differences. And s stands for sum, obviously, and d for difference. And multiplicative energy is defined, obviously, in a similar way. When we look at this energy quantity, so if we had a power one here instead, then we just count the total number of realizations of all sums, and that would be a squared. And if we took a maximum number realization, which is a itself, then it would be a cube. So there's a trivial estimate on both sides for the energy. And Cauchy Schwartz, of course, tells us that the cardinality of a plus or minus a is bounded by this ratio. In other words, in other words, and this has how so many things have been done, in order to bound cardinality from below, you need to find, you need to bound the second moment from above. So most in so many things, like, say, say the Guth and Cauchy's resolution of the order distance conjecture, which I still think is one of the most, one of the most impressive papers that I've ever seen, if not the most impressive paper. So this is what's being done. So instead of estimating the cardinality in that case, the set of distances from below, you estimate the energy from above. And then use Cauchy Schwartz. And just for bookkeeping, exponential sums can be used. So if you just define a function on a circle, and just as an exponential sum with the frequencies in your set A, then this energy is just the fourth power of the of the l4 norm of this exponential sum, because basically complex conjugation response to the minus sign. And so there are two of these fours come from here, and there are two more of these fours come from there. So this is just a tautological, just tautology. In other words, if this relation doesn't take place between the between the exponents, when you when you take, I mean, when you when you take the fourth power of this expression, you just get an integrate over the circle, you get the right. So traditionally, the sum product problem was approached in the following way, one would try to bound energy via the opposite sex set. And say one of the versions is a well known estimate by Schoymusher from 2008, which bounds the multiplicative energy via the sum set. So it just says that the multiplicative energy is bounded pretty much by the sum set squared with a log that you can that you cannot actually get rid of.  In other words, if we have few sums, if a plus a is above the size of a, then the multiplicative energy of a is pretty trivial. So as we said, as we've seen before, energy always sits between the size of a squared and the size of a cubed. So if a plus a is roughly a, then the energy is pretty much a squared. And this is kind of the trivial case, which automatically implies that the number of products is almost as big as it gets up to the log in Cauchy Schwarz. So a few sums, many products issue closed. It's true. Sorry. Yeah, a few sums, many products is true for reals. So for integers as well. Now, a few products, many sum. Here, we only know about z. We don't know. We don't have an analog for the reals. We have some partial results for the reals that I'm not going to talk about. So this is, these are the estimates that were started by Buggan, that come from Buggan and Chang and their demystifications. And the estimate is now in this form, so that if the product set, if the multiplicative constant is m, if the product set is m times bigger than a, then there is a large subset of a and throughout a prime will always denote a large subset of a. So basically, you can think of a prime equals a, at least in cardinality, a large enough subset. Such that the, such that this subset has a reasonably small energy. So a squared is, again, this is the minimum energy, the minimum possible. Well, there is a four epsilon. Okay, I mean, we all often have to pay in, in, in various abstinence. But on top of this, unfortunately, there is this factor, which of course, grows pretty wild as epsilon goes to zero. So these estimates are really asymptotic. So, so they hold for m perhaps equals cardinality of a to the power one over 1000 or something like this. But, but for the genuine, some product conjecture, when say when we think of a such that is product set maybe is a to the three halves in size or something like this, this is pretty use. I mean, this is completely use. But having this estimate, having so this estimate suggests that perhaps so here, but we basically prove that, that, that if a has a small product set, then we have a large subset whose energy is as small as we wish pretty much. Maybe we want to maybe is it can we conjecture the following statement, the following sort of product set versus energy statement, which would weaken a little bit, which would, which would, which would be stronger than our some product conjecture. Can we say the following, is this true that, that, that a has, well, again, has a large subset a prime, the way I read this estimate a prime doesn't have to be large, but, but let's think about this large. So is that true that any every set a has a large subset a prime such that the following takes place either the product set or what, what the Cauchy Schwartz would have given me for the cardinality of a prime plus a prime. So this is what the Cauchy Schwartz would give me for cardinality of a prime plus a prime, right? There it is. So, right, so either the product set or what I would get from all my Cauchy Schwartz estimate for, for all the consequence of my Cauchy Schwartz estimate for, for the energy of a prime would give me almost a squared. So this is a stronger statement than the some product conjecture. The answer is no. The best you can expect is the power five thirds rather than the power two. And the example is very simple. It was done by Balagouli 2017. And there it is. So what we're going to take, we're going to take an interval between one and n, one and n squared, one little n squared. So the cardinality of a is n cubed. So we have an interval n squared. And then we take n dilates of this interval by powers of some huge prime. So p is just bigger than the interval. So we take this interval and take this gigantic dilates. And the dilates, I mean, the dilates differ from one another so much that different dilates just have no additive interaction with one another. And so if we look at the product set, then of course, when we, when we do products, so these powers g, they come from there, they're just there, they're an arithmetic progression between one and n. So when we, when we multiply, we sum the powers and the maximum power is going to be just two n. So in other words, on the, so the, the size of the product set is smaller than a to the power of five thirds. So why is that? So again, when we multiply these, when we multiply the interval from one to n squared, we get almost n to the fourth. But we don't really get n to the fourth, we get n to the fourth divided by some log n, log to some power. And on top of this, we get different powers of p and we get n powers. So we get, we get, we get almost a to the fifth, but not quite. And since, sorry, we'll get almost n to the fifth, but since the cardinality of a a is n to the third, we get a to the five, a to the five thirds. This is the product set. And on the other hand, when we do the energy, oh, well, again, we have a problem here, because every element of a, every element of a is a member of some arithmetic progression of length n squared. So when we look at this element of a as an element of a plus a, this element will have n squared the length of the arithmetic progression in realizations as a sum of product. So we square this n squared, we get a to the fourth. So we get n to the seventh, which is eight to the seventh thirds. And that accounts for this estimate five thirds is the best that we can get.  And on top of this, nothing will change. If we take any large, this argument will not break down if instead of a itself, which is just a union of arithmetic progressions, which are exist on kind of different scales and don't interact with each other, additivity, and nothing will change if we take reasonably large subsets of these arithmetic progressions. So this five thirds is what is the best we can get. And this is the main result I'm going to talk about. So suppose a is the subset of z and then there exists a prime subset of a such that a prime is large in cardinality and the estimate I've just claimed holds higher with the little so in this here over here that there's a little off one just just subsumes all sorts of logarithms. I mean, well, this specific logarithm, but here there's a little all that depends on R. And there is no R in this formulation. So there's unfortunate condition to this there. The condition is that if each member of the set A has at most are prime factors. It doesn't mean that the set A, of course, is spanned by a few numbers, a few primes. No, not at all. I mean, each member of A has its own prime factors. But what matters is that the number of prime factors for each A is bounded by log by almost by log A. And I wish I could make it log A, but I can't. So it has to be an EPS. If we return to this example, what I want to say is this is certainly true a proposal of this example, because because I can just take instead of this interval, instead of this interval, I can just take an arithmetic progression of primes. We know that there are arithmetic progression of primes as long as they want. And then I'll take this extra prime, just really gigantic, much bigger than, I mean, gigantic in comparison to this arithmetic progression of primes. And I will still get these five thirds. And if I do this, then in this case, my R would be just equal to two. Every member of A will just have two prime factors, this common prime gigantic P and one of the primes from the arithmetic progression. So already for two prime factors, this problem is not true. In fact, that was Simireti who asked this question. So at some point he was, so I told him at some point, oh, like I mentioned, this error distance problem is solved. And he said, oh, no, no, no, it's not solved. What about the single distance problem? This is the real problem.  Can you actually do something maybe in this case when every member of your set, or let's work with integers, he said, when every member of yourself of your set has, say, 10 prime factors. And this is how we started thinking about it. And then we realized that even two prime factors pose a problem. So we started thinking about just two prime factors. And then it went on to more prime factors. So now we can handle this. Okay, and there is an interesting corollary which follows from already methodology. So it's not obvious from the theorem. So parallel to the sum product problem, people were studying this quantity. So a plus or minus AA. And here's an interesting estimate that this a so of course, if we take either an arithmetic progression here, so it would take an integral from from one through N. And then AA is pretty much everything from one through N squared. And A plus AA is still everything from one through N squared times two, whatever all constants are equal to one. So the estimate would be just a squared in size, or we can take a as a geometric progression. Of course, if a is a geometric progression, then a times a is a itself. But when we add, it's when we add a geometric progression to itself will will square its size as the sum said. So but here it says in this year is an interesting corollary that this quantity is always much bigger than a squared, unless there are two endpoint cases. And the endpoint cases are either the product set is large. So either M equals either M equals A in the size of A, or when the product set is very small. So when when M is very small. So now what are the ingredients and now why why is this a number theory? So there are three ingredients. The first ingredient is a structure theme. And the structure theme is combinatorics. All the three ingredients so far would break down if we removed this few prime factors assumption. Some of them require some of them more stringent in terms of the number of prime factors. Some of them are less stringent, but weirdly enough, they're quite compatible with all the three. I mean, the number of prime factors they can digest is kind of more or less the same. So one is the structure theme. This is just basic combinatorics and pigeonholing. The other one is, well, we worked on this one pretty hard. And we did most of it ourselves. And then we discovered a paper which was called a Marcengale that occurs in harmonic analysis. This is the title of the paper by Gandhi and Veropoulos from 1976. This was a review paper. And that paper, and we realized that that paper can be just used as a black box for what we want. And there is another, well, application of a result back from around those times, which is Schmidt's sub space theorem, a special case of the subspace theorem. And this is, of course, I mean, this is the number theory. Well, I mean, miles beyond my understanding of number theory. And interestingly enough, it also comes seemingly indispensable. So this is kind of genuine harmonic analysis, not just bookkeeping. So I've written exponential sounds above, but I said that those exponential sounds are just for bookkeeping. No, this is harmonic analysis proper. I mean, you really can't see it just on one side of the Fourier transform. And the subspace theorem, well, the subspace theorem is the subspace theorem. There it is. So there's the version that we're going to use. So suppose we have r primes, and they generate a multiplicative group, gamma. And then we take some number L, and we compose a linear combination. So we take a bunch of coefficients from A1 through L, whatever they are, we fix them. And now we look at the number of solutions of the equations of, when we have a linear combination of these fixed A's and some elements of our group G, such that the sum equals to one. And we need no degenerate solutions, of course, because if we had degenerate solutions, if some subsum was equal to zero, we could have come up with a much larger number of solutions altogether. So if we count these non-degenerate solutions, then the number of solutions is bounded by the length. L is the length of this linear combination. Two, well, a large power. But most importantly, there is this rank here in this bound. So L times R. And then these three pieces will come together. Okay. So first let me show you how that without any number theory, without any harmonic analysis, the exponent three halves is easy. And all it needs is the structure theorem and element and structure theorem and basics. So here's the statement of the structure theorem. It's very convoluted, but I'd like to sort of, to demystify it because it's very simple and it's very easy to prove. So it says that there is a large subset of A which has structure. And the structure is as follows.  So altogether, every member of A has R prime. So there exists a set of common primes. So this set A prime is spanned. So every member of A prime is divisible by one of the common primes. So the number of common primes is R prime. And now every member of our subset A prime looks like this. So we have some sort of set B which I think of as a base set. And each element of this B is multiplied by a bunch of powers of these common primes. So it's a pretty easy statement. So in other words, every member of A prime looks like B an element from the base set times the element of G. And G is exactly this group generated by these common primes. So every element of A prime is the element of a base set B times some element of G. And moreover, everything can be regularized. So the set of Gs multiplying different Bs can be different. But what is important is that, and this is general kind of pigeon holding, not much to do really, so that essentially the number of powers of each of these primes multiplying every B is roughly the same up to say power up to say factor of two or something like this. So and this is the expression of this. So that every every B in the base set is multiplied by L1 prime, L1 powers of the first, by L1 powers of the first prime by some number L2 powers of the second prime and finally of the last prime. So in other words, every element B of the base set is multiplied by approximately some number L of the element of Gs. So G is the element of the group generated by these common primes. And this number L is pretty much the same for every B. And therefore, therefore, we have an estimate, of course, that roughly speaking, the size of A prime is just L, the number of primes multiplying every element B and the size of B. And this is pretty much A. So let's just think that LB equals A in size. And on top of this, when we multiply A with itself, or one thing, one more important thing I didn't say is that 50% of the pairs of the base set are co-prime. So when we multiply B with B, we get B squared. So B, in other words, pretty much has no multiplicative structure. All the multiplicative structure has been taken into this part, into this group gamma over here. And so the product set, the size of the product set is at least A squared times L. In other words, when we multiply, we lose from the maximum possible value, we lose the factor of L because we know nothing about these powers of these primes and all these powers can be in some kind of arithmetic progressions. So that's the structure there. In addition to this, there is an old lemma by Chang from 2003 that was an annals paper of Chang in 2003 on the sample of the conjecture. And this whole paper was based on this lemma. This lemma is very easy. So this lemma evaluates additive energy over the set A. It says that suppose A is a subset of Z, symmetric. Symmetric means A and minus A is the same. So we don't have to differ between sums and differences. So B is some prime. And let us just call A, V the part of A such that the P variation of every A in this part equals V. So in other words, A, V are the elements of A which are divisible exactly by P to the power of V. Not a bigger power, not a bigger power of P, not a smaller power of P. And then the energy of A is bounded by the sum over V. So V corresponds to different powers of this P of these energies. And what does that mean? So the energy, the total energy is the number of solutions of this equation. Each of these As is divisible by some power of P. All this lemma says is that it is not possible that the powers of P divided by these four As are all different. Because if they're different, that's a contradiction. Say if this one is not divisible by P at all, and these three are divisible by different powers of P, then we get a contradiction because it would imply that this one actually is divisible by P. That's it. So this is the content of Chiang's lemma. And if we now have this estimate, and we're Cauchy-Schwarz this estimate, so this is just the usual Cauchy-Schwarz inequality with energy notations, if you haven't seen, it doesn't matter. So there's a usual Cauchy-Schwarz inequality that tells you that this is what it is. Now you cancel the square root out and apply it to and combine it with this statement. So when you combine it with this statement, so basically this lemma tells you that the energy of A prime equals L squared times the energy of B. A prime itself is in size L times B. The worst possible case for the energy of A prime would be L cubed times B. In other words, when you estimate the energy of A prime, you win a factor of L. So the worst case is L cubed times B cubed, but then you get L squared times B cubed. On the other hand, as we said on the product set, we lose exactly the quantity L. So when we take, when we put these two things together and we optimize, we get this estimate with your exponent three-halves, done. Everything else that I'm still going to be talking about in the last 20 minutes, 10 minutes, in the last 10 minutes, is how to improve these three-halves to five-thirds. Three-halves is basic. There is no analysis, no number theory is in a sense, and there's only pigeonhole principle, that's it, and divisibility. So this is this, this can be taught to anyone. Now from two-thirds to five-thirds, this is the main thing in a sense, that's an improvement. So the main claim is that the energy of A is bounded by a much stronger, so there's a much stronger bound. So here in Chang's Lemma, all we require is that the P variations of these two guys are the same, and the P variations of these two guys can be anything. The strengthening is that as a matter of fact, as a matter of fact, the P variations here have to be equal, and the P variations here have to be equal. So I've written it, new gamma of A1 equals new gamma of A2, which means, which means that the valuations of A1 and A2 must be equal relative to all common primes P1 through PR. So we have common primes P1 through PR, and all valuations of these two, of terms in the left-hand side, have to be equal, and all variations of the two terms in the right-hand side have to be equal. So this is a much stronger quantity of bounds. And for that, this is kind of, well, this is kind of harmonic analysis-proper in a sense, so use maximal functions and stopping times and standard, but 20th century difference. So from here we conclude, so the conclusion of this is more or less immediate, so when we decide that if we assume that this is true, then the conclusion is that the energy of A prime, so that's at A prime that we got from the structure theorem, is A prime squared, this is just the trivial term, these are trivial solutions, this is when these two guys are equal and those two guys are equal, so this A prime squared, and on top of this, on top of this, this is the case that, so this is the case, this is what's left, why is that so? So because if we use a structure, if we use a structure theorem, so each of these A's is B times some element G, so and this says that the G is corresponding, so there are two B's here underlying these A's, and this says that the elements of the group here have to be the same and the same thing here, so basically, so there is some G here and there is some G prime here, and when I divide them this is what I'm going to get, I'm going to get an element of the group, so the energy is bounded by this expression, in other words I can think about it like this, so suppose A1 is anything, then what do I know about A2? I know that the group element multiplying A2 is the same, so for A2 I only have the B, and as far as A3 and A4 are concerned, all their options are going to be subsumed in this quantity, so when B, well this is going to be B3 and B4, B3 and B4 fall into the group, and now how do I evaluate this quantity, and this is where number theory kicks in, to evaluate this quantity unless the rank equals one, if the rank equals one I can do, if there is only one common prime I can do it by hand like in a one-page induction proof, but if I have more than one common prime then I need the full power of the subspace theorem and this is the statement, and this statement says that this quantity is pretty much B, it's B times something very small, it's B to the power, it's B to the power one plus little so in other words, in other words if I look at this solution and I say B1 minus B2 equals one, then of course the number of solutions can be as large as B, but if B1 minus B2 lies in a whole multiplicative group, then the number of possible solutions is not much worse, it's still pretty much B times something which is a little low of the size of B, that's the subspace theorem, and if I put these things together, you can trust me, if I put these things together, I'm going to get my statement, my exponent five-thirds, so essentially what does that tell me? This tells me that, so I know that I've lost the quantity L, that size of yeah, I lost the quantity L on the product set, and now if I look at the energy, how much do I win? I win A prime and then I have B squared, so A prime is B times L, so this is L times B cubed, so I've won L squared on the energy. In the trivial case, I've won L on the energy, but here I win L squared, and when I put this together, it's an optimize instead of three-halves, I get five-thirds. Right, so in the last five minutes, I'll just give you a few hints on how this is proven and just drop a few names, really, so suppose we have just one common prime, so our set A, suppose A and the same as A prime, so our set A looks as full, so there's a base set B and every element of the base set B is multiplied by a bunch of powers of the prime P, and these powers, this set V of B, can be different for different B's, but the cardinality of each V of B is roughly the same and equal to L, and this is the main proposition, the proposition in the case rank one, so that if we do this energy, then the P valuations of A1 and A2 must coincide, so A1 and A2 have some P variation V, and A3 and A4 have some P variation V prime, so therefore what happens is this, so when we calculate the energy again, so there's a trivial term, this term corresponds to A1 equals A2 and A3 equals A4, and now suppose we're dealing with non-trivial terms, so we have A prime choices for A1, knowing A1 we know the P valuation of A2, so we have B choices for A2, and now we know that A3 and A4 have an equal P valuation, so suppose this B corresponds to A3, B prime corresponds to A4, so then B minus B prime must lie, well maybe not in G itself, but in a coset of G, which is defined by this quantity, but in a fixed coset, and of course it doesn't matter whether it's gamma or coset of gamma, because I mean we can just divide the B and B prime by gamma, so the estimate doesn't, so if I want an estimate like this, it's a very easy estimate, because gamma is just, so I can just, so gamma is just rank one group, so I'm just talking about powers of the prime P, I can write everything in digits mod P, I can write all the elements of B and digits mod P, shift things around and prove this estimate, and there this little of one is actually a log, so there's not much to do here, it's like one page exercise, but this only works for rank one, so for rank one I don't need any subspace there, for rank one, namely for one common prime, namely for the Balagwuli example in a sense, well for refined Balagwuli example, whenever the arithmetic progression of primes multiplied by powers of some other prime, then this five thirds comes for, well the main thrust of these five thirds would be in this margin-gill-harmonic analysis proposition, so just one word about the proof, so just again this is name and term dropping, because there is obviously no time, and it would be too much, so what I do is I consider an exponential sum over the set A, so I have one common prime, and I consider an exponential sum, and what I do here is I group this exponential, I mean I partition this exponential sums basically by the powers of prime P multiplying A, so these powers of V, and then I define the square function, so the square function is kind of a standard quantity in harmonic analysis, in margin, I mean in maximal function theory in little wood pally and whatnot, and this is a standard definition, so what I do, defining a square function, I take each piece, so each piece of the exponential sum which is divisible by, where the frequency is divisible by specific power of P, take the square of the L2 norm, sum them over V's and take the square root, so this is the square, this is the square function, and this is the theorem from 1970, and this theorem tells me that for any Q between bigger than one, the Q norm, the LQ norm of the FT itself is of the same magnitude as the given, is of the same magnitude as the LQ norm of the square function, and this is exactly what my statement about energy says, about equal P variations on the left-hand side and the right-hand side, so the application of this theorem is a totology, so this is a maximal function, so this is a little bit, but again we don't have time for this, so these are just the standard additional constructs that have to be created in order to prove this inequality, moreover this inequality works in the opposite direction as well, and this is necessary to embrace more primes, so on the proof all I want to say and finish probably at this point, yes definitely finish here, so on the proof all I do is so I take my exponential sum, so this is just the sum of complex exponentials where frequencies line my set A, and I split this exponential sum into pieces where the valuation of where A is divisible exactly by P to the V, but I also need to consider a cutoff of this sum, so I will cut off the sum by those As which are divisible by say P to the 10th or higher power of P, and then all I need to notice is that I can just rewrite this in this form, so in other words if I just if I if I take the part of the exponential sum where I have As which are divisible by P to the power 10 or higher, I will obtain I can obtain this the value of this exponential sum as a point T as follow as follows, I would take the point T on the unit circle and then average my quantity around the right polygon with P to the 10th vertices, so and that's why these quantities, these cutoffs form an inverse martingale, so I will be I will be taking a point on the unit circle T and then average my exponential sum over the right polygon with P to the P to the V vertices, and of course the bigger V the more detailed average I'm getting and that's why it's a martingale, and then all I need is I can basically go on Wikipedia and and and and kind of dig out some some martingale inequalities and apply them in the correct way and apply Cauchy Schwartz and get the result, get the main proposition for rank one. And for rank higher than one I need more harmonic analysis tricks, I need some hinching, I need the hinching equality, I need some randomization, I need the inequalities going the other way, but this is all doable and well if I erase through these pages I arrive in the in this quantity which is again the same thing B1 minus B2 falling into the group where the group now has r generators and for that I have my I have the subspace there getting there yes I use this formula there's a little lemma in there but this r is crucial and this this really this really imposes this is this is the most stringent imposition of this condition and I guess it's time to stop.


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It's much more important for me to introduce her and to show that she has such a solid background from New South Wales University graduating with honors some years ago and going on to do her neurology practice within the system here at St. Vincent's and Royal North Shore before heading over as often as the case overseas, Britain, America, Europe and Dr. Chang's case has been to America where she had fellowships to the Mayo Clinic which is very highly regarded and even more so to Mount Sinai where she had a research fellowship for Estonia Fellowship. We've been very happy to support her research here in the pathophysiology of Estonia and to get that research award from the Brain Foundation Dr. Chang had to compete nationally so you can be very sure that our selection committee doesn't hand them out unless it's a very, very best of the best and that makes it very tough for people competing for funds from the Brain Foundation because we're an independent research funder the biggest in Australia but it means that to gain an award is very prestigious and I'm very, very pleased to be able to have this opportunity to introduce Dr. Chang tonight. Thank you very much Florence. Thank you very much Gerald for that kind introduction. So I just want to thank the Brain Foundation for their kind award and also for this opportunity to give this presentation about Estonia. So I'll just open up my presentation now. So as Gerald said I want the neurologist at the Movement Disorder Unit currently at Westmea Hospital and hopefully with this presentation I'll give you a general overview for Estonia and I'll list out the various types of treatment and its effectiveness but the figures on these slides are only an average and so there's quite a broad range over how people respond to the various treatments. Of course this presentation cannot replace a neurological consultation so I still advise if you're worried that you might have Estonia you should go and see a neurologist for proper consultation and hopefully will raise some public awareness for this condition. So Estonia was initially described by a prominent neurologist in Germany called Oppenheim who described four unrelated Jewish children having a childhood torsion in Estonia back in 1911 and these children all had sustained or intermittent muscle contractions which led to abnormal and often repetitive movements postures or both and to the right is you can see a picture of this description by Oppenheim. However, focal Estonia which is Estonia affecting only one part of the body has not really been recognised as a condition until the 1980s prior to that you were sort of as a stressing juice condition partly because of its rarity and also its reaction and positive response to things such as a sensory trick which I'll talk about later. It's not until in the 1980s where there was consistent abnormal findings during the recording of muscle electrical potential studies that neurologists started to think of this as a brain condition and they also noticed on these studies there was again persistent and intermittent muscle contraction between the muscles that doesn't usually act together at the same time. So with the current definition of Estonia which people notice that it tends to get worse when somebody is trying to perform an action and at the same time the muscles surrounding those muscles that supposed to perform the action actually activates when they're not supposed to and many years later on then people can develop abnormal postures which becomes fixed because of development of contractures. So how common is Estonia? Well we don't know so far in Australia because we don't have the research numbers to be sure but it's a third most common movement disorder throughout the world and based on the North American and European data the Estonia that only affects one body part is as common as 1 in 3,000 to 1 in 8,000 people whereas the Estonia that affects the whole body or generalised Estonia affects 1 in 28,000 people according to American study but the Austrian population study was quite surprising for people above the age of 50 and in their study group they found people 1 to 1.8% of people actually had Estonia and recently it's been a changing the doctors well classified Estonia we mainly look at two main sections number one is what we see in the patients for example the age or onset it's body distribution and how Estonia can evolve over time as well as neurological exam findings and secondly we try to look for the underlying cause which is what we mean by etiology and we're looking for any underlying brain or spinal cord problem and also if it's a possible genetic condition by looking through if there's any positive family history and the pattern of inheritance and that way we'll be able to narrow down the likely cause of Estonia throughout this extensive list and so far through scientists and doctors study of Estonia what do we know about it so there's various ways of studying Estonia either with human studies or animal studies and the various ways are for example measuring electrical potentials and currents within the brain for example using brain magnetic stimulation measures and other measures are looking at functional imaging for example functional MRI it measures the changes in the blood flow within the brain which is thought to be directly reflecting the brain cell activity and during the brain MRI we ask people to perform certain tasks for example that triggers Estonia to see what's going on in the brain and certainly there are ways of measuring the brain chemical levels in the fluid that surrounds the brain and the spinal cord also known as cerebral spinal fluid and also by doing special brain scans that analyzes the chemicals within the brain so the fourth method is looking at the brain under the microscope either in animal models of Estonia or through autopsy or post Morton analysis of the brain through the brain donor program so just going through what we know so far through measuring electric currents and potentials within the brain so in people with Estonia so far we found there are increased excitability not only within the brain but also in the spinal cord and the brain stem as well and there's abnormal brain plasticity and what we mean by this is there is increase of electrical potential during brain cell communication and there's a loss of inhibition or inhibitory control within the brain cells and so therefore this is thought to arise in a consolidation of abnormal motor program which then leads to Estonia but so far it's not certain why abnormal brain plasticity occurs and how it occurs and we know that there are abnormal communication between parts of the brain that receive signals from the body and to the parts of the brain that's responsible for motor programming for example researchers have found people with Estonia have difficulty discriminating two pinprick feelings if they're placed very close to each other compared to normal people or if those two pinprick feelings are separated closely in time compared to normal people and so far with imaging studies we've discovered in people with Estonia there are abnormality in the function of the basal ganglia section of the brain and as well as the cerebellum which is the back of the brain and again the parts of the brain that receive signals from the body and executes action within the body and we also found there is reduction in the connectivity between the cerebellum to the part of the brain as well as abnormal body part representation and processing within the brain and so far people who carry a certain genetic forms of Estonia have these changes in their imaging study and it's interesting that even people who carry the gene but do not have Estonia also have these changes on their imaging study so the question is now whether there's other environmental influences or other genetic factors that might be at play that cause people to have symptoms of Estonia so that's just a picture of for example a functional MRI just displaying on the left hand side normal finger representation in normal people so yellow dot is the thumb and the red square represents a little finger so you can see the representation of the thumb and the little finger in the normal person on the left hand side is quite separated whereas people with hand Estonia they're quite they merge quite close together and almost overlapping so this is what we mean by abnormal body part representation in the brain and certainly ways of studying Estonia is by measuring brain chemicals so we know Estonia can happen when there's abnormal dopamine signal pathway and dopamine is the type of neurotransmitter or chemical in the brain that allows the brain cells to talk to each other so we know when there is a decrease in the production or dopamine in genetically inherited condition called DOPA responsive Estonia that people can manifest with Estonia because of dopamine deficiency and once this is replaced Estonia completely resolves and secondly there are medications that block dopamine receptors within the brain that can also give rise to Estonia if given long term and certainly in some people with very early Parkinson's disease they can actually have foot Estonia probably as part of dopamine deficiency and when this is treated with liver DOPA it tends to resolve so we also know from the new mutations that we discover genetic forms of Estonia there are calcium and chloride iron channel mutations are being linked to neck Estonia and rightus cramp and so somehow calcium and chloride channels can change the cell potential and ourselves talk to each other within the brain and certainly we know certain types of mitochondrial dysfunction and mitochondria is the type of energy powerhouse within the brain cell and so when there's lack of energy or battery to the brain cell they also disrupts the way that the brain cells can talk to each other and certain types of mitochondrial condition can also manifest with Estonia symptoms and fourthly in brain studies looking at inhibitory brain chemical called GABA in Estonia subjects they found there is a reduction in this inhibitory brain chemical so we know for sure there are changes in the chemical within the brain in Estonia subjects and what happens after during the autopsy in Estonia patients so in patients they have discovered damages to certain structures can give rise to Estonia for example the basal ganglia of the thalamus part of the brain called the pride cortex and the cerebellum and top part of the spinal cord but not all Estonias we need to bear in mind the due to damage to the structures I just mentioned and there are really no consistent damage within the brain in idiopathic forms of Estonia and in those people who just have dystonic tremor people have actually found which is brain cell density within the cerebellum and so how do we investigate and manage Estonia so in the way that we I just mentioned how we classify Estonia then we work out a targeted way for investigation and usually it's by a neurologist who's trained in subspecialty of neurology called movement disorders so I'm just going to talk briefly about the management of various forms of dystonia and the first one is about childhood dystonia and as I mentioned we try to look for the underlying cause because treatment of this can is actually the treatment for the dystonia otherwise usually we give a Libodopa trial to see if the patient has Libodopa responsive dystonia and usually the response within a few days quite dramatic with the low dose of Libodopa certainly if we if Libodopa doesn't help then we try anticholinergic medication called artang or trihexiphenidol and various doses depend on how generalized or focal the dystonia is then usually in generalized dystonia for children in the quite large doses and they can tolerate quite large doses and with the addition of aurobacliphon children with generalized dystonia has been shown to have benefits in terms of walking and function and there is also a consideration for botulinum toxin therapy or if for additional therapy to the medications I just mentioned or as main therapy if the child has vocal dystonia and finally if medication and botulinum toxin injection doesn't seem to help then we would consider DBS for generalized form of childhood dystonia so DBS is deep brain stimulation and usually the target is deep in the brain in a region called globus pallidus internal which is a part of the basal ganglia so in terms of response to deep brain stimulation it depends on the genetic mutation of the patient they tend to say those with DYT1 tend to do a lot better than the other genetic forms of dystonia and so far for the DYT1 patients we have seven years of data which has shown sustaining improvement in more than 200 patients and improvement is quite significant about 60% of people improving the clinical dystonia rating scale and a disability score which is what we use to assess their dystonia severity and their function and about 60% of children then later didn't need to continue taking medication for dystonia and around about 90% on average had medication reduction it's known that if the DBS or deep brain stimulation is done early that can be quite useful because as I mentioned before when contractures develop they're irreversible and so the aim is try to do the DBS early to avoid contractions from forming because once it's formed there's markedly less improvement with deep brain stimulation however people still need to bear in mind before going for neurosurgery to think about the risk involved and it's not only the neurosurgical risk it's also the maintenance of the deep brain stimulator device and its pacemaker battery and so there is about 8% chance of fracture of the stimulator lead and 8% chance of battery infection rates for these children so in terms of DBS for what they used to call secondary dystonia due to cerebral palsy so you can see the average improvement is a lot less than the DYT1 form of dystonia run about 22% of dystonia in a functional disability scale the pain has a similar amount at 12 months and it's very hard to predict the individual's response because there's a quite a wide range between no improvement to about 60% improvement and so all these numbers are average figures so I'm going to move on to talk about the characteristics and management of adult onset isolated vocal dystonia so dystonia that we can't find the cause for and dystonia only affect part of the body and so I'm going to talk about neck dystonia, dystonia involving the eyes of vocal cords, writer's cramp, dystonia in the hand that only happens with writing and most of these are what we call sporadic which means it is not inherited in the family and usually they don't spread to other areas however around about 20% or people can later notice and spread to the body region only so with neck dystonia usually the average age of onset is around 50 and people experience involuntary neck or shoulder muscle activation twisting postures or tremors that are irregular and jerky and these things also result in quite a lot of neck or shoulder pain most commonly the cause is unknown but there are other causes as well like Parkinson's disease or atypical Parkinsonism and occasionally medication induced so I'm just going to talk briefly about the management of neck dystonia so the main state of treatment is botulinum toxin injection type A is available in Australia and type B is only available through a special access scheme and available in overseas so it's both equally effective at four weeks after injection and usually the type A1 lasts a lot longer three months compared to type B which is 10 weeks and people the researchers found about a 25% improvement in the neck dystonia rating scale but also similarly in improvement in the disability and interestingly 30 to 40% improvement in the pain scale and the type B toxin which is only overseas have more side effects of dry mouth and trouble swallowing so usually for neck dystonia in general tablet medication usually don't help but there have been some people who found some certain medications helpful such as levodopa or chronazepam and so far there's a Dutch physiotherapy trial whose results we're waiting for to see whether this is helpful for neck dystonia patients and usually if medication and botulinum toxin injections are not helpful and they still have quite severe refractory neck dystonia then we proceed to consider deep stimulation again to the deep part of the basal ganglia called the glopis pallidus and these people then tend to have a lot greater improvement in a severity disability and pain scale compared to the botulinum toxin injection and also improvement in the general health and depression scores and so far there is enough data to suggest this improvement is sustained up to eight years after the brain surgery so moving on to blepharospasm which is dystonia affecting the eyes and so it causes involuntary contraction of the muscles around the eyes and it comes on gradually at the average age of 50 and usually patients notice eye irritation or dryness which then later becomes excessive bleaking and involuntary closure of the eye which is worse when they're doing certain tasks or looking at bright light and some people can be as bad as causing functional blindness and inability to drive and as I mentioned before about 20% of people can notice dystonia spreading to surrounding areas of the face such as the vocal cord neck or arm so the management again is mainly with botulinum toxin injection and this time people notice quite a marked improvement in the majority of patients and last for about three to four months in its benefit and about 10% of people notice transient side effects such as drupiness of the eyes, blur vision, bruising at the side of the injection and about some patients can benefit from a dose of conazepam or trihexylphenidol or tetrabenizine but that's the minority of patients so there has been other therapy that's described to help with blepharospasm if botulinum toxin and medications don't help so there are surgery that can be done to partially section the eye muscles that causes the blinking that some people have found benefit if they don't respond to the previously mentioned therapies and people have tri-lubrication drops but it may or may not help and similarly to this rose color FL41 lens that can be a little bit helpful with light sensitivity and finally there hasn't been a lot of patients considering deep brain stimulation for blepharospasm partly because the botulinum toxin injection tends to do so well and so far there's only nine case reports in a scientific literature but they do improve around about 70 to 90 percent which is quite encouraging so I'm going to move on to talk about spasmodic dysphonia which is like laryngeal or voice box dysphonia and again the average azot onset is around 50 and only comes on when somebody is speaking and interestingly when someone whispers reads out loud things or shouts it does not affect them and so there's different types of spasmodic dysphonia so there's the AD doctor type where the vocal cords come together when they're not supposed to and so that leads to like a strangle voice break in between the boughs whereas the AB doctor where the vocal cords come apart when they're not supposed to leads to a breathy prolonged breathy voice and that happens within the consonants so again management is with botulinum toxin injection usually with ENG guidance to make sure that we are in the muscle at the time of injection and this is a main method or therapy and patients found usually a moderate improvement usually the type that improves the most is the one that where the vocal cords come together and so on average these are studies from I think New York they report about improvement of up to 91 percent of normal so that's up to it's not the average but there are side effects of breathiness and hoarseness that may not come with each injection and the AB doctor type where the vocal cords come apart when they talk patients report their voice quality of improvement of 70 percent of normal and just going to talk briefly about writer's cramp so the average age or onset for these conditions a lot younger at the age of 30 and again only comes on during writing and not when typing or doing other things with the hand and patients can compare not tightness or stiffness of the arm or forearm muscles with writing and that goes away when some of the stops writing and so that can lead to reduced speed of writing and difficultly doing cursive writing compared to printing and similarly hand dystonia can affect other occupations such as musicians blackjack dealers and typists and golfers and this is also known as ip in golfers and similarly can affect the 14 runners and the hand in dartsman and trap shooters and so there's a theory that maybe repetitive hand or foot use might be associated with development of dystonia later on and there has been certainly monkey animal models demonstrating this so just some pictures showing you what some musicians dystonia look like for pianist and violinist flute player and the trombone player and again the treatment is botulinum toxin injection for writers cramp and as we mentioned before side effects could be temporary weakness and bruising as the botulinum toxin injection usually only lasts for two and a half to three months we use a method where we get them to write with the non-dominant hand to look at which muscles we should inject in the dominant hand and that's called mirror dystonia guidance. About 30 percent of people can report some benefit with medications that I mentioned before in addition to benzodiazepines and with musicians dystonia patients about 60 percent improvement with occupational therapy so what they do is they're temporary immobilized finger that is dystonic and then the musicians undergo period of rehab with the occupational therapist and about 30 percent of improvement with trihexin phenodol but this is difficult to use in people who play the brass instrument because it can cause dry mouth and about 40 to 50 percent of improvement with botulinum toxin injection particularly with the finger flexion type of dystonia however with usually with the brass players dystonia of the mouth they need to undergo retraining of their embouchure rather than botulinum toxin injection or medication. So lastly I'm going to talk about psychogenic dystonia it's about one-fifth of all psychogenic movement disorders and it's thought to be the theory behind it is thought to be reaction or the method of coping with either current past stress or trauma and this is not under any voluntary control and so patients are not making this dystonia up and so far it's not well understood how this would lead to to increase connection between the emotional part of the brain and the brain involved in movement preparation and this has been shown in brain functional brain scans in people with psychogenic dystonia and similarly it's also shown there's decreased connection between emotional part of the brain and part of the brain that plans movements however people with psychogenic dystonia which is different from the organic dystonia as I mentioned before people with psychogenic dystonia they have normal brain plasticity and also normal body part representation in the brain so usually psychogenic dystonia can happen intermittently or becomes fixed at onset or sudden onset they can have previous spontaneous improvement and resolution of dystonia often it can happen after just minor trauma and body part affected by dystonia can have changing color temperature associated with pain and how we diagnosis is through knowing what organic dystonia look like and finding that psychogenic dystonia really lack the typical findings of organic dystonia however it causes just as much as significant disability as organic dystonia so so far this condition is quite under diagnosed and under treated because it's under recognized and it's a difficult diagnosis to make because the neurologists themselves have to be quite familiar with organic dystonia which is quite rare as we saw the figures of commonness in the previous slide and in addition there is also a lack of acceptance of diagnosis often in both the doctor and the patient and so this can be misdiagnosed as other organic conditions and can lead to unnecessary surgery or medication trials and it's unfortunate because this condition is potentially curable with inpatient rehabilitation plus or minus psychotherapy and psychiatric support and so early treatment of this condition can lead to increased chance of recovery and usually the treatment involves intense motor reprogramming with the physiotherapist and rehab center that specializes in this and studies have shown there's about 50 to 60 percent of patients who have marked improvement or resolution that is sustained at the follow-up period that two years but just got to bear in mind not all centers are trained in motor reprogramming of psychogenic movement disorders so you have to find a center that is willing and recognizes this condition so I'm going to talk briefly about research studies on dystonia that I have contacts with so far and so leading up from the psychogenic dystonia there is research from the psychiatry department within our hospital looking at how those with psychogenic movement disorder and normal volunteers manage stress and they also compare the methods of treatment where they give from psychotherapy plus or minus the traditional physiotherapy treatment route and the criteria is that they need to be diagnosed by somebody in west minirology with a psychogenic movement disorder and is an adult between the age of 18 and 65 who can read and speak English and have enough vision and hand dexterity to use a mouse in a keyboard and performs on web-based memory tasks so if you're interested in this you probably should let me know and I can give you the contact details so the next one is which I'm helping out with is called dystonia coalition project and this is like an international observation study across the world and we aim to try and recruit 5000 people worldwide and to get a database of DNA medical history demographic medications and physical exam findings and we're recruiting people who have idiopathic isolated dystonia and we follow them up every one to four years with questionnaires about things like depression social phobia and anxiety as well as physical exam findings and just some their medical history again and so far the dystonia coalition has made quite a lot of discoveries in discovering new genes for like dystonia for example so if you're interested you can head to this website to have a look at the publications they put out so far so I'll give you a few seconds to write that down and I'm nearly finished so we should have about 15 minutes for questions later on and if you haven't got this one I think later on are recording this session so you should be able to get this web address later on so the last research project is part of my phd in movement and posture control in dystonia patients so I'm trying to recruit people with writers cramp or neck dystonia and our theory is that dystonia is a difficulty or problem in posture control pathway of the brain because so far in monkey or animal studies they found there's a separate movement control and posture control pathway within the brain so we're going to do surface measurement of muscle activity potentials which is lasting one hour when somebody pushes against the risk against the lever while sitting down and we're going to measure their brain excitability using magnetic stimulation methods which last for one and a half hours and at the brain and my institute hopefully we're going to start doing functional brain MRIs on people with writers cramp and comparing with normal control studies normal control subjects so as I think Gerald mentioned before the internet is not a reliable source of information you really had to pick and choose where you should get your source of information from so these are all the I think the reliable sources of information to get more information about dystonia so maybe I'll move on to questions now so looking at all the questions so far that's been posted Jane was asking should all dystonia patients have a MRI yes I think so um they should at least have a brain and it's a by called spine MRI to make sure there are no structural abnormalities within this upper spinal cord or the brain causing dystonia because that'll um it probably wouldn't affect your management but then it would sort of give you an idea what's causing it and so if it's due to previous childhood stroke for example then possible ways of avoiding avoiding the cause causing further damage later on so then Lucia wanted to ask is there anything known about how DVS helps to revert symptoms so that's a very good question um because it's interesting how DVS revert symptoms in a different speak within different types of dystonia so the ones that are dragging juice the DVS pretty much reverts the symptoms within within 24 hours which is very different from the genetic forms of dystonia like the DYT ones I talked about so the DVS tends to improve the symptoms over a longer period for example three to nine months um and then even slower in other types of genetic forms of dystonia so there must be different underlying the mechanisms that causes dystonia in these three different groups and so so far we don't know exactly how DVS can revert dystonia but we know um it somehow restores the brain plasticity but we don't know how because it's such a complex thing yeah so that's why it's a good question because no one knows and then Brian wanted to ask are we sure that the basal ganglia is a correct place for DVS as a target so I think for the genetic forms of dystonia and childhood dystonia I mentioned before um it seems that they seem to have a very good response to deep brain stimulation and they have long term data showing sustained response so I think it is um the right target um and however I think there are researchers also looking at different targets for dystonia um so it's um I haven't heard of any other targets that's being shown to be better than the glubus pallidus which is the part of the basal ganglia that we were just talking about and then how second question from Brian is how do you feel about the non-invasive technique of magnetic impulses outside the head being used to treat cervical dystonia so yeah this is um like uh theoretically it's a um research project to see if there's non-invasive ways to change the brain excitability through repetitive magnetic impulses so um I think so far it's still a working progress so researchers are still testing to see if that helps people so it's not mainstream therapy yet because it's still under research and then just looking at the next question from Brian what is the life expectancy of a rechargeable metronic neurostimulator so for dystonia it really depends um if somebody depends on the setting uh if somebody is on a higher setting for generalized dystonia for example uh then usually the battery can last only like two to three years but there are ways of changing the setting around so battery can last for about four to five years there's batteries called rechargeable batteries available which then you can recharge every like twice or three times a week and then so you wouldn't have to worry about battery depletion that way try to see what I'm up to okay so question from Ian first question from Ian why is australia so behind in its acceptance of this diagnosis when it is medically accepted in canada us uh europe and the uk so it's a good question I think um um probably because of lack of public awareness um but hopefully with more support groups for dystonia coming up we should be able to raise more public awareness for dystonia and secondly I think also with the lack of electronic medical record system um that's probably why we still don't know the exact um frequency and how common dystonia is in australia whereas I think in centers like the US it's got a pretty uh long history of the electronic medical record system up to 15 years so I'm going to go through the second question from Ian so with only three percent of people with dystonia worldwide why does the psychogenic diagnosis appear to prevail more and more in these cases I'm not sure what okay psychogenic I'm not sure what you mean by that question three percent of people with dystonia worldwide yeah I'm not sure what you mean by that question maybe you could rephrase it and so I can try and answer it again Ian um so I move on to your third question so psychogenic suggests it's a conversion from psychological to physical symptom even if there is no previous history how can this be a valid diagnosis so even if there's no previous history of psychological stress or trauma is what I assume you're talking about so it's a valid diagnosis if the clinical formal dystonia doesn't really fit into what we observe from organic types of dystonia and it's really like a diagnosis made by like a neurologist who is has seen a lot of forms of organic dystonia and we know that from treatment of people with psychogenic dystonia about 50 to 60 percent of them go back to completely normal after reprogramming or physiorehab therapy and so I guess in that point you could argue unlike most forms of organic dystonia which is not reversible with physiotherapy and the psychogenic forms can and so people often argue what the mind can do onto the body the mind can also undo and plus there is no abnormal brain plasticity there so there is a potential for improvement and recovery so okay lots and lots of questions so next question is from Kim so Kim says I have cervical dystonia as does my sister and my daughter and so I call dystonia was spoken about as a later onset condition rather than childhood and how many cases have been found where it appears to be hereditary from birth so yes childhood neck dystonia is relatively less common than those who come on during adult childhood and if there's a positive family history that you were mentioning Kim so it's probably not the idiopathic or type of dystonia where we don't know the cause so it could be how to consider a hereditary form of dystonia and I don't know how many cases were why this is being described but it's certainly less common than the adult form of dystonia you can I don't think there are I think I don't think there are exact numbers detailing how many cases there are in people who have neck dystonia from birth you're going through a list of questions so next one is from Grant Grant says I received a mild traumatic brain injury five years ago about eight months later I started to get symptoms of the pharospasm as then diagnosed with mage syndrome my question is are there any studies of proof that dystonia can be attributed to head injury so I think so far there has been some studies alluding to that dystonia can come on after stress psychological stress or even some minor trauma but so can things like psychogenic dystonia so I think I still have to be sure undergo like a neurological consultation I don't know the exact condition behind and the circumstances behind the minor head trauma so I can't I'm afraid I can't really answer that question because it's a clinical judgment question so I can't answer that online sorry okay lots of questions I got two minutes so I'm afraid I can't answer all these questions but I'll do my best where can I so Paula is asking where can I go to see a neurologist in Australia New South Wales that is familiar with dystonia so besides Westmead I think there are also centres in St Vincent hospital in Sydney that have neurologists familiar with dystonia and also I think Concord Hospital there is also a movement to saw the specialists there and I think those are yeah I think those are the main centres I can that I can think of oh and of course there's also a Royal North Shore hospital as well so the next question is is it common to have both a B doctor and a D doctor spasmodic dystonia and the question is from David so it's it is also possible I think it's around 20 to 30 percent of people with spasmodic dystonia who has both forms of it so it's not that common that's about 20 to 30 percent okay Angela asked does Botox affect bone density if you use long term for nectastonia so I'm not aware of Botox causing osteopenia or osteoporosis for long term use there might be a good research question to do because I don't I'm not aware of any studies that suggest that okay so next one Margo is asking about the postural control research that I'm involved in and so she's asking does this mean the vestibular system may be involved if it is proven to involve postural control and what does this mean for treatment as well as the understanding of the causes so yes I think for nectastonia there has been alluded to that the vestibular system might be involved as well and certainly the of the eyes is quite closely linked to the vestibular system and also with the dystonia can be affected by various positioning of the body such as lying down versus sitting up and standing so certainly I think the vestibular system probably contributes a little to dystonia and probably adapts and adjusts to the changes whatever changes that causes dystonia so yeah I think on this we understand what's causing the postural control difficulties in in dystonia then we wouldn't be able to I wouldn't be able to comment on what it means for treatment yeah so unless we understand it won't be able to understand how to treat it uh so the next one is my son is eight and I think this will be the last question from Kylie my son is eight and has paroxysmal dystonia I find he's worse in winter do you think the cold makes the patient worse so certainly I know during the cold some people might get more psychological or physically stress and people with dystonia have certainly noticed that stress can make dystonia temporarily worse so I do think it's certainly possible okay so unfortunately I can't answer all the questions today so thanks very much for everyone who's participated and thanks for Gerald and the Brain Foundation for inviting me to talk about this my favorite topic well Florence do you hear that yes I think I'm on can you hear me yes oh good Florence we thank you very very very very much for your wonderful presentation whilst I'm involved with all the neurological disorders I don't know of them all that much but I certainly astounded to find how widespread and the varied types of dystonia affects people I thought it was a very small subset of Parkinson's but apparently obviously I can't expect too much I might say that we could give you a little extension of time if you're if you're not committed because there's only a few more questions to go if you'd have my dancing them we have a last we have written a line under the last one and that's from I'll just go to this now the last question was from here Kylie that's 757 so she did get in over the line if you like to think of that in terms of the timing of submitting a question but I was surprised to find that this activity occupational one I always saw the piano players suffered arthritis rather than dystonia maybe and both or either either or or both do you think properly hands not going too well is that always dystonia or is it sometimes oh it's not always dystonia yeah so some people can have overuse and paying associate with it whereas the musician dystonia they tend to be relatively painless and the dystonia comes off pretty much at the very beginning of playing rather than later on during a longer longer practice yeah I understand well they do have to practice professional ones they play a lot and a lot but the other thing that if I go back maybe I'm going too far back in time with repetitive strain injury is that a form of dystonia or no that's um that's what I mean by overuse so there is a lot more pain compared to dystonia and also the repetitive strain injury tends to happen like as people later along and say do the task repetitively rather than dystonia which happens pretty much immediately upon playing yeah or upon doing on the task that their hand repetitively does but I'm thinking all the literatures like in the 80s people didn't know about dystonia so they often call that repetitive strain injury and so I think that the last one was Kylie her son now there is one from day Anna yeah tms safe and so on if we wouldn't mind just dealing with those if you can a little quickly to give people who kindly heard us out and that we did say they could have questions up to later clock thank you oh okay sure so yeah tms is fairly it's quite safe it's been used I think since the 80s for research purposes and I think overseas now it's been used for even treatment for things like depression and various psychiatric conditions so there's possible side effects so some people get discomfort over the scalp where the stimulation occurs and in some people it causes a mild headache but it shouldn't cause anything more severe than that certainly people who have a seizure disorder probably shouldn't probably should be careful before they undergo tms study but I know my colleague has been using tms to study patients with seizures so even I think that's been shown to be relatively safe sorry to silence my fight so I'm gonna go down from Anna's question from down further so David is asking do you know much about usage of palms in terms of neuromodulation stimulator in the help of dystonia apart from invasive deep brain stimulation so haven't heard of that one so I don't know very much about it sorry yeah it could still be in an experimental research phase I think and generally you can tell which one which treatment is actually being scientifically proven by going on to websites such as google scala and looking about there and making sure it's from like a reputable scientific journal but it's just a lot faster to probably ask a health professional so the question after that is after David okay so Mary is asking um about DRD genetic mutation and taking levodopa very successfully very grateful so I'd like to know about levodopa being a treatment for depression and anxiety which in ways was worse than dystonia yeah um and she apparently the levodopa also helped with dystonia and anxiety yes so yeah certainly dopamine is not only a neurotransmitter for the motor system it also is also a neurotransmitter for part of the limbic system which is the emotional aspect of the brain and certainly in patients such as Parkinson patients who suffer quite a lot from anxiety depression as well as slowness and stiffness um taking a levodopa actually helps with both anxiety and depression as well as their motor symptoms so yeah I definitely agree that the levodopa can help with depression and anxiety but yeah depending on the condition because if there's a dopamine deficiency treating that condition with levodopa is the way to try and fix it so not all people with depression and anxiety should be treated with levodopa depends on the course so next one is Kate is asking do you know if the trigeminal nerve affects dystonia um no I don't think so because um with dystonia it classifies the central nervous system conditions so we think it's abnormality arising from the brain or the upper part of the spinal cord so I don't think trigeminal nerve affects dystonia unless somebody gets trigeminal nerve pain which can cause stress and that can indirectly worsen dystonia and then so Joanna is asking I'm 32 year old with dopamine responsive dystonia um based on levodopa my zycomerical cure for me but get return or symptoms with physical illness and stress and just stress and illness can normally do this so yeah definitely stress can cause return or symptoms and physical illness in people so it's also important to address on psychological needs as well as stress as we mentioned several times can worsen symptoms of dystonia uh moving on to next question so is it possible for huh sorry Joe well Kylie yes Kylie that's one that that would be a pretty new line for Kylie thank you oh is it possible for paroxysmal dystonia to go into remission uh so I think with with some forms of paroxysmal dystonia under treatment they can go into remission um if it's due to psychogenic dystonia that can also go into remission so it's definitely possible so yes oh okay that was the last question well thanks everyone for all the excellent questions well thank you very much indeed for Kylie extending your time we know how much pressure you work under on a time basis Florence and thank you for those people who stayed with us for the presentation and if you found that very useful please let us know on the website and tell others you may know about how we're striving to help you as much as we can and of course the missing link always in many areas of medicine as the funds are the funds for research and so raising the money is the next step towards getting a solution to the problem and thank you all very much and good night


You are about to witness an epic Tarot Magnus reaction. What's happening y'all, so I'm about to react to this dude gives a bell collector the Marchion Lynch treatment and I'm laughing because this is I'm looking at the look on his face in the thumbnail. I just know this shit's gonna be funny man.  Alright let me let's do this. He used to be the guy that kneeled here and now he ain't trying nothing but I think he moved. So you're telling me right now that I'm not speaking with James Ellister when you said yes? No, no, no, I ain't. I was in there cooking some bacon. Another bacon.  Can I speak to Mr. Ellis? Mr. Ellis, who is that? James Ellis. Nope, no. I think. I was in there cooking bacon. Foolishness and fuckery. This is dead man. This is cooking bacon. This is Jimmie Johnson. Jimmie Johnson, so you heard Jimmie Johnson. Yes. That's cooking bacon. She gonna hang out. That's cooking bacon. Cooking breakfast. I'm eating Sasha's bacon and eggs and toast. I was eating bacon. Mr. Ellis. Sir. Yes, who is this? Johnson. Johnson Jimmie. Okay, Johnson Jimmie. I was in there cooking bacon. Mr. Jimmie. I was in there cooking bacon.  And he shouldn't have been answering the motherfucking phone. That's the funniest response to a bill collector that I've ever seen. I was in there cooking bacon.  You know what I mean? What you talking about? You saw me? I was in there cooking bacon.  You know what I'm saying? Time for order.  I was in there cooking bacon. I was cooking breakfast. I was cooking bacon, sauces, eggs and toast.  I was in there cooking bacon. Anyway motherfuckers, post comments down below. Let me know what you think. And how he make me want to go cook some bacon. What makes subscribers? Subscribe.