OK? So let me recall the fundamental solution for the Laplace equation. So we found that maybe the notation was phi from the fundamental solution. Phi of x was equal to constant. The log, this was the notation, yes. And the log of modulus of x. And then another constant here. This is n equal to 2. There is no minus. Now we have to look. OK, so there is a minus. So it was OK. And then 1 over n minus 2 omega n, 1 to the x n minus 2. n bigger or equal to n 3. Actually, we can also, so these are singular functions. Maybe we can also see in one dimension. So these are radial functions, which solve the Laplace equation out of the origin, OK? So these are harmonic functions out of the origin, radial. OK, and then we can also take this. Maybe we can add this in one dimension. So let us see in one dimension what is the function phi. So phi is, so minus phi of x in one dimension is just equal to x over 2. Therefore, it's something like this, something like this. Therefore, the derivative of minus phi prime, so this is x. So the derivative here is negative minus 1 half, 1 half, which is, of course, an L1 log is locally integrable. However, phi second is, so minus phi second is not yet defined as far as we know. So phi second would be something like 0, then rapidly increasing here and 0 again. So I don't want to say what is phi second minus phi second for the moment. I don't want to say what it is. Actually, it's called the Dirac delta. We will see what does it mean. In any case, you see now the jump here is 1, the length of the jump. And this is the reason for this constant 1 half in front, essentially, so minus phi sort of convex function like this, minus phi. And the second derivative of minus phi is somehow concentrated at this point with the sign. I mean, this is a convex function. Now the log of modulus of x, so the log of modulus of x with the minus, well, this, again, is a singular function of this four near the origin of this four. We have, and also this, the integrability, we have already checked that the integrability property of this in two dimensions. So this is L1 log. This singularity can be integrated. Also, this can be integrated. This already we already know. Maybe this was an exercise. The gradient also can be integrated locally around the origin, but the second derivative cannot. This may be where exercise is. Now in two dimensions, some remarks. So if remark, if f is holomorphic in omega, then nf, let us write it as u plus ev, then umv are harmonic. This may be a homework if you want. Conversely, assume that u is harmonic in omega. We look for function f of the form u plus iv such that f is holomorphic. Let us see whether this is possible or not. So we look for v such that this system holds. Now let us consider the following differential form. Consider the following one form. So given u, we can consider this one form here. So compute the differential of this one form, which is minus u, y, x, dx wedge dx, which is 0, minus u, y, y, dy, wedge dx, plus u, x, x, dx wedge dy, plus u, x, y, dy wedge dy. And so this is 0. This is 0. And we have that this is equal to u, x, x, plus u, y, y, dx, dy, which is 0 because u is harmonic. So if u is harmonic in omega, then this differential form is closed. So omega is closed in omega. Now, if we assume that omega is simply connected, so conversely, assume that u is harmonic in omega. And so let us add also the following assumption to continue on the argument here. Assume, suppose, omega simply connected. So we have that omega is closed in omega, capital omega. But capital omega at the moment now is we have supposed it to be simply connected. And therefore, omega is exact. Since capital omega is simply connected, omega is exact. Hence, it admits a potential. Therefore, there exists, say, v, function v, smooth, such that omega is equal to dv. What does it mean, omega equal dv? This means vx dx plus dy dy. But omega was minus uy dx plus ux dy. And so this must be equal to this. Hence, we find that minus uy must be equal to vx. And the coefficients ux must be equal to vy. Therefore, we have solved the Cauchy-Riemann equations. So v is the function that we are looking for. It's exactly what we are looking for. With this v, the Cauchy-Riemann equations are satisfied. So we conclude that, no, no, v is not unique. It's determined up to a real constant. So v is determined up a real constant. So the point is the following. So conversely, under the assumptions in green, there exists an holomorphic function determined up to a purely imaginary constant such that this is holomorphic. So since v is determined up to a real constant, f is determined up to an imaginary constant. What does it mean, this? What does it mean? It means that, well, this is the theory of one-forms. So do you know what is one differential form in the definition of one-form? Do you know what it is?  Don't worry. Doesn't matter. Doesn't matter. In any case, the definition of exact one-form, I recall it. But so if the one-form, say, omega is one-form in R2, yes, in R2, or in Rn also, it is called exact in omega. It's called exact in omega. So if it admits a potential, it admits a potential, which means exactly if there exists a function phi such that omega is not any one-form, but is a differential. But since the theory is a differential form, it's non-trivial. If you have not studied, don't worry. You can skip this part. This was just a remark, maybe an exercise. OK. Maybe another exercise that we can do. Let us consider the function in one dimension phi of x equal 1 half of x. And let us compute, so this is in one dimension, take, take, so this is exercise, take so-called test function. So take a function psi in C infinity with compact support in R, so-called test function, and compute the following quantity, U psi second in the x. OK. Compute this. OK. This is, let us compute it. So this is sometimes also, well, let us compute it. So this is equal to what? This is minus. So U is this, which is therefore, so we can use integration by parts here. And this is U psi prime dx. And then there is a boundary term, but this boundary term is what? It's 0. So now what is this? This is minus the integral over R minus the negative integral, the negative part of reals. So this is, this function is minus 1 half and plus 1 half. This is U prime. OK. Therefore, this is minus. Then we have. So let me compute the, let me put the minus here for simplicity, OK, minus, plus, plus. U prime is minus 1 half here. Therefore, it's minus 1 half psi prime plus dx plus 1 half psi prime dx. OK. Ah, sorry, this is phi. Excuse me. Phi. Sorry, sorry. Phi. This is phi prime. Thank you. Phi prime. Yes, but it is differentiable almost everywhere. So this is an integral which is respect to the Lebesgue measure and you will. OK. Then what is this? Sorry. So then this is compact support. So we can integrate by parts once more. So this is 1 half. So there is this minus 1 half. So this is, let's say, the integral between psi of 0 minus psi of minus infinity, which is 0, plus 1 half. And then we have minus 1 half, again, psi of 0. OK, so we have concluded that the integral of phi psi second r is exactly equal to psi of 0. For any psi infinity c, OK? This is just, for the moment, remember this as an exercise. For any test function, phi psi second equal psi of 0. OK. So now let me continue with the properties of harmonic functions. So as you can see from what is written here, the theory in two dimensions of harmonic function is very, very close, is strictly related to the theory of volumetric functions. However, in higher dimensions, we have not anymore that strict relation. So we now pass to more general results in any dimension. And so we will not use now the theory of volumetric functions. Let me also remember maybe this also was done. Let me also recall the second green identity. Also, this has been done last time. So maybe it is not necessary to rewrite it. So definition. So let omega be an open set of rn. We say that u is subharmonic, and let u in c2. We say that if u is subharmonic in omega, if minus Laplacian of u is less than or equal than 0 in omega, and we say that u is superharmonic in omega, if minus Laplace of u is larger than or equal than 0 in omega. And of course, it is harmonic if it is both at the same time. If it is subharmonic and superharmonic in omega. These are definitions. So then we have the following theorem. Maybe this is called weak maximum minimum principle. So let omega be bounded. Let omega be bounded. Let u be subharmonic in omega. Then the max of u over the boundary of omega. Sorry, subharmonic let u in c2 intersection c0 of the closure. Because in the definition of subharmonic, we just need c2. But now we want to consider also the values of u at the boundary. So it is important now to assume that we can speak about the trace of u on the boundary. So we assume that u is also continuous up to the boundary. So the max of u is equal to the max on the closure of u. So this is the maximum principle for subharmonic functions. It is the analog of the maximum principle for subcaloric function. I would say, I mean, we proved a similar statement for the heat equation. Where the operator was not minus laplacian, but the operator was ut minus laplacian. And in that case, we found that the maximum value was assumed on part of the boundary. Remember? So here, in place of this, in the parabolic case, there was this part of the boundary. So somehow, this, on the other hand, says that this is time. On the other hand, if there is no time, this says that the maximum on the boundary is the maximum value of the function. So in some sense, if you look at the parabolic problem, as where t were any variable, not special, but any variable, the parabolic weak maximum principle says slightly more than this. Because it excludes this part of the boundary. Now, we proved this result. We have already proven this. Remember, in the parabolic case, we have proven by constructing maybe a strict sub-solution. Remember? So in the parabolic case, we were reduced essentially to this. And now, we will do the same. The idea was to slightly perturb the function u. In the parabolic case, the idea was to define v, tx. Maybe it was u, tx, minus some content like this. Thank you. Thank you. Yes, the statement is still not complete. Now, these were comments. OK, so just to remember, the proof was based on reducing to the case of strict sub-solution and then proving the assertion. Passing to the limit as epsilon goes to 0. Yes, this is the weak maximum for sub-solution. Of course, there is the complete equivalent. Since now, the operator is you can change u into minus u, changing the inequality, changing minimum with maximum with minimum.  This is the assertion for. So this is concerning the minimum principle. And of course, if the function is harmonic, then you have at the same time the two equalities. So the weak maximum and minimum principle at the same time. Now, again, why the word weak here? Well, this does not exclude that there is an interior maximum. It says only that the maximum value, it is assumed here, but it doesn't say that it is only assumed here. So in principle, you could have also another interior maximum for the moment. This is why we call it weak. So I think that the proof is quite similar to the previous case. So we can consider the function v of x equals, say, u of x plus epsilon e to maybe x1. If x1 is the first coordinate, epsilon, say, is positive. Let us try this. So what happens to the Laplacian? So the Laplacian of v of x is equal to the Laplacian of v of x plus epsilon e to the x1 again, right? OK. So minus Laplacian is minus, minus. OK. But we are assuming now the case of sub-solution. So this is by assumption less than, so this is for any, so this is a definition in omega bar. And when x is in omega, we know that this is non-positive by assumptions. Because we are assuming sub-solutions. OK. So for a sub-solution, this is less than or equal than 0 by assumption. OK. But this is strictly negative because epsilon is positive. Therefore, this is a strict sub-solution. This is a strict sub-solution in omega. So a slight perturbation of the sub-solution u gives a strict sub-solution. OK. Now, we claim that, now what happens? Assume that x0 is a maximum of v. Well, if it is a maximum of v of v and it is interior because omega is open, but omega, of course, is open. Sorry, I have not written, but it is always open. And bounded. Bounded is very important, because otherwise we don't have max here. And also, actually, the result is false. Remember, what happened for the just parenthesis? What happened for the heat equation? For the heat equation, we had the weak maximum and minimum principle on bounded domains. This gives uniqueness of the Cauchy problem, say, on bounded domains. But we know that on unbounded domains, this uniqueness, in general, is false. So something is happening on unbounded domains. This was the message. And the same is here. So for a bounded domain, we have this. And we will see that uniqueness actually, this is false also in unbounded domains. For instance, as a consequence, also, say, uniqueness is false in unbounded domains. So just a comment. So the theory in this case parallels very much the parabolic and elliptic case are, in some sense, very similar, at least under this point of view. Very, very different from the hyperbolic theory, the wave equations, which was completely different behavior. OK. So this is a strict subsolution. And therefore, assume for the moment that we had, if we have an interior maximum of v, then the Laplacian of v has a sign at the maximum. The Laplacian of v at the maximum is less than or equal. Right? Which is a contradiction with this. Because from here, we have that inside the domain, side omega, the Laplacian is always positive. So we have a contradiction. This means that concerning the function v, the maximum points of v are assumed on the boundary. So we have proven, for v, for a strict subsolution that x0, the maximum points of v are. So now take an arbitrary point x bar. So take now any arbitrary point x bar in omega. So this is now. So u of x bar, it is what? Well, u of x bar is, by definition, v of x bar minus this. v of x bar minus epsilon e to this x1 bar. This is u x bar. Thank you, sorry. u x bar. This is by the definition of u of v. And this is clearly less than, instead of v, I take the maximum of v itself, 1 omega bar. But this is equal. This is equal. Because we have here seen that the boundary for v. And this is now replaced. Now we want a search on concerning only u. So we replace u here in place of v. And so again, this is less than or equal than what? The max of u, because u v is this, plus the maximum of this on the boundary of omega, which is bounded by a constant times epsilon, clearly. Because this is x1 ranges in a bounded interval. And therefore, I take the maximum value of this interval of the exponential. So I have a constant here and an epsilon in front. At the end, this is, and I consider, maybe I can also take plus epsilon. So there is a constant times epsilon. There exists a positive constant. So now, letting epsilon to 0 plus, in this argument, gives that u at x bar is less than or equal than this max. And therefore, since now x bar is arbitrarily inside the domain, this immediately implies that the max of u on omega bar is less than or equal than the max of u. Do you agree? Since the opposite inequality is immediate, since the opposite inequality, this one, is immediate. Because this object is contained in this. The boundary is contained in the closure. We have the equality, OK? So we have a proof which parallels, say, the proof of the weak minimum principle in the parabolic case. Which are the corollaries of this? As I say, there is an interesting corollary. So corollary, weak comparison. So assume that u and v.  And u is less than or equal than v on the boundary. Then we can conclude the interesting assertion that this relation, or the relations, must be true also inside, OK? The proof, well, the proof is, so let us consider u minus v. Then u, OK? So maybe you can continue by yourself at this point. Because this is, by assumption, is sub-harmonic. So v minus Laplace v is less than or equal than 0 in omega. Because it is minus Laplace of u, which is non-positive. And that's minus, minus this. So plus this, which is, again, non-positive, OK? So this is in omega. And in addition, by assumption on the boundary of omega. Therefore, v, sorry, w is less than or equal than 0 in omega. Why? Well, because the maximum point of w, the maximum value of w, is the same as the maximum value of w on the boundary. And the maximum value of w on the boundary is less than or equal than 0. Therefore, also the maximum value everywhere is less than or equal than 0, which is equivalent to, say, this by the maximum principle, OK? So we have this interesting conclusion. And we have also the following remark. Maybe another conclusion, theorem. Again, I am sorry. Throughout this course, for the moment, we have never considered the existence problem. We have just either constructed a special solution of our PD or proved uniqueness once you have existence. So existence requires, usually, the notion of weak solutions, sobole space, and so much for the moment theorem. So let f be a continuous function on omega, say. And let phi be a continuous function. Boundary of omega, assume that omega is bounded, open bounded. Then the problem has at most one solution. So this is maybe the Poisson equation, called Poisson equation. And so we have a boundary value problem, minus Laplace in a view equal to f, u equal phi. And this is at most one solution, because proof, if u1 and u2 are two solutions, assumed by contradiction, that you assume that you have two solutions, then you want to prove that they are equal. So take the difference. The difference satisfies minus Laplace of u, minus Laplace of omega, equal to 0. The difference, of course, is in the right class of objects, and satisfies the Laplace equation in omega, and also it is 0 on the boundary. And so now we can apply the corollary. Because the corollary say, w satisfies both the maximum and the minimum principle. On the boundary is 0. Therefore, from the maximum principle, w is less than or equal than 0. And from the minimum principle, w is larger or equal than 0. At the same time, therefore, w is 0, but w is less than or equal than 0 in omega on the maximum principle, and w is larger or equal than 0 in omega from the minimum principle, unnecessary. So w is 0, which means that u1 is equal to u2. So we have uniqueness of the Poisson equation with the boundary conditions on bounded domains. Again, the remark is that there is no uniqueness in unbounded domains. So now we do not require a so difficult example like the Tykonoff one. You remember, the Tykonoff one is very clever. The Tykonoff example was very clever. The Tykonoff example was the construction of a function that satisfies the heat equation in the half space, which is 0 at the initial time, remember? But here is more easy. You can consider, for instance, the function on, say, take omega equal the half plane, positive half plane, say. And then define and take u of x, y equal to x. So this is an example. Then minus Laplace of u is equal to 0 in omega, obviously, because this is linear. So when you do two derivatives, this is 0. And u is equal to 0 on the boundary of omega, because the boundary of omega is y equal to 0. So this is a non-zero function, harmonic non-zero function in the half plane, 0 on the boundary. Of course, another solution of this problem is the function identically 0. So we have two solutions, so there is no uniqueness, because u is omega is unbounded. This is much more easy than in the Tykonoff case. Now, another remark, maybe. Can you imagine what does it mean, the characteristic vector for this operator? What could be the definition of characteristic vectors? The set of all characteristic vectors. Can you imagine what it is here? So remember, you have to take the principal part of the operator. This is all principal part. And do you remember in the case, say, of the heat operator which was the definition? It is the same. Do you remember the definition in the case of heat operator? In the case of heat operator, here there was n1 plus n, maybe. So c0, c1, cn. And then it was only the principal part, so c1 squared plus c2 squared plus cn squared equal to 0. Do you remember? And we deduced that in this case of the heat equation, planes parallel to the horizontal plane were all characteristic. This was the situation. Now, here, which is the definition now? c is equal, however. c1, c2, cn. There is no c0. So now c1 squared plus plus cn squared equal to 0. Yes, it is empty. Therefore, there are no characteristic vectors in the case of the Laplace equation. This means that if you take, for instance, a plane, then this is non-characteristic. So there are no characteristic vectors. So for instance, this is non-characteristic. So this means that if you take, this is say, x and y. And now take this as a, so if you look at the Cauchy problem, now you do a strange thing. I mean, you think as y as time, very strange. Then you look at the Laplace equation, writing the second of u with respect to the y squared equal minus du squared. And you interpret this as time. So and you impose to this problem an initial condition, u0 equal u bar. And du over dy in 0 equal to u1 bar. These are analytic. If I assume that this is analytic, this is analytic. This is a plane, so it is analytic. Then by the Cauchy-Kowalewski theorem, you surely have a local solution. However, this is not very natural because in general these are problems which are static. I mean, the Laplace equation has no time in some sense. There is no time. So it is not so natural to look at this variable as a time. I mean, it is not natural to solve a Cauchy problem for the Laplace equation. So even if this is a solution at the end in the applications for elliptic equations is not very useful. Not very useful. Analytic, analytic, not useful in elliptic equations. So now we pass to, well, before starting the part of functional analysis, I think that we have to say something more on harmonic functions, which are so important because they are so important in general and also in physics that we have to say something more. And so let me try to prove the following result. So let u in C2 be subharmonic in omega. Be subharmonic in omega. Take any point. Take a point in the interior. Now omega is just open. Omega is open now. Omega, open. C2, subharmonic, an interior point. And take rho positive so that, small enough, the open ball centered at x0 with radius rho is, say, far from the boundary. Oh, my god. So take a positive radius. Since x0 is interior, surely there is a ball with this point. Now consider the following. Now then, d over d rho of this, of u, is bigger. So if you take the notation, b rho of x0, this means the mean value. So it is the volume of the ball of radius rho, which goes as rho to the n up to a constant. This is the volume of the ball of radius 1, remember. So by scaling, the volume of the ball of radius rho is this, times u of y, d1. This is a definition. So this means that, then you have the similar inequality for a superharmonic function with less than or equal than 0. In particular, for an harmonic function, if this is true, in particular, if u is harmonic, then the map function, which takes rho into this, is constant. This is a very strong assertion. It says that the value, now, which constant is it? Is the value of u at which point? At x0, at the center. Simply pass to the limit in this. This constant equal to u of x0. So for an harmonic function, there is this very strong assertion that if you take a point x0 and you take a small ball around x0, the value of the function at the center is equal to the mean. You take the mean of the function on the whole ball. They are equal. This is a solid ball. It is a solid ball. Of course, in two dimensions, this reminds a little bit the Cauchy formula. The Cauchy formula says if you have an holomorphic function, then you can write the value of f at the point as a mean value of something around a circle on the boundary of a ball, on the boundary of a circle. Well, there is some difference, because this is, for the moment, is a solid ball. And this result is valid in any dimension. Of course, in two dimensions, it's strictly related to that one. But in any dimension, this is true. This is a consequence. And this assertion here will have, in turn, a lot of consequences. So maybe it is worthwhile to prove another consequence of this remark. Consequence, maybe before proving this formula, which is called maybe the mean value property. Yes, the mean value property. This is called the mean value property. The mean value property says that this is true. And then let us see, before proving this, let us see a consequence, an immediate consequence. So theorem, strong maximum and minimum principle for harmonic function. Strong now for the first time. It is strong. So it says the following. Assume, for simplicity, that omega is connected. Otherwise, you reason connected components for separately on any connected component. So assume that omega is connected. If x0 in the interior is a maximum point of u, then u is constant. And the same for the minimum. Same for the minimum. So if you have an interior minimum, then it is constant. So this result now excludes what was left open by the weak maximum and minimum principle. But the weak maximum and minimum principle was saying, OK, I don't know. Surely, I mean, for instance, for a sub-solution, the maximum are assumed at the boundary, surely. So if this is the maximum, maybe it may happen something like this. But the maximum are assumed at the boundary. But this does not exclude that there is another maximum point in the interior. This was the content of the maximum principle. This says that if this happens, then actually, the function is constant. So necessarily, if it is non-constant, you have this picture. So it's a strong qualitative property on the graph of the solution knowing only something on the Laplacian. Because, of course, for a convex function or a concave function, some of these results are much more understandable. The point is that here, you're not assuming an equation on the action. You're assuming just an equation on the trace just only on the Laplacian, but nevertheless, assuming an information only on the Laplacian gives such a kind of result. So let us see the proof of this. Let us see the proof. Well, assume that you have x0. So it is enough to prove that define m as the max of u take omega also bounded. Sumo can connect it and bound it for simplicity. And define m as the maximum of u on omega bar. Then the set of all points x in omega such that u of x is equal to m, the claim is that this set of points is at the same time open and closed in omega. If I prove that this set is at the same time closed, my closed is obvious. But open also in omega, since omega is connected, then necessarily this must be equal to omega. And therefore, u is constant equal to its maximum value. So it is immediate to see that this is closed because u is continuous, so closed. Yeah, I'm assuming that omega say is bounded, so it admit the maximum. If all maximum points are on the boundary, there is nothing to prove. It is enough now to show that it is open. And to show that it is open, we use the following. Something missing. What do you mean? If this is harmonic. Yeah, but I mean it's constant. And therefore, if you put here omega n, then the constant will slightly change. Yes, this is actually constant. It's independent of everything. You're right. If you want exactly the value at the center, you have to put omega n. Otherwise, if you don't put omega n, this is still constant equal to omega n. Thank you. So let us prove that this is open. OK, take a ball. So take a point x such that, take a point x not in omega, such in omega, such that u of x not is equal to m.  And then this is constant. Then 1 over rho to the n. So the mean value of u is constant, independent of rho. Rho, this function rho that goes to the mean value of u on the solid ball. This is constant. But u in this ball, but u is less than or equal than m in the ball because m is the maximum. Therefore, u is less than or equal than m in the ball. So how is it possible that u at the center is equal? So the maximum value at the center is equal to this mean value. And at the same time, that u is less than or equal than the maximum in the solid ball. Necessarily, u must be constant, right? Otherwise, it is impossible. I repeat. I know that u at the center is its maximum value. And I know also that this maximum value is the mean value of u on a ball. But I know also that on a ball, u is less than or equal than m. So therefore, I conclude that necessarily u must be equal to m in the ball. Is it clear? It's immediate. So but this shows that this ball is contained in this set. So if you have a point in this set, there is a wall ball inside this set, which means that this set is open. And so this shows that it is open and closed. And so we have this very strong qualitative property. So I have to prove this. And this, in turn, this strong maximum and minimum principle has also many other consequences. By the way, concerning the heat equation, there is, again, there is also a strong maximum principle. And one can prove it using also in the heat equation case, there is a mean value property. But it is much more difficult than this. So maybe this is, again, another remark. Also in the case of the heat equation, there is a mean value property. The point is that but b rho of x naught is replaced by much by strange, I strange, strange ball. However, there is such a kind of formula. And from that kind of formula, you can, again, prove the strong maximum principle. OK? So as a consequence, you also, in the case of the heat equation, you have that, necessarily, the maximum and the minimum point is on that strange part of the boundary. There cannot be interior. If you want to look at this curious mean value property, for the heat equation, you can look at the book of Evans, for instance, in the Evans book. OK. So now let us try to prove this, define function phi of x, which is this form, define this function here, OK? And consider, so phi of x, maybe let me call rho, sorry, rho squared. And take x naught for simplicity equal the origin, OK? So this is actually the same rho. And take x naught equal the origin for simplicity. Now, what are the properties of this function? So phi is equal to 0 on the boundary of the ball. Because on the boundary of the ball, the norm of x, the boundary of the ball, centered at the origin of radius rho on the boundary, this is 0. So, OK? Also, it is positive in the interior, OK? So just a paraboloid, say, vanishing exactly on the boundary of the ball, OK? So therefore, I have that, now I'm integrating on the ball, phi Laplace of u. And this I know the following. Phi is positive in the ball. And minus Laplacian is less than or equal than 0, because it's a sub-solution, it's sub-harmonic, OK? Therefore, plus Laplacian is larger than or equal than 0, and phi is positive, OK? Therefore, this has a sign. Now I apply the second green identity. So let me rewrite the second green identity.  This was the second green identity. So now I apply this formula with phi equal to v. So the integral over n omega equal to b rho. So b rho phi Laplace of u dy is equal now to u Laplace. So let us compute the Laplace of phi here. So it is equal to, so let me compute the Laplacian of phi. So the gradient of phi is equal to minus x i. If you differentiate with respect to x i this equality, this, of course, is a constant. 1 half cancels with these two. And then it is clear that the gradient of the norm square is just the identity map. It's just x. Therefore, the Laplace of phi is equal to what? It is equal to? Is equal to? No, it's not 0. It's minus? Well, we have 100 variables, minus n. Minus n, number of variables, OK? Because the Hessian of this is just minus the identity matrix. And if you take the trace of the minus the identity matrix, the identity is n times n, and so you sum 1 n times, OK? So this is equal to minus n. Do you agree? Is it OK? So let us consider now this. So this is equal to this plus this. Then I have n times u in dy. And then I also know by this remark that phi is a function which is 0 on the boundary of the ball. Therefore, this is 0, OK? Because u is equal to phi. I'm taking u equal to phi, v equal to phi. So I'm taking v equal to phi, OK? If v is equal to phi, v is 0 on the boundary of the ball. So this term is not present. So we have only this, 0 u d phi over d nu, OK? And we know that this is larger than or equal to 0, OK? Now I have to compute the phi over d nu. So I have already written that the gradient of phi, so this is equal to n integral on the ball u dy minus u. Now, the gradient of phi is minus the identity, minus x. Therefore, this seems to be plus scalar product dot nu, d h and minus 1. If I make some mistake, please correct me immediately. So now who is nu? The exterior normal is what? It's x over rho, right? Because it is exterior. So this is, so nu is x over rho. So this is the scalar product of x with x over rho. And so at the end, it's equal to rho. Do you agree, please? n integral over b rho of u in the y plus rho integral over b rho u d h and minus 1, OK? It seems that there is a mistake because there is minus n. So there is a minus n here. And there is a minus n here. Sorry, there is a mistake. Because I have u Laplace of phi on the right-hand side, and Laplace of phi is a minus n. So let us look at the inequality that we have obtained. So minus n, the integral over b rho of u plus rho, the integral with the boundary of b rho of u is larger than or equal to 0. Let me check that I am correct. Yes, yes, yes. So this is the inequality that we have. And therefore, we can write it as follows. u less than or equal to rho integral over b rho. This is our inequality. And now let us compute that derivative, OK? So now let us compute the derivative of that map. So the derivative of 1 over rho, the integral of b rho of u. What is this? So this is minus n over rho to the n plus 1, the integral over b rho u dy. So this is a product, the derivative of a product. So I differentiate this. And then now what is the derivative? Can you imagine what is this or not? Can you imagine what is this? It is not difficult. I mean, you have to integrate on this ball. You can b rho. You can take the differential, different quotients, for instance, b rho plus h, the integral over b rho plus h minus the integral over b rho. Therefore, you are integrated, actually, on this circular annulus in any dimension, of course, in the differential. I am discretizing this derivative, OK? This is almost the integral over b rho plus h minus the integral over b rho divided by h. And h is exactly this. This is h. Therefore, if I now integrate the functions only on this object here, this circular annulus, divided by the height, what is reasonable is that this is equal to, converges to what? The integral on the surface. So indeed, this is equal to minus n. So I rewrite the first addendum, b rho, u dy, plus 1 over rho to the n, the integral of the boundary of b rho of u in the h n minus 1.  And you see immediately that this, now, OK, this, yes, it is exactly by this inequality is immediately larger than or equal to 0. Because if you simply divide by rho, rho is positive, you can write this inequality equivalently like this. And therefore, this minus this is larger than or equal than 0. So this minus this is larger than or equal to 0. And this concludes the proof. Of this mean value inequality, which has a lot of consequences in the theory of harmonic functions.


I've been a customer for about two years and I liked it and so I just thought that it would be a good fit for real estate because I like to do it as gifts too. Yeah. Really really cool. Okay so is it kind of just something you'll implement on the real estate in the real estate side of everything or do you actually want to try to get this out to more people? No I want to try to get it out to more people. Yeah for sure. So what you what you I mean what I would highly recommend doing is is really I mean it just comes down to what you want to do. I mean everyone has a different marketing approach especially when it comes to this type of a business which is word of mouth and simply networking so some people just rely on building a business and getting the product out or even building a team via word of mouth but today it's so easy to run ads to attract people but that's right if you want to kind of take it to a whole other level like if you want to take it to a whole other level that would be that would be running simple Facebook ads targeting people who have this interest to get them to see your product like no one not many in the industry of multi-level or network marketing or whatever you want to call it I love this industry first of all I started my entire entrepreneurship journey in this industry of network marketing and word of mouth so I'm very familiar with this type of industry but very few actually run ads most just try to recruit friends and family or just word of mouth so I just truly believe from a marketing standpoint where we're at today with social media marketing it's so easy to get this product in front of thousands of people while you're literally sleeping right you know but but again that that's for someone that's really looking to take it to the next level that's for someone that actually wants to invest and and and has a budget to even run a Facebook ad you know but the very first ad of what I reached out to you yesterday on is definitely the first ad needs to be that like ad no matter what that has to be there has to be a comma in that number as soon as possible and then after that you know we can always talk in the future if you have you know even a more budget to start actually selling the product first is just the the the social proof and the credibility of the page you know coming here and seeing 1100 likes versus 117 it's that social proof that's step one and then after that it's just yeah taking taking ads to a whole other level by actually selling the product you know so I just don't know how deep you are into this and how how how because I mean again it could be simple it could be super super simple but it does take some kind of budget you know to run any type of ad right right now I don't have a problem with that you know so I would like to take it to the next level do you have what's your web actually okay so here's your website right here so this website what would be necessary which most company websites do not allow you to do is install your Facebook pixel that's that's number one and you may not know what a pixel is just no I do because I have a pixel that goes back to my real estate website perfect perfect so you're very familiar so the only thing that these companies don't do is they don't allow you to install the pixel on the on the website that they provide for you so that's that's when you'll have to come up with a different web page to get people to so you can run Facebook ads and so you can really take it to the next level because you wouldn't I would not at all advise you to run a Facebook ad to this website right here okay and it's a beautiful website but that's number one that's the problem it's too beautiful and so if I run an ad and and people are seeing an ad see here's let me go back you when it comes to ads and it's very it's 100% the same with real estate in real estate this would be a post on one single listing and when I click on that I go to a web page where I can enter my name my name and number because I'm interested in that one specific listing the right why we wouldn't run an ad to a website like this is because the moment like we're for example if we were promoting this exact product right here we're running an ad we're literally paying to get people to see it we're getting we're paying to get people to click it and so the problem with the website is the fact that when I click it I'm on the website and all of a sudden there's a million things that I'm going to go look at a million things and before you know it I don't end up buying anything because overwhelming I might bookmark it I might come back to it later but I paid to get that person to click and I and I paid to get this product exposed but again the moment they come over here they saw a million other products and that's what's overwhelming because we only have a short attention span and that's how it is with marketing as well you have a consumers have a very short attention span so I need to put one product in front of their face I need to get them to click it they go to a website they see that one single product and they purchase so when it comes to physical products like this like for example if I can run an ad and it takes me straight here so this image would be this over here I click on it I come here there's only one product there's nothing else to click on I don't see any of this stuff I see add to bag check out that's how you run ads when it comes to physical products when it comes to anything when it comes to your listing whatever it's taken the click to one single product versus a website right so so that that's what you would have to do in this case is you would have to have a single web page which the company they don't provide that you'd have to get a third-party software which there's a ton of them out there I mean I use I use one for sure for landing pages that's what you would need you would need a landing page okay where it's a one it's it's not a website it's a web page and and again it's promoting that one product and and it's getting people to this one page to get them to click the one button and buy that single product you know so so that that that would be more for for marketing different products so what I would do is I would maybe go through this and see which one is your highest margin where you make the most uh on any of these products and then and then simply take that one product and run ads on that or or or it's either it's either you're going to do that because you're not going to run ads on the entire website that's not going to happen at all you don't want to do that at all at all you'll waste your money so it's all about running an ad for one single product in this case or running an ad to get people familiar with the company and exposed to actually building a team with you right so so those are two different ad angles and those are the the only two those are the best two either we're going to sell one single product and the profit margin is going to justify what we're going to spend in advertising or I'm going to run ads to get people on my team and and as I build a team that income that residual income can obviously build from there but but the strategy today again as I mentioned it's all here it's a it's a it's a simple Facebook ad it's either that I'm going to expose because your company has a ton of videos promotional videos showing how amazing the company is right recruiting videos they already have those types of videos if you started running ads to get people to click on the video and come straight to your sign-up page to sign up that could be very powerful and and and I just from a marketing perspective I truly believe that's where we should be today where 99 of people that are in the industry not only just in this company but in the industry as a whole because it's a huge industry so many different amways herbal life this industry has been around forever 99 still recruit their friends family when trying to build a team right right so and that's how you probably got exposed a pride friend of yours you know a couple years ago exposed you to it because that's that's the most powerful way word of mouth but at the same time people are kind of sick and tired of that and if we can leverage a simple ad to get that exposure why not especially someone like you that's building a real estate business and you don't even have all the time in the world anyways right so your time is very limited so to run an ad and leverage an ad to get people to expose to the company and in hopes build a team with you that could be simple and that could be powerful and it's not that it's it's not that expensive at all at all you know but then again that's that's if you're looking to build the team but it's either it's either grab a handful of videos that I know the company already has like if I go to the youtube channel there's probably a ton of videos on their youtube channel yeah amazing videos promotional videos showing how amazing the company is they're recruiting type videos which which you can easily use to run to run ads on let me let me let me go to their to their corporate youtube channel yeah this one right here 31 000 subscribers this is their main channel all of these videos again whether it's a video on the company and and and it's a promotional video to try to get people involved or it's a video on the product and and and now we're running ads on the product that could be simple like all these videos are already done these are professional videos that I can easily download upload to your facebook page and run ads on like that's that's powerful that's super simple that's super powerful however I wouldn't be taking them to this website I'd be taking them to one webpage where I can capture the lead or I can keep their attention on this one specific product and get them to buy that way you know so so for example if I was running an ad I would run up to this one single product when they purchase and they enter their their their credit card number and they actually purchase then they can go to the website and see all the products but that's after they already bought the product right you know and again that's the only strategy because I'm running an ad for it you know I I want to keep the ad very very narrow and very targeted and very straight to the point on one single product so there there's just two angles you can go either we're gonna you know run ads on on promoting and in in recruiting or run ads on products that could be super powerful as well but again step one I would say just take that number up like your next dollar needs to go in into into exposing this to a few thousand more people right because you're going to click invite and that's probably as high as you're going to get and then and then now it's just it just comes out of Facebook ad so I think that should be step one step one take that light count up and then and then we can definitely start what I would do is I would I would if I were you I would go to the website and just look at the commissions and see okay which product do I make the most amount of money on and and and and would it make sense if I actually ran ads on that one product because you could you can look at all these products and let's say you do make a you know a I don't know a $20 commission a $25 commission whatever maybe let's say let's say on any of these products let's say let's say on one of them you make a $20 commission if that's the commission $20 it might not seem like a lot but once we once you sell a few of them per day it it definitely adds up it definitely adds up right example the way I would start looking at it is what's my profit margin what's the highest margin I want to run an ad on that one single product and if my profit margin is 20 bucks that means that I can spend up to 20 dollars per day before I break even so if I can spend 20 bucks a day and sell at least one I break even and that's how you want to look at it you want to look at it what's my profit margin because whatever that is I can afford to spend that much per day as long as I'm getting to sell as long as I'm getting one sell per day and the way you know this can possibly work is where you're selling you know five six seven eight of them a day right at that at that same budget you know you can spend 20 bucks a day and start selling 10 of them a day and so although there there's a million different products here if you literally took the highest profit margin one and it was one and let's just say that was under let's just say that was something under wedding let's say let's say we come to the gift guide and we go under the wedding category and we start running a let's just say let's just say this one right here 50 bucks you start running you start running ads to for that one single product targeting everyone who has an interest in weddings so at 50 bucks I don't know exactly what your commission is maybe maybe maybe 10 bucks 15 bucks but whatever it is that's how you would want to look at it is is what's the highest profit margin and let me run an ad on that one single product because I'm telling you although the website has a million different products if you came out the gates and started selling 10 15 20 of these per day I'm here to tell you right now and I don't even know the company but I know of the industry I'm here to tell you right now that no one in the company is even doing that right not even one single person out of tens of thousands that are in the company not one single person is selling a crapload of one single product per day right they're not not in any company so when you can really take today's marketing which is social media marketing you can take today's facebook advertising and leverage that and do that oh my gosh you can crush it you can crush it you can crush it so I'm just kind of planting seeds with you I don't expect you to do this exactly right now I want you to do your research I want you to kind of see which look this one right here 150 bucks your commission has to be at least something I mean you have to hang on it'd be 30 bucks 30 bucks so if that was the case I'm telling you right now Amy $30 if you were spending $30 per day and we were selling at least one at least you're breaking even but at the same time I truly believe at $30 a day you'd be selling several of those right you'd be selling several of those so it would be in no time when you're at a hundred bucks a day and you're closing escrows you know or that's just running behind the scenes while you're doing your real estate deals you know so this 150 that that could be powerful you know you target everyone who has an interest in wedding in weddings everyone who's getting married you know facebook has all that data like I could target people if I was a wedding gown you know manufacturer or if I was a wedding gown retail store I can literally target women who are getting married this summer right like it's absolutely crazy and so this right here man that's what you could do with that but again it wouldn't go straight to this one page it would go to a web page not a website so it would be a completely different page which will now have what you what you would have to budget for that as well now you got to have a completely separate web page well could it go in with my click funnels oh yeah oh yeah for sure for sure I use a different one I use cartra only because it comes with the email otter responder as well i mean so that's that is my subscription with um click funnels so you're spending what are you spending 300 a month with it yeah oh man amy you need to get on the one that i'm that i'm using it's 97 dollars a month for everything oh really i left click funnels in fact i made a video over here on my youtube channel i'm over here building a youtube channel but i made a video back in 2018 as i was leaving uh click funnels to sign up with with this new software only because this new software has has multiple tools all for the same price only because i need i need first of all when it comes to running ads you need the lany page you need an email otter responder and in your case with real estate you want some type of online calendar so as people are coming to your lany page if you're running an ad on a listing they're inquiring on on your lany page they're entering their name and email because they want more information your email otter responder sends out more information but in your email otter responder there's also a link for your calendar so it's it's mainly those three softwares in one for the same price and so i literally yeah i i've been on this new software for for for two years now and it's just it just saves me a ton of money that's all saves me a time i'll send you a link i'll send you a link and there's a 14-day trial just compare it like if you're already using because i just signed up i just signed up for quick funnel why actually i'm in the hundred i just signed up for the 30-day challenge to learn how to build a funnel gotcha gotcha okay so if you've already paid for that part what was like 100 bucks yeah yeah so if you did that then then go through it just so you know it but at the same time you're you're spending way more money than you need to way more money that extra 200 a month so you're spending 300 on that i'm telling you come over here and spend 97 for way more that extra 200 a month needs to be your facebook ad budget right bottom line bottom line bottom line that extra 200 needs to be a facebook ad budget and you would crush it you'd crush it with real estate at a 200-dollar monthly budget or you'd crush it with this with with a 200-dollar a month budget so and that's just with me teaching you how to do it like i i'd be open to you know just teach you how to run these simple ads right but we'll we'll definitely get there work out work out the products look at all these different products and see which one you make the most on okay and then yeah we'd build a page around that one product and just crush it with that one product and as people buy that one product now they're on your email list now you can email them this website that has a million more right that right there is simple amy super powerful and super simple and i'm super excited to be talking about this with you because i i just have a completely different view on it and how you can really go to the top quick because yeah network marketing has been around forever but internet marketing not many has even taken advantage of it yet you know social media marketing so what what we should do first is let's let's take that light count up what's our budget for the like let's run one facebook ad i'll run it for you you just pay for it just let me know what your budget is what can what does it need to be it could be whatever i mean you like for example for every for every for every let's call it a hundred bucks for every 99 dollars for every 100 dollars that i it's a thousand right yeah that's still the same so those numbers are still the same that's how much we can always get no matter what so either we go but thousand we go but it's a it's a one-time ad i'm not going to want you to run it all the time like let's run this one time take it up as high as we need to and then we shut it off and then we talk again on which product we want to start running okay you know so i just think you have a ton of potential because well let's go ahead and do the do the hundred so we can get it up over a thousand okay perfect so all i need you to do is just go to your are you actually you're on your ipad right can you get to your business page can you go to facebook yeah okay go to your um go to your business page really quick and all i'm going to do is just request access to the page so i can start the ad tonight okay where do i go where do you where do i say where you gain us for access okay so you should either get a notification here in four seconds or do you see uh settings at the top so in the top right hand corner of that page okay perfect so then if you don't receive a notification right now okay i just got it perfect so just follow that through it's gonna ask you for your password and that's it oh gosh now i gotta remember my password yeah i know most of us don't know it so sensei is it is it mainly scented candles candles or it's it's not candles it's wax like wax wax wax gotcha so it's the warmers so it's the warmers but they also have cleaning products pet products i love it i love it i mean i'm gonna have my wife buy a few products off of you tonight oh cool yeah really cool let's see oils pods laundry i bet this laundry the diffuser the diffuser is a big thing right now the diffuser diffuser diffuser diffuser diffuser where's that at uh it's the mini diffuser if you type in the search yeah right there where you just were fan diffusers and pods oh gotcha gotcha okay yeah mini fan diffuser mini fan diffuser i never even heard of a mini fan what is a mini it's perfect for the office your car or anywhere there's a usb port hand just wow and it just gives off a fragrance right that's amazing yeah and it smells really cool really good so are these are these like scents and fragrances supposed to be like healthy for you or it's just a random scent it's just it's just something that smells good well they're not you know they don't burn like the waxes and stuff if you put your finger in it they don't burn and so but they're not like they we do have some essential oils and stuff as well for the regular diffusers really cool okay did i just give it to you let's um refresh okay perfect yeah so now i have access so i'll start that ad tonight and then just give me whatever card i can use to run it either you still have my card for the other that you run for my business page um i can check is have you changed it all recently no no okay so i should still have that same one then yes i'll message you the last four digits and just confirm if that's the right one okay perfect yeah and then i'll start that tonight and do you have any any like images like i can i can for sure run it on this image right here but if you just actually this is a beautiful image right here can i run it on this on this image should i run it yeah okay i'm gonna grab this image i will email you i'll snap i'll send you a snapshot later on um of the ad and i'm gonna use this image okay okay it's a perfect image perfect image i'll email you later on once we're live and then we'll go from there okay perfect cool okay me talk to you soon thanks to david thanks bye bye


It's my pleasure to introduce our presenter today, Natasha Simons. Natasha is probably known to many of you already, but some of you may not be aware that Natasha joined Ann's earlier this year coming to us from Griffith University, where as a senior project specialist amongst many other things she rolled out data citation at Griffith University. And that's going to be the topic of her presentation today. So thank you Ann, we'll hand over to Natasha. Okay, so at Griffith University we've been supporting data citation for quite some time now. We were the first institution to mint DOIs for our research data sets using the Ann Site My Data Service and we went on to put a Site My Data element into the research hub, which is our premier discovery service for all things Griffith Research. We also ran a project to engage with our researchers and our academic liaison librarians about data citation practices. So in this talk today I'm going to share our journey with you, the warts and all, and I'm going to talk about what a data citation looks like, the minting of DOIs using the Ann Site My Data Service, developing guidelines for minting and managing DOIs, some engagement strategies around data citation and the lessons that we've learnt on our journey, and there'll be time for questions at the end. So a little bit about Griffith to start with so that you can contextualise it. So Griffith is a medium sized university that's situated in southeast Queensland. We have five campuses that are spread out from Brisbane to the Gold Coast and we've got around 43,000 students for 4,300 staff and you can see from the list of schools and departments that we have basically four academic groups and they're quite diverse. So from arts through to business, health and then science, environment, engineering and technology. For our research we also have 32 research centres and a whole lot of priority areas that are quite diverse. So you can see in there we've got sustainable tourism, physical sciences, nursing, Asian politics. So we're very cross-disciplinary at our institution. We have in place some good research infrastructure for research data management. We are very fortunate to have a strong commitment from our university readers to improving data management and we also have had as a result of that some staff resources that have been allocated to important things to do with research data management at an operational level but also at a contract project level. And Griffith has been quite successful in seeking funds from ANS and also from NECTA and other external sources to build our own infrastructure and contribute to national infrastructure around data management. And we have had that strong emphasis on also seeking internal funds. So our research hub, for example, was built initially with a spark of funding from ANS which we then contributed more than what ANS had contributed to build our research hub and really significantly invested in that as a resource, not just for managing data but for profiling our researchers as well. And we have policy frameworks and service models for data management under discussion as well. So what does a data citation look like? Well, this is our research hub which probably a lot of you have already seen because we have talked a lot about it. So the research hub is built on vivo, open source software, and it was built in-house at Griffith and it's our researcher profile system that gives profile page for researchers but also connects everything. So it connects the researcher to their publications, their data collections, their grants and so forth and has landing pages for those things within it. So this is a profile page for Associate Professor Rodney Stewart and you'll see a number of tabs underneath his photograph. There's overview publications, projects, and I've got it defaulted in the screen on the collections tab. So you can see that he is the owner of a number of datasets to do with Southeast Queensland domestic water usage. So there, if you click on those, one of those, you open up the collection in the research hub and that is because we've worked on a gold standard project that was funded by Anzac Griffith. We have some nice metadata for this particular record to describe this data collection. If you then scroll further down this record, you get to right at the bottom there you can see site this collection. So that's what the data citation looks like. It's got the creator names and the date that the dataset was published, the dataset title and the producer of the dataset. And then there's also a DOI link that is a persistent identifier that links through to the dataset. And people can copy and paste that site this collection. So if somebody, a researcher uses this collection and they want to site that data in their research, they can copy and paste that site this collection feature into their reference list for their article. Okay, how is data cited? So that's one example of how data could be cited. I'm going to speak from personal experience here using my own example, mostly because it enables me to talk about it in detail. But a couple of years ago, I conducted a research project with my colleague Joanna Richardson on the training needs of repository staff and it involved data collection through a national survey. We then had the article published in the Journal of Librarianship and Scholarly Communication. And while the peer review process was going on for the article, we put the dataset in our institutional repository and we used the site my data service to mint a DOI for it. And we then provided a little citation reference to the Journal of Librarianship and Scholarly Communication and they put it in the supplemental content. So if you scroll, that's just scrolling down from that previous top record at their website and you'll see supplemental content and it's got identifying skill sets from repository staff, data file and survey questions. And if you click on that DOI link, you will, you have to do a few extra clicks but you will get through to the actual dataset and the survey questions. And right at the bottom there is the recommended citation for the article so that's not to be confused. The supplemental content is the dataset and the recommended citation is actually for the article. So that gives you an example of what a really nice workflow is and how the Dryad data repository works in terms of the workflow for people publishing their datasets, getting the citation and including a link to the dataset in the article when it's published. So it's an example. So now I'm going to talk about our journey into how we're able to get to this point. So what do you need to pack if you're going on a data citation journey? Well, there are really only two things that you need before you start your journey. First of all, you need some research data collections at your institution that have open, embargoed or mediated access. So you obviously don't apply DOIs or data citation to datasets which are private or closed because no one's going to cite them. Secondly, you need a publicly available metadata record that describes each of these collections and provides access to them or advice about how you can access to them, how you can access them. So you can see that data citation actually comes further down the track after you've done some management of the research data resource. So at Griffith we have a research data repository that's built on Equela software and it hosts our data collections, the files as well as the metadana. And we also have a research hub which I've explained and the research hub draws metadata records automatically from our research data repository along with a number of other sources. So the data repository is feeding the research hub and the research hub is the main discovery service for our data collections and for our researchers and research. So on our journey you might also need managed support and I've given you some pictures there so you can see what we've had at Griffith. So you might need management support to do things like approve the commencement of your data citation journey, to assign resources to carry it out, to review and approve related policy workflows and guidelines, to sign the forms that you need signed to use the SiteMyData service and to be an advocate of what you're trying to do. You will probably also need technical support because you need to develop a technical script to mint DOIs but don't be scared off by that because it's not very complex and we've made ours available for reuse if anyone wants to use that. And you need technical support to mint and manage the DOIs over time as well and to create the citation element display in your discovery service. So just to give you a bit of a picture that these when and why DOI, that it didn't actually happen overnight for us, we've actually been doing this for a while as I mentioned. So in August 2011 we started thinking about persistent identifiers and I wrote a... PIDS is persistent identifiers, so PIDS for data options paper which recommended that we adopt DOIs and then in August at the same time and launch the Site My Data Service pilot and we were able to get agreement from our management to actually go ahead with joining the pilot and becoming guinea pigs. And then September to December we started developing our machine-to-machine scripts and started minting DOIs for our collections. I can't remember exactly what month it was but around May of 2012 we put a site list collection feature into the Griffith Research Hub and October we commenced a data citation project and by that I mean this was our outreach project to go out and talk about data citation to our researchers and to trial some data citation products like the Thompson Reuters Data Citation Index. And then in 2013 that project concluded in May and in September we produced our own DOI guidelines which we've also made available and we're going to talk about them a bit later and we developed a roadmap for where we want to go with our research data management and also with our DOIs and data citation. So when we first looked at DOIs we weren't actually thinking data citation right at the start. We were thinking we needed a persistent identifier and we needed that to fill gaps in persistent identifiers for scholarly works so we had long and incomprehensible URLs for metadata in our data repository and they're still there if you want to take a look they're pretty ugly and we needed a persistent identifier that would be short and easy to read and that would signal long-term management for our research data collections. We also needed a persistent identifier that would contribute to the semantic vision for data in the research hub and by filling in gaps for persistent identifiers for scholarly works I mean we had persistent identifiers for publications through our institutional publications repository but we didn't have persistent identifiers for our data collections, for our theses and for our grey literature like unpublished reports and conference papers and any policy documents that don't go to ERA or Herdsea but that we want to make available for people to discover and also other digital objects like a video lecture with link to research projects and so forth. So later on we needed it as a foundation for data citation as well. So we chose DOIs to meet our needs for a number of reasons first of all because they're a global persistent identifier that are already used in many scholarly publications so Crossref issue DOIs for publications and they're used in many journal articles. Also because DOIs can be assigned to research data, theses, grey literature and even software code now using data site as the registration agency and that is the registration agency that you'll use when you use the Ansite My Data Service. We also needed DOIs to improve the visibility of an access to research data and it gave us a responsibility for managing persistent access to our data collections. So when you meet DOIs you are also making a commitment to maintain access to at least the metadata page of your data collections and if that page changes like you get a new repository software and it gets a new web page for your data well you need to update the DOI with that URL. The signal is that you're going to maintain these data collections over time not just sort of have a transitory thing so also DOIs won't break the institutional repository software. DOIs won't break when institutional repository software has re-indexed sorry about that because handles sometimes do if you re-index software in your repository and DOIs won't break and later we needed DOIs because they facilitate data citation they greatly assist in tracking the impact of data sets through the collection of metrics and altmetrics which use the DOI. So the Ansite My Data Service provided a partnership with an international DOI registration agency that just data site. They provided minting DOIs for metadata records about open mediated or embargoed research data VCs, grade literature and software we haven't done the software part yet but I know the CSIRO have just begun to do that which is great. It's a machine to machine workflow and there's an easily achieved small amount of metadata that is required to mint a DOI. You can also trial it in a safe test environment there's a lot of high level documentation provided and there's a lot of information about data citation on the Ansite website and also it's free. So this is why some of the reasons why we decided to become the first getting pigs to site my data service. How does it work? This is to give you an idea of your workflows so you sign in agreement to use the site my data service and give you an institutional idea. You prepare your machine to machine script and in your script you're going to include the required metadata for each, for minting each DOI which you will already have because you've got metadata for your data set. So it's very easy, the metadata is data set title, creator, publisher, publication year and identifier. And the identifier is actually the landing page for the metadata of your data set, so URL or URI. You execute the script against the site my data service and the site my data service returns the DOIs and you can store the DOIs in your own system and use that to create a citation element which you can just write in your discovery service and you can also feed that citation element in your RIFCS feed back to ANST for display in Research Data Australia. So as an example of our scripts we've got a Python script that you are most welcome to use it's available on GitHub and the link is there if you'd like to read it. So we've minted DOIs but it actually raised a whole lot of questions. So the actually machine to machine technical part was quite easy but there are a number of questions that arose like what's the criteria for assigning a DOI to a research collection? At what level of granularity should a DOI be applied? Is it just for collection of all items or is it for items within a collection like a collection of film and then you have a DOI for each film within the collection or what? Also should the DOI link to the landing page for the actual data or should it link to a metadata page? Which landing page for us? Was it the research hub? Was it the research data repository? And what if the data's changed or updated like a new wave of data is added or a spelling mistake is made and then corrected? Should a new DOI be issued? Should researchers be able to mint the DOI or should we mint it for them? And how are DOIs assigned if the research data is the result of a collaboration between various institutions who can all do DOI minting? If a Griffith University researcher collaborates with Simon from the University of Sydney who gets the data set? Who mints the DOI? Because theoretically there should be one DOI for the data collection. And what happens to the DOIs we've minted if Anne's closed the shop? And finally can you cite data without a DOI? I wrote these questions up in an article called Implementing DOIs for Research Data in D-Lib and that's freely available if anyone wants to read it. We've actually learnt a lot since that time and we've answered most of those questions satisfactorily although the one about collaboration I think is still quite difficult. And I think TURN, Terrestrial Ecosystems Research Network has actually got the best experience in that particular area and we haven't had that actual question arise just yet. But to answer a couple of those questions we decided the DOI does need to link to a metadata page and for us that metadata page is our discovery service, the Research Hub. If the data is changed with a new wave of data yes you should actually create a new DOI. Can you cite data without a DOI? Yes you can, but it's certainly beneficial to have one and I'll talk about why later I've already mentioned a few reasons and what happens to the DOIs we have mentored if ANS closes shop? Well of course they are still maintained because data site is the registration agency used and that's international. So the questions and answers that we found we wrote up in our Digital Object Identifiers and Management Guide and I'll put a link there if you'd like to read them or adapt them yourself. Also ANS helped us answer some of those questions because there was a very good community of practice around DOIs and data citation that ANS facilitated and it wasn't just Griffith asking questions there were other institutions coming up with the same sort of sticky questions and we had quite a lot of events, workshops and online discussions about this and the ANS DOI FAQs have answered a lot of those questions and we also documented our experiences of minting DOIs in the gold standard blog which is now closed because that project is closed but the blog's still there if anyone wants to read some of the painful experiences but the good ones that we had too along that particular journey. So once we'd done the DOIs we put the site's collection feature in the research hub and we fed it through to Research Data Australia so in this particular record it's the same collection as the previous page and you can see how to cite this collection there in the Research Data Australia service. So just some discovery services that are useful on your data citation journey to know about so Thompson Reuters has launched a data citation index and ANS is negotiating for Research Data Australia data sets to go in the data citation index for discovery and also you can link from ANS you can actually log into your Orchid ID and link your Research Data Australia data set in your Orchid profile and on the top right there you'll see there's a video about how you can do that it's very easy to do. On the bottom right there's a little snapshot of one of the Griffith records in the data site content service that's there. So once you meet the DOI because it's done through data site you can actually search for that through the data site search service and that has driven a little bit of traffic to the Research Hub too which was unexpected and we're quite pleased about. So it's just more ways to expose your data I suppose and also put the old metric badge there because DOIs are really important in being able to collect metrics and citation metrics for your research data sets. So to talk briefly about our engagement experiences so after we'd done that we decided we went on this project to talk to our researchers about data citation or a select number of researchers really just it's a trial. So we established a blog for this particular project which again has now closed because the project is closed but the blog's open if you'd like to read some of our experiences there. So we did things like we spoke with our academic liaison librarians about citation practices in different disciplines and we included data citation as part of some standard consultations with a group in health and an individual in environmental economics so it's a relatively small portion of Griffith liaison librarians that were involved in this and also of Griffith researchers. We looked at what kind of workflows we could set up and we're looking at how to incorporate those workflows into our new research data repository that we're building to replace the current one so that you get an email when you've lodged a collection saying here's a citation you can use in your article or wherever to cite this data now that you've registered your collection in the research data repository. And we reviewed our existing information and workflows around Griffith policies and procedures, academic style guides, training materials and so forth and we included data citation in the best practice guidelines for researchers managing research data and primary materials and I need to acknowledge that the work of my colleague Sam Sehl is really critical in this, she led this particular project on the engagement strategies. So the lessons we learnt through this project is that one size won't fit all and it's important to be aware that there are major differences across the disciplines that you would be likely to encounter in a university like Griffith. So we've talked a little bit about style guides which are generally don't talk, this is citation style guides don't generally mention data, but in discussing citation practices with some of our subject librarians it became obvious that there are many other factors that would make a researcher more or less open to a discussion about how data might contribute to the impact of their research. And this could include the types of publishing outlets, their target audiences and the processes by which their work is currently assessed. So we also observed some differences in a fairly unscientific way really that seem to do really with the age and career stage of the person that you're talking to. So more than ever younger early career researchers need to build a profile and seem to be more prepared to investigate nontraditional ways of getting their research out there and that was also a lesson we learnt through launching our research hub project that those early career researchers where they had a profile, they were the ones who were most enthusiastic about keeping it up to date about embellishing it, adding things to it, making sure that they looked very good in their profile. So in working with the group of health researchers we observed that the people who maintain the most interest in the possibilities of data collections being cited were the postdocs, not the more senior staff members. Another lesson we learnt was to choose your time and to be able to find hooks with researchers. So unfortunately at Griffith we don't have any way of knowing when a researcher is going to publish their data. We still get our data collections incidentally when someone comes to us with data or where there's a particular project where we're collecting those data sets and that makes it very hard because it means we could get a data set after an article has been published that the data set has informed and therefore how does the person then put the citation to their data in that article if it's already been published. So ideally an ideal kind of workflow is the one that I described earlier where while the peer review process goes on somebody submits their data set, gets the data citation and then puts it in the article that way and that is the nice workflow that Dryad have. So we've done our best to find other hooks and the first is data deposit and notifications that can be automated around that and we've tried this and during the course of the project we minted DOIs for 14 newly deposited collections and sent the notification email to the researchers similar to the one in the Dryad workflow and these data collections were being identified again after the end of the projects and the final reports had mostly already been published but it was still slightly disappointing to not get a response from the researchers over this communication. So we also thought it was better to have a need to know basis around DOIs so we were interested to hear that other organisations are taking an approach in which the minting of DOIs is by request we'd interpret this to mean that it is necessary for a researcher to know what a DOI is and to have at least a basic understanding of why they might want one but our view is that the assignment of a persistent identifier to publicly accessible collections has benefits above and beyond those that might accrue to the data collection owners through citation and making the minting of DOIs as a rules driven rather than demand driven exercise should remove the need to communicate about DOIs and citation before a DOI is actually generated. So we would still want to include DOIs in the context of full citation information on display pages and in notifications and various kinds of training and information resources but the researchers shouldn't have to understand the ins and outs of DOIs in order to make a decision about whether they should have one or not. So we also think it's important to be honest and realistic with researchers and be careful to not oversell the benefits of DOIs and the benefits of data citation. So there's still a relatively small body of literature around the benefits and because they're researchers they're going to ask about it and we really need more research to be done in this area not just in one discipline but in other disciplines as well to make our case stronger. And it's good that that is happening. So here is a quote from an article that was in Peer J recently from Heather Pivoir and she says that previous studies have found that papers with publicly available data sets receive a high number of citations than similar studies without available data. We find a robust citation benefit from open data although a smaller one than previously reported. We conclude that there's a direct effect of third party data reuse that persists for years beyond the time when researchers have published most of the papers reusing their own data. So this is really about data reuse and publications but it's really selling the advantage of having open data and allowing it to be citable. And just mentioned here that Heather Pivoir is actually going to be one of the keynotes at the e-research Australasia conference. This year in Melbourne if you can make it along to that. And our fifth lesson was not everything can be solved now or by you alone. So it feels messy because we all like things to end neatly and all of our questions to be answered but it's really not possible to be able to do that. So you'll see in this guide that the white circles are collective action that's needed for change in these areas. That's not just us at Griffith but it's actually everybody really. So things like a change in funder mandates around data, publisher policies around data saying that which are starting to change. So we know that costs and nature are requiring data now as part of their publications. So when these change then you've got more of a case for researchers, more of a motivation researchers to do proper data management and to be able to get the citation and cite their data set in their publication. We also need changes to style guides for citations to include data and tools like EndNote and Zotero to include the ability to add data sets which I think is in Zotero that recently made that adjustment. And research quality exercises too at the reportability of data. So in the pink boxes we've got things that we're investigating now and in the near future which is things like information and training for our librarians and also for our researchers bibliometrics and altmetrics. And in the slightly red box we mostly know what we're doing with these. So we mostly know about identifier registration agencies and DOIs. We've got a data repository and institutional procedures around data. So we wrote some of our experiences up in a DLIF article which is also openly available and we did do a more extensive webinar on this when we first finished the data citation outreach project and there's a link there if you'd like to watch that because that has more on our experiences with strategies. I'm sorry to say that we did well but we didn't conquer the world. And on the to-do list are things like embedding DOIs in automated data collection workflows. So someone, it's a bits data set and they automatically get a DOI as part of a data citation email that comes out automatically from our data repository. We'd also like to mint DOIs for grey literature for things like our theses, reports, discussion papers and so forth. We know we can do it but we need to be able to do that. We need to improve the link between research publications and underlying data. So we have the ability to capture that in the research hub but again we can't really do that if data publishing is not yet routine at the institution. We also need to review our DOI guidelines, rules and workflows at future points in time and embed types of metadata such as coins into landing pages so that people can import that into citation tools. So finally just some reflections on our experience. So I think it's important to do what you can with what you have available to you. And the technical minting and maintaining of DOIs is relatively easy and something that, you know, if you've got those metadata records and you've got your open, mediated or embargo data collections then you can mint DOIs and you can start looking at putting the SiteMyData element into your Discovery Service and Research Data Australia. So getting the citation element is as easy as getting the SiteMyData service up and there's also a lot of materials available now on DOIs that is setting up DOI minting and maintaining and there's a lot of material on data citation which is aimed at researchers and research data managers. So you don't need to reinvent the wheel and I think as guinea pigs we did actually go through a lot of this and would be really pleased if people can reuse any of the things that we did so that you don't actually have to start right at the beginning. So you could decide, so the answer is a machine and SiteMyData service is machine to machine but you could set up an administrative interface for minting and maintaining DOIs. So that would be if you want your librarian for example to be able to mint a DOI without requesting the script from the tech... without basically liaising with technical support to be able to do that and Tern have actually done this and they have made that... I believe that they've made a code open... open source but you'd have to have an investment into being able to do that because that front end would run over the top of the machine to machine scripts in the background basically a humanly readable interface that the librarian or research data manager could use to mint and maintain the DOIs. Also establishing workflows for DOIs and data citation is not easy you don't know when your researchers are going to publish their data and if data publication is not routine. I've talked about that in a bit more detail and data citation is not yet common practice but there is a large international community supporting data citation both as a principal and to encourage practice in this area and there's a growing body of evidence on the positive link between open data and citation counts that we use in your arguments for promoting data citation with your researchers. So I'm going to leave it there. Thank you so much Natasha that was absolutely fantastic and a lot of content there so I'd like to take this opportunity to thank Natasha once again for a fantastic presentation.