I'd like to compliment the IEA as well and their great work. It provides a great forum for the nature change of ideas. We're firmly in Europe and we intend staying there. I'm committed to European myself that this forum gives us an opportunity to share ideas and discuss issues. It's very important in civil society that organizations such as this would be there to reinforce democracy. It's my third time in government, as Brendan said. This one is entirely different. It's also different in Europe. I go over back to Brussels and Luxembourg quite a lot and things have changed from the previous council meetings I used to attend. It's got very informal. It's all first names now. It's Michael and Christine and Elena and Wolfgang and everyone chats away all the time. So that's very comforting. Secondly, English has become the lingua franca of the community. Occasional breaks into French. But compared to what it was like when I started in the 80s when everybody spoke their national language and you were picking it up in your earphone. It made it very stilted and formal. Now since they're all fluent English speakers it moves all of them back in real debate. And it's quite interesting. That makes it interesting for ministers in one way and difficult in another way because in the olden days, if I call the 80s the olden days ministers frequently use the pre-prepared speaking note and just read it out to give the national policy position. Now there's a real debate that goes on all the time and you're challenged on your views across the table.  So that's probably the good side of it. The downside of it is that the commission isn't as strong as it was when I was, say, Minister for Industry and Commerce dealing with the internal market. The bigger countries now are taking a lead role. That's even truer in the 17 rather than the 27 because in the 17 there's a tendency called France and Germany to think of the euro as their project and not only did they put it together in the first instance but they feel responsible for keeping it going and keeping it strong. So in that respect, the commission isn't as central as it was and that's bad for Ireland. So one of our policy positions is to always be committed to keeping the role of the commission strong and reinforcing it if we can because big countries, all countries act ultimately in their own interest and big countries always act on their own interest in the long term and smaller countries need to have the protection of their own collegiality and also the protection of the commission. So I think that's a very important point. It's also the case now that the IMF and the ECB are equal partners at meetings. So again that has diminished the role of the commission somewhat but the IMF is a different IMF from the kind of IMF that was portrayed as intervening and wrecking the lives of poor people in sub-Saharan Africa. It's a totally different IMF now and the present IMF leadership is very supportive of Europe and Christine Lagarde is particularly supportive of the Irish position and is very, very helpful. Firstly, to get down to a few words I want to share with you the euro has been a great success. The euro was put in place 12 years ago and since then over the 12 years inflation in Europe has always been below 2% annual inflation. It actually has been a better corrector of inflation than the German mark that Germans like so much. As well as that European trade has increased by 50% since the euro was established and that has led to growth and wealth and good lifestyles for European citizens. As well as that the value of the currency has gone up. Even now that it's under stress it's in the 130s where the euro has been put in place I think it's after the 117 to 120 around the era. And you'll notice that when the Swiss wanted to bring down the value of the Swiss franc recently just four or five weeks ago they didn't benchmark against the yen or the dollar or go back to the gold standard they benchmarked against the euro at 120 which was a very recent vote of confidence in the future of the euro and also in the value of the euro. So I think we should remember that the crisis is not a euro crisis the crisis is a euro land crisis and it's the difficulties in certain countries including Ireland to adopt to a common currency. That's the crisis, not the currency itself and we can be very confident in the currency itself. The reason that there is a problem in euro land is that when the currency was put in place 12 years ago the kind of policy instruments which will be familiar to anybody who knows the United States were never put in place in euro. Things like automatic stabilizers fiscal transfers fiscal bonds being issued by the Fed none of those are available in Europe. So when the euro came under threat the policy instruments weren't in place to defend it and then there was a mad scramble to retrofit the policy instruments to protect the currency and in that mad scramble I'm afraid European leadership has failed until very recently to get ahead of the curve but it's not that nothing was done, a lot was done you know just this time last year there was no ESFF there was no ESFM there was no ESM agreed so you know we have other institutions in Europe now that can give money to countries like ourselves in Portugal and programs none of that was in place 12 months ago when the first bailout for Greece occurred it was done on a series of bilateral arrangements but now there's an institutional framework to deal with that and of course issues of governance have come up the line as well and there is a great movement on that but the failure all the time has been that over the two year period particularly in the last 12 months the solutions have fallen short of the problem and while the markets would be convinced for a week or two or three market turbulence would reassert itself that the solutions were proven adequate so the building of the policy instruments has to continue at long last we thought we had a major breakthrough at the heads meeting last week because for the first time rather than taking individual problems and trying to tailor a solution to them there was an approach to have a comprehensive and integrated solution and I would think it was a very good approach you know recapitalize the banks and deal with all against contagion deal with Greece advance the governance issues so that we don't go back into this again in two or three years time make the fix a generational fix and finally have a growth program for Europe by structural reform across the community and encourage individual growth programs in individual economies that's the package that's there now and you know we thought we had a solution and I think we have a solution institutionally when the work continues and these proposals are fleshed out but then Mr Papandreou called the referendum and that has thrown the markets into chaos again and I presume there are political problems in Greece and I suggest that the solutions will have to be political I've said already to a number of people that you know democracies live by elections and we should never fear changes of government in the last year you remember would the Greenstein government would the leave government would the budget go through would the budget not go through would the government continue would the heaven and charity would the finance bill go through should there be a new leader should there be a new Teshik is there going to be leadership even for you to fall so we shouldn't be surprised when we look at Greece because we've had a very recent experience with a donor leader in an election and usually in a change of administration so you know that's democracy and in the nation which founded democracy I don't think we should be looking to a scans at the fact that they are now look as if the government may be losing its mandate or indeed Mr Papandreou may be strong enough to reassert himself and move forward but I think the solutions of the firewall the gap and all the rest of it are the solutions on which the new Europe will be built on which the currency will be stabilised because for the first time we will have instruments of policy along the lines of the United States which I suppose is the most successful common currency area that we can bring forward as an example and you know imitation is a sincerest form of flattery but if something is working well there are policy instruments that you can model and bring them in for the Europe well then that's what should be done I'd like now to move to our own government here we're seven months in office I think it's an open secret that we we're surprised ourselves that we are further up the road than we thought we'd be just seven months ago we're fulfilling the programme and that's being acknowledged by all our colleagues in Europe and by the European authorities we're also restoring Ireland's reputation in Europe we had a bad reputation I think it came from the Celtic Tiger there was a lot of hubris and there was a lot of arrogance and I'm not just talking about a political level you know we had Irish people lecturing Europeans on how to get rich by selling houses to each other and and they said that's a bubble and now they were inclined to say I told you so when the thing collapsed there was a bad feel there was a very bad feel but we have repaired that the Tarnished have brought all the diplomatic corps back to Dublin and kind of reset the programme for the diplomatic corps and they're they're on a single message now lobbying influential people right across Europe ministers are attending all the council meetings and our staffs are integrating and mixing and making friends and we have a lot of friends in Europe and our reputation has improved and that's very important because you know the thing give a dog a bad name and a lot of what's happening in Greece is give a dog a bad name if you look at their all figures in Greece in terms of the government making fiscal corrections they have made huge strides and yet they're getting no credit at all and you get caricatured images of Greece in the media so reputation does matter it allows you to move forward we're growing again economically the first two quarters have shown significant growth the third quarter we know from many total evidences growing as well and even though we'll have to mark down growth for next year it will still be quite positive growth in our customer countries are falling away and if you have an export growth model obviously if your customers can't buy as much you have to pull back a little bit but we'll use the best evidence in putting the budgetary figures together and we had last April said the growth into 12 would be 2.5% it won't be that now and we'd be pulling it back so that our budget calculations are realistic we're in balance of payments surplus as well and we're going to have another strong surplus in the balance of payments this year and that's very good news as well because if you're earning more than you're spending it's not a definition of insolvency anyway so balance of payments surplus is a measurement of insolvency it's not the only one but it's also very good news if you take Greece about 20% of its economy in exports over 100% of the Irish economy is volume exports a huge difference in the model and in terms of the reputation we're always stressing that Ireland has far more in common with the North European economies like the UK and the Netherlands and Germany in terms of the way we're structured in terms of our competitiveness in terms of the way we do business then we have with the peripheral economies of the Mediterranean where we were bracketed until recently so in terms of resetting the reputation of the country we're strongly pushing the line that we're a North European economy we're prepared to do things of the way and our Europeans do things with their economies and we're prepared to take the correction measures necessary to stay in that group of countries rather than on the Mediterranean group the banks have been restructured as well if you'd be familiar with that that has been quite successful we were very fortunate to get private sector interest in Bank of Ireland and that was one of the confidence building measures during the summer the banks are still building confidence there's an inflow of deposits now in September and October so after deposits declining for a long period they're growing again and also the banks are accessing money on the market so the banks are actually back in the markets now the banks are getting a wholesale a couple of the banks have that wholesale money at 4% on 3 month rollover basis so Ireland may be out of the market but as soon as you get the banks going back in we're moving in the right direction we've renegotiated the program as well you know we said we would and we got a mandate to do it but we don't see renegotiations as a ones off event we see it as a rolling event and we have two phases of it behind us and there's a third phase coming up the first phase was around the time of the jobs initiative I suppose the flag there was the minimum wage but it was only a minor part of it and what was there was we got permission to bring the vet rate down from 13.5 to 9 and to focus on the hospitality industry because you know tourism obviously has to be one of the big industries in Ireland and it had fallen off by 30% over 3 years and all the infrastructure is there it doesn't require additional investment the hotels, the golf courses, the airports the roads it's all there so what you need really is to make the country competitive this was an attempt at that and it worked as well as well as that the adjustment period for the programme is now going to 215 so we negotiated an extra year for the correction process the second phase of the negotiation was something that we argued long and hard that the programme was incorrectly priced and that the interest rates were too high and after kind of five months of constant battle and argument we got that revised in July at the heads of state meeting we got interest rates reduced to effectively the cost of the money on the bond market without margins being added that has made a huge difference it makes a difference like in this year's budget now we'd be in extreme difficulty if we didn't have the interest rate reduction because it reduces our costs on interest rates by about 900 million and that compensates for the fall off and the growth rates which I drew your attention to and for some fall off and better seats as well doesn't give us extra money to spend but if we didn't have it we'd be in dreadful difficulty going into this budget and now it has the swings have cancelled out the roundabouts and this was one of the big swings the third phase of the negotiations is very important and it's something that we're trying to position we want the overall burden of debt to be reduced and this is the argument that we use when we're talking about the promissory note in England Wires Bank but that's an example to get the issue on the table in Europe and we're open to suggestions from them as to other means of reducing the overall burden of debt because while we are sustainable I would prefer if we were 15 or 20 billion lower on the overall burden of debt going back into the markets in 2013 so this phase of renegotiation is more a medium term project but we have set up our negotiating positions already and they're engaging with us they haven't said they'll cut the debt yet but they're engaging with us in preparing policy papers so while I can't tell you that this is going to happen I can tell you there's a process in place which may lead to we getting a reduction in the overall burden of our debt by some mechanism which we will identify as things go forward so I'm quite confident about the future of Europe you can lose your way if you just look at particular events but if you can rise above particular events and look forward Europe is very strong it has 27 democracies working together I mean it's not so long I'll go back to the time when the Berlin Wall was still there and Eastern Europe and it's great civilization was like something that where the deluge had come in and kind of cities that we know from our history books have disappeared from view now Eastern Europe is back there they're in with us, they're thriving Poland has the presidency at the minute they're just having, after having a successful election from the government's point of view because they are re-elected and they're thriving they're moving forward, they're shall grow Eastern Europe they really love the community they really aspire to be members of the community and they're working it hard so we shouldn't be cynical about the community the European project is an absolutely marvelous project it's one of the most historic things that has happened in this generation or in any other generation and we shouldn't let it slip from us through lack of effort there are difficulties one is the diminishing role of the commission which I referred to already another is I suppose the best way of putting it is the growing nationalism across European countries that's an emerging problem which we need to watch very carefully and it's manifesting itself all the time now at council meetings where ministers say quite openly I'd agree to that but I can't get it through my parliament because we have coalition partners on the right or on the left they're taking a very narrow nationalistic view and the country's interest coming before the community's interest and that making it difficult to go forward and you know examples of it across Europe in different countries you've seen the true fins on the part that played in the election in Finland so it's something I just want to put a marker down on the other thing I think where Arlene can play a role is the danger of two Europe's you know there are 17 in the Euro and there's 27 all together and we meet as the Euro group first in Brussels and then we meet at 17 and then we meet at 27 and there is a danger that you'll get two agendas you'll get two policy agendas emerging so I think Ireland and the smaller countries have a role it's in our interest to keep Europe integrated but it has a unit of 27 and not a kind of a twin track Europe with a 17 in the common currencies led by France and Germany driving it forward and the 27 been somewhat adrift you know already there have been suggestions on the margin that as the 10 nations that aren't in the Euro see us meeting every month as a group of 17 and all key decisions in effect now being taken in the group of 17 and being wrong by the 27 subsequently I've heard suggestions that the 10 should start meeting separately you're going down a very dangerous road if that happens so it's again as I presume many of you here are interested Europeans I'm flagging one of the risks I see and I'm flagging an area where Ireland can help to integrate so generally I'm optimistic the budget is coming forward and we'll deal with that the first budgetary document will be published tomorrow and there will be a lot of economic analysis about where we are and what the basis for the assumptions of where we are but more importantly there will be a table in it which will set the targets for the deficit right up to 215 with the one in 215 being below 30% and it will go on then to say what the annual quantum of adjustment will be in each budget up to 215 to arrive at those targets and the quantum will be divided between tax increases and expenditure reductions now we're obviously doing this at the interest of transparency and accountability but more importantly we think that many of our people both in their personal lives and in their business lives are very uncertain of the future and actually think that things are worse than they are and we think that this will help to build confidence by putting it out starkly this is where we're now this is how we're going to get to minus 3 by 215 and these are the modifications we have to make in each budget going forward we won't be breaking it down department by department that will happen later on because there's going to be a number of pre-budget announcements and my colleague Brendan Howlin will give the break down the department the break down before the budget itself so thank you very much you've been a very attentive audience I hope I haven't bored the pens off here so I love the question


Hi, I'm Nathaniel, and in this video I will describe our work on calibrated adaptive probabilistic ODE solvers. Ordinary differential equations or short ODEs are used to describe dynamical systems and allow us to model, for example, the motion of stars or even the progress of an epidemic. Numerically solving an ODE corresponds to simulating this dynamical system forward in time. In our work we take a probabilistic numerics perspective which allows us to describe a posterior distribution over the solutions of the ODE. And in particular we investigate the uncertainties returned by such a probabilistic solver, we propose multiple methods for uncertainty calibration and we demonstrate the use of these uncertainties for adaptive step size selection. But first a bit of background. Probabilistic ODE solvers treat the numerical solution of the ODE itself as a problem of Bayesian inference. A prior chosen as a Gauss-Markov process is related to the solution of the ODE with a non-linear measurement model and artificial zero data points. The posterior distribution can then be efficiently computed with Bayesian filtering techniques such as the extended Kalman filter. Let's look at the solver in action. The probabilistic solver is able to find the correct solution trajectory but we observe that the uncertainties over the extrapolations do not accurately reflect the actual error. In our paper we propose multiple methods for uncertainty calibration and to model the diffusion parameter. For instance, if we model the diffusion with a step function we see that the probabilistic solver becomes more flexible and the uncertainties become more reliable. These calibrated uncertainties can also be used in order to estimate the local approximation error of the solver. And similarly to classic ODE solvers we can use these local errors in order to adaptively select the step size of the solver. These adaptive steps are useful not only for the efficiency of the solver but also to solve stiff problems such as for example the Van der Poel equation shown here. We also compare probabilistic ODE solvers to a classic Runge-Kutta 45 method and we observe convergence rates of similar order. But again, the probabilistic ODE solver returns not just point estimates but posterior distributions and we compare these uncertainties for the different calibration methods and different approximate inference algorithms. So in summary we present calibrated adaptive probabilistic ODE solvers. They provide meaningful uncertainty estimates, they make efficient use of computational budgets, they are able to solve stiff problems and they display polynomial convergence rates. We also develop software so we encourage you to try these solvers out for yourself. Our Julia package provides drop-in replacements for classic solvers from the differential equations.jl ecosystem and in Python we develop PropNum, a package for probabilistic numerics. It provides probabilistic ODE solvers but also algorithms for filtering and smoothing, linear algebra, Bayesian quadrature and much more. Thanks.


When we type, we need to follow some basic typing rules. This video will teach how to type a capital letter. Remember the capital letter rules from writing? Follow the same rules when typing. First, capitalize the pronoun I. In the example I am studying English, the letter I is capitalized. Always capitalize the pronoun I. Second, use capital letters with proper nouns. In the example she is from Canada, the letter C is capitalized in Canada because Canada is a proper noun. It is the name of a country. Other examples of proper nouns are names of people, holidays, and languages. Third, use a capital letter at the beginning of a new sentence. In the example, I check my email every day. My inbox is always full. The letter M is capitalized because it is the beginning of a new sentence. Fourth, don't use all caps. This means that you are yelling. All caps means all the letters are capital letters. It looks like this example. Yelling is rude! Don't type with all caps when you post online because it means you are yelling. In this video, I will explain how to make a capital letter using the shift keys. The shift keys are circled on this keyboard. First, make sure that the caps lock is off. The red arrow is pointing to the caps lock. If the caps lock key is on, all of the letters will be capital letters. To turn the caps lock off and on, press it one time. Let me show you. I will press my caps lock key one time. Now my caps lock is on and all of my letters are capital letters. I will press the caps lock key one more time. Now my caps lock is off. Now all of my letters are lowercase or small letters. Now, let's learn how to make one capital letter. First, hold down the shift key with one hand, type a letter with the other hand, then release the shift key. Watch this video from YouTube for an example. The video is from 123Kevin. Creativity will make it possible to give today's lessons. What you are going to do with the shift key is to use the opposite hand. Here I am going for a capital T. What I do is I bring down my small finger, shift, capital T. Now if I wanted to go for a capital letter on the other hand, shift, capital I. Over on my left hand I press shift, capital I. Let's go for capital E. Shift, capital E. So you use the opposite finger to touch the shift key when you are making capital letters. Typing update, thanks. So remember, you need to use two hands to type a capital letter. For example, to type a capital P, I hold down the shift key with my left pinky finger and press P. Then I release the shift key. To type a capital R, I hold down the shift key with my right pinky finger and press R. Then I release the shift key.


So what happens when we divide a polynomial by a monomial? So remember, a polynomial is a sum of monomial terms. And so we might consider what happens when we have a fraction where the numerator is a sum. And so this goes back to a theorem for c not equal to 0. The fraction a plus b over c is a over c plus b over c. Now we're used to reading this from right to left, because this is how we add fractions. They have to have the same denominator. But we can also use it backwards to split up a fraction whose numerator is a sum. So let's divide 15x plus 3 by 3x. So again, the order of operations requires that multiplication and division be done before addition and subtraction. So if we read this, we have 15x plus 3 divided by 3x. We have to do the 15 times x first, done. And then the 3 divided by 3x next. To emphasize this point, we'll throw that division inside its own set of parentheses. So 3 divided by 3x, well, that's the same as the fraction 3 over 3x. So we can rewrite our expression. And we can simplify that. A useful thing to remember here is that any number a can be rewritten as a times 1. So I can rewrite my numerator 3 as 3 times 1. My denominator is 3 times x. And now I can rewrite this fraction as a product. 3 over 3 times 1 over x. Now I can simplify. 3 over 3 is 1. And so we don't really need to include a factor of 1. And 1 over x is 1 over x. Equals means replaceable. So instead of 3 over 3x, I can write 1 over x. And that's as far as we can go in simplifying this expression. Again, parentheses make a big difference. Here, I'm taking 15x plus 3. And all of that is being divided by 3x. So I can rewrite this as a fraction. Since my numerator is a sum, I can split this into two fractions, 15x over 3x plus 3 over 3x. 15x over 3x. Since numerator and denominator are both products, we can split this into a product of two fractions. So let's rewrite it and simplify. And from the previous problem, we already figured out what 3 over 3x is. And so our final expression, 5 plus 1 over x. Well, let's take a look at another division. So again, every division can be rewritten as a fraction. Since this is a subtraction, we can split our fraction into two parts with the same denominator. And then we can simplify each part. 8x to the 12th over 2x to the fourth. Because numerator and denominator are products, we can split this up into a product of fractions. And then simplify. Similarly, 4x squared over 2x to the fourth, numerator and denominator are both products of terms. So we can rewrite this as a product of fractions. And simplify. And again, we'd prefer not to have negative exponents, so we'll take it one further step. I lie, we'll take it one more step. And so instead of 8x to the 12th over 2x to the fourth, we can write 4x to the eighth. And instead of 4x to the second over 2x to the fourth, we can write 2 over x squared. And we can do this with more terms. We'll rewrite our division as a fraction. Since we're adding and subtracting in the numerator, we can rewrite this as an addition or subtraction of fractions with the same denominator. And now each of our fractions is just a product over a product, so we can simplify by rewriting each fraction as a product. We'll rewrite our first rational expression as a product, separating the variables. Our first fraction, 12 over 2, can be reduced. x squared over x can be reduced. We're kind of stuck with the 1 over y, so we'll leave that alone, but we'll reduce z to the fourth over z. And we'll rewrite our product as a single rational expression. And if it's not written down, it didn't happen. We'll rewrite our second rational expression as a product. We'll simplify the fraction for over 2. x over x, y over y, and z over z are all equal to 1, so this reduces to just 2. For the third rational expression, we'll rewrite it as a product. Then simplify and combine them back into a single rational expression.


Stay put. It's riding up on me. There's false. Massive false set. There's my pit. Very much stuck. False set. There it is. Open. Oh, even in frame. Look at that. This is an ABIS 4145, one and three-quarter inch shot goal. It rates a number six on the ABIS Global Protection Standard. It's fresh. Despite the condition of the package, it is just arrived in the mail from Amazon today. There's the lock. Standard laminated looking thing. There it is. Let's see. Looks like it uses a rotating cam detainer, so I suspect it's not bypassable. I don't know if it's key retaining, but we'll find out. So there it is locked up, and it's not key retaining. You know what? It might be shimmable, although with the square edges, it may be difficult. We'll give it a try at some point, maybe. But there you are. ABIS Padlock SPP'd in probably not record time, but not bad. Anyhow, this is Alex. Thanks for watching. Have fun, and please keep it legal. Cheers.


Thank you very much, Dina, for the opportunity to speak to you all today and for the invitation. I'm just sharing my screen now, I guess you can see it, okay. Okay, so yeah, happy new year everybody. And again, a massive thank you for the invitation. I'm really happy to be able to talk to you about our work on, let's say coherent actually imaging, but for the application for 3D magnetism that we've done over the last few years. And today, specifically, so I'm not going to be going into too much of the details, you know, of the coherent defective imaging techniques, but it's much more of a, sort of a few examples of how they can be applied to be, or they can be incredibly useful to by being applied to specific magnetic systems. So you'll see at the top of the screen that I have three affiliations here. So as I'm, as Dina said, I'm currently at the University of Cambridge doing with my fellowship. But some of the work that I'm going to show to you today was also partly done during my time at the Palshire Institute and ETH Zurich where I did my PhD in a postdoc. So before we get into the details of 3D magnetism and how we can look at them with coherent X-rays, I thought I'd first start off with perhaps the most important part of the talk, which is a massive thank you and acknowledgement to the huge number of people who were involved in the work that I'm going to show you to today, without whom it really would not have been possible. So this ranges from the group of Laura Hyderman at the Palshire Institute and ETH Zurich, though that the Swiss light source specifically at the CSEX beamline and also at the Pollux beamline. And more recently my collaborators in Glasgow and Cambridge and of course the funding, which is always very important. So now on to the topic of magnetism. I thought it'd start with a quick introduction or motivation of why magnetic systems are particularly interesting. And I think the reason that I like to think of it myself is that with magnetism we have a wide range of very rich and interesting physics, but we also have direct possibilities for applications. And this is kind of can be thought of in a number of ways. And there's three main examples that I'd like to tell you about today. First of all, I mean, so the reason why we have so much physics and so many applications is because we can actually use the magnetic materials and tailor their properties in a number of ways. So for example, we have the case that the micro and nano structure of the magnetic material very much influences its behavior, leading to possibilities to create new types of physics in pattern systems, but also being very important for for example permanent magnets and the micro structure is a key to achieving very, you know, efficient energy generation. We also have the formation of topological structures in magnetic systems and I'm sure you're all very aware of the magnetic scourmillon which is has received a lot of interest and a lot of research in the last couple of decades. And of course it's not been long. It wasn't long until there was applications based on scourmillons proposed, such as new possibilities for data storage. And it's also possible to tailor the magnetization and with, let's say external effects, such as here, both with the spin, so we can tailor the spin with for example charge so with the spin tronic so applying currents, but also with other, other, let's say, parameters such as heat or indeed strain. And in this way, as you can imagine, this has already led to a number of applications, including data storage, memory and also sensing devices. So we've hopefully shown you in this slide that magnetism has a lot to offer. And the specific part of magnetism that I am interested in is, let's say going to a higher dimension. Now, when we think about all of what I've shown you today and what we use when we look at magnets, you know, and in everyday life and also in everyday research. The one thing that most of them have in common is that our understanding but also the systems themselves are quite limited to our generally consist of two dimensional or planar systems. So how about going to the third dimension. So we can already see from the schematic that when we go to 3D we have a huge number of new possibilities for geometries. And we actually find in magnetism that there's a, you know, a huge number of advancements in the actual sort of magnetic properties and the magnetic behavior. And a few examples of why this is so interesting. So perhaps the most well known example of a 3D magnetic device is that of the racetrack memory, which was first proposed over a decade ago now. And the idea is here that we take a magnetic nanowire and we wrap it up into a 3D architecture, allowing for very high density data storage in the end. It's not only, let's say, density, though, that the three dimensionality can give us an advantage in. We also have the possibility for new sort of dynamics in the magnetization with very, very fast to main wall dynamics that indeed have been recognized or realized in the last few years experimentally. We have the possibility for really complex energy landscapes and new efforts, going into new regimes of physics and patterned magnetic structures. And of course in topology, so when it comes to topological structures and are very well known magnetic skirmion. And when we go to the bulk, so bulk or three dimensional systems, we can get these skirmion tubes and actually topological transformations within the bulk. And perhaps the most recent example of a 3D topological structure that people are very interested in is that of the magnetic hopfion. And this is kind of the one dimension up from a skirmion and not been experimentally observed yet, but people are very much, you know, on the lookout for them and hoping to observe them in the in the coming years. So, now that we have, hopefully I've shown to you that going to three dimensions in magnetism is a very, that's the interest and exciting direction to go in. However, if we want to explore these things experimentally, we need a new methods. And there are two main regimes of, let's say method development that are needed for 3D magnetism. First of all, the fabrication so realizing these 3D systems, but also characterizing them. So in the fabrication, the fabrication side, there's been a lot of advances in the last few years, and essentially 3D printing techniques of magnetic materials, both with kind of coating 3D scaffolds with magnetic materials, but also directly printing magnetic materials themselves. And as you can see from these examples, we've now got a huge amount of freedom and flexibility in realizing three dimensional magnetic nanostructures. So the next question is the fabrication we've made huge progress in or the communities make huge progress in the next challenge that we needed to advance in was going to 3D characterization and really being able to image three dimensional, you know, magnetization vector fields. And of course, in the last few years, there's been a number of work done with essentially different props. And in order to determine what, let's see, what probe you need, you need to think about your sample and what kind of, let's say the pros and cons of these different systems. So, for example, there's been a 3D imaging of magnetic systems with electrons. Here with electrons we have very high spatial resolutions on the order of nanometers of sub, yeah, on the order of sub 10 nanometers, let's say. But we of course were limited to really thin films on the order of, you know, a couple of hundred nanometers at most. And then we have the opposite extreme where there's been examples of the imaging of 3D magnetic fields in with neutrons. And then here we're looking at much larger length scales. So here, you know, field of view or sample size of even millimeters up to centimeters in size. But again, your spatial resolution is therefore a bit lowers on the order of 10s to hundreds of micrometers. And finally, we have x-rays. So, and this is what I'm going to be talking to you about today. And x-rays are particularly interesting for 3D systems because they bridge the gap between, let's say, electrons and neutrons, I like to think. We can retain the high spatial resolution of electrons, but by using higher energy x-rays, so hard x-rays, we can actually penetrate larger amounts of material up to micrometers in size. So today in the in this talk, I'm going to be talking to you about our work on 3D characterization of magnetic systems with x-rays and specifically coherent x-rays. So when we think about 3D imaging, essentially what we're talking about are the techniques where the idea is that we measure two dimensional projections, so transmission projections of our sample of our structure at many different orientations with respect to your x-ray beam. Now, that's your standard tomography that you get in your of the electronic contrast, you get this the same thing, you know, in hospitals and stuff for your CT scan. So what happens when we go to magnetic tomography? Well, there's a few ingredients that we need in order to realize this technique. First of all, 2D imaging of the magnetization, so these projections of the magnetization for this we need a highly sensitive technique and this is where coherent refractive imaging techniques feed in. So we need to combine these with new types of, you know, setups to essentially work out what combination of projections we need to probe the magnetization fully. And thirdly, we also need reconstruction algorithms to recover the 3D vector field in the end. So first of all, 2D magnetic imaging. And this is, as I mentioned already, this is where coherent refractive imaging techniques, let's see, take their place within, you know, the work that I'm going to talk to you about today. So when we're talking about the imaging of magnetic systems with x-rays, the contrast mechanism that we mainly make use of is the x-ray magnetic circular dichrosis. The idea here is that the orbital angular momentum of our light can couple to the spin angular momentum of our magnetization, a little bit of an oversimplification. But through this mechanism, we gain, let's say we're able to probe the component of the magnetization prior love to the x-ray beam. And what is particularly important to note is that the energy, also the absorption edge at which you're working at, because it's a resonant technique, really determines the strength of the magnetic signal that we're going to probe. Specifically, the vast majority of magnetic imaging, so that has been done in the last few years, has been mainly done with soft x-rays. And this is due to the fact that we have very, very strong X and CD signals in the soft x-ray regime, even up to 100% of the total absorption of the material. However, as I mentioned before, one of the advantages of x-rays that for looking at 3D magnetic systems is that we can go to these higher energy x-rays in order to probe thicker amounts of material. The main, let's say, drawback of hard x-rays is that we have a very weak signal because we're indirectly probing the magnetic electrons of our material. And for this we need a very sensitive and high spatial resolution technique in order to probe the magnetization. In order to, let's say, address this challenge, we turn to coherent imaging. Specifically, we make use of dichroic dichography, where we measure dichographic images of our sample with C plus and C minus polarizations, and we make use of the amplitude part of the complex transmission function in order to get both a quantitative of, let's say, our transmission, but also a very high spatial resolution. And you'll see in this first demonstration of hard x-ray dichroic dichography, we were able to get a spatial resolution of sub 50 nanometers, bringing the hard extra magnetic imaging, or the spatial resolution that we can achieve about 50 times higher than had previously been achieved. And we have our, let's say, our basic ingredient, which is high resolution, high sensitivity to a dimensional magnetic image. The next question is what combination of these images do we need. And what we first of all need to think about there is what are we actually probing. So I mentioned with the XNCD that we're sensitive to the component parallel to the magnetization parallel to the x-rays. And specifically if our x-rays are coming along Z, we're sensitive to the Z component, meaning that if we rotate our sample in the standard tomographic axis, then we are sensitive to the magnetization in the plane. However, we're not sensitive to the component parallel to the rotation axis. And in order to get around this, we actually measure two different tomographic measurements, one with the sample vertical and one with the sample tilted. And then we have the, with this sample holder here, that allows us to probe all three components of the magnetization. Now that we have our 2D images measured, let's say, around these two tomographic axes, we can then turn to a reconstruction algorithm that we've developed in the house in order to recover the three-dimensional magnetic vector fields. So without having gone over this kind of first introduction into the technique, I can introduce you to the first demonstration of this technique where we looked at the gadolinium cobalt pillar, cut from a nugget with a focused ion beam. And the key thing to note here is that it's five micrometers in diameter, which means that with the other techniques that I've talked about before, it would not be possible to look inside. So actually imaging is really the only technique that we can use to look at the magnetization within this structure. So we can, first of all, use a 2D look at the magnetic configuration in two dimensions to get an idea of what's going on. We see, let's say, quite a strong evidence of the weakness of our magnetic signal because with a single polarization, it's very much dominated by the electronic contrast. So when we take the difference between the two circular polarizations, we get these bright and dark patches which correspond to the magnetization point in parallel and anti-parallel to the X-ray beam, showing that the sample is magnetic, but also that there's quite an intriguing or complex internal magnetic structure. So we measure such XMCD images for over, or single polarization images for over 1,000 different orientations of the sample with respect to the X-ray beam. So we use our reconstruction algorithm to reconstruct the internal configuration with 100 nanometers spatial resolution. And as you can see here in this video, can I want to emphasize that this is a static configuration, we're just showing it in a relatively dynamic way. And we have a relatively smoothly varying magnetization, but there's a number of twists and turns in the structure of which are particularly interesting. So we can have a first insight into what's going on inside by looking at a horizontal slice where we've plotted the in-plane magnetization with the streamlines and the color corresponds to the component perpendicular to the screen. And what we can immediately see is that we have a number of topological structures within this system. And this is relatively, let's see here, familiar, maybe of weather forecasts and everything. And this is due to the fact that these topological structures, of course, are not only seen in magnets, but are seen in many different types of systems. We see vortices where the magnetization curls around a central point. And we also see anti-vortices, which are the topological opposite of a vortex. They're more saddle-like structure. And again, these vortices and anti-vortices kind of form what is known as a cross-tie wall that spans the diameter of our micro pillar. But of course, this is a very 2D way to look at our data. So we can go on and look at the volume instead to work out what's going on in three dimensions. Specifically, we look at a sub-volume which surrounds the central vortex. And when we look at what happens to the vortex within this sub-volume, we can notice a few different things. So first of all, we can notice the color, which corresponds to the vertical component of the magnetization. On the left, generally, everything's pointing up. On the right, everything's pointing down. And in between, we have this white surface, which corresponds to the magnetic domain wall. We see actually that the core of the vortex crosses the magnetic domain wall at two points within the sub-volume. And when it crosses the main wall, it changes its topology actually, so it changes its polarization with the direction of the core. Meaning that we expect the presence of singularities of the magnetization. And indeed, when we plot the magnetization in the vicinity of these crossing points, we see what looks very much like a circulating block point, what is known. So a magnetic singularity with a circulating structure in the plane and pointing up and down above and below. And at the other point, we see a more twisted structure that we believe to be an anti-block point. So just as we had the vortex and the anti-vortex, here we have a block point and an anti-block point. And this was the first time that the surroundings of these structures were observed, even though they were predicted back in the 1960s by Feldkiller. Meaning that this is a very nice demonstration of the new insights that we can get with these 3D magnetic imaging techniques. And of course, we've got these new results. Perhaps what everyone may be thinking is, can we really trust them? How do we know that these are really, let's say, true? So of course, we wanted to validate our measurement and we did this by looking or simulating magnetic tomography on three-dimensional micro-magnetic simulations, which had a number of features that were quite similar to what we saw in the experiment. Vortices and block point and anti-block point, so these magnetization singularities. So essentially by simulating magnetic tomography with all the same, let's say, parameters as we had in the experiment, we were able to determine that we're able to get a very accurate reconstruction of these features. And in general have, let's say overall, a pretty accurate reconstruction of the magnetization vector with the vast majority of the individual pixels being, you know, the error of less than 2% in the magnitude, but also a very small error in terms of the direction, giving us a lot of confidence in that what we see in the experiment is really something real. So this was the first kind of demonstration of our technique, but the challenge is not over yet. And indeed, what we are soon finding or what we see with them, we have these huge datasets, and I'm sure many of you in the audience are very familiar with big datasets, but here what we have, the challenge that we have is that we have these millions of pixels, each with three components of the magnetization. And the question is how can we reliably and sort of efficiently identify the relevant structures within these systems. This was a main challenge, how can we delve into these big datasets and identify, let's say the interesting magnetic structures. So in order to do to address the challenge, we've developed a new type of data analysis for our magnetic configurations. And specifically by implementing a calculation, which is that of the magnetic forticity. So I put this equation up on the slide for those of you who are interested, but essentially what the magnetic forticity is, is a quantity that is related to the topology of our system. So we think of our magnetic scourmions, and the topological index that quantifies the topology is known as the scourmion number. Essentially what the magnetic forticity is, is the flux of the scourmion number density. Now what this means is that for topological structures within our system, we would have a non zero magnetic forticity vector. So for example for vortices we would have a vorticity vector pointing parallel to the core of a vortex. And for anti vortices which have the opposite topological charge we would have the magnetic vorticity vector pointing anti parallel to the vortex, again, emphasizing that this is a mathematical parameter that really is related to the topology of our configuration. So we can use this now to essentially identify the relevant parts or the relevant features within our very large data sets. By first of all plotting the regions of high vorticity within our magnetic pillar, where you see immediately that we have this kind of complex network of loops and tubes, which correspond to the cores of our vortices and anti vortices. But it's not only, let's say the presence of topological structures that we can identify with this vorticity vector. We can also look for regions of abruptly changing topology, as we saw before, this would lead to the presence or imply the presence of singularities of the magnetization. So indeed by plotting the divergence of this vorticity vector, we are able to locate singularities or block points and very, very easily compared to, you know, looking for crossing points of different structures here with a single calculation, we're able to identify the presence of over 50 block points and within again millions of pixels. This is a very nice demonstration of how, let's say being a bit clever or creative with our types of data analysis can really help in identifying the relevant structures that are hidden within the bulk of our system. This again, so it's not, not only is perhaps a very overused phrase in this talk, but not only can we use this quantity to identify the location of our structures, but we can also use it to interpret or to understand a little bit more, but some features that we've actually observed. One of the features that I want to talk to you very quickly about is some loops that we've observed in the magnetization. These loops are formed of, again, cores of vortices and anti-vortices where you can see in this cross section, this is a vortex here and an anti-vortex here. And what is very interesting with these structures is that they are about 400 nanometers in diameter and they are very much, you know, a loops, they're very much a kind of contained three-dimensional structure. So we were kind of interested and intrigued by wondering what these are, but it wasn't until we plotted the magnetic vorticity around these structures that we realized that they have a circulating magnetic vorticity, meaning that these are actually magnetic vortex rings. And they're directly analogous to hydrodynamic vortex rings that we're very familiar with with smoke rings or bubble rings and fluids. In more than one way, not only in the fact that they have a circulating vorticity vector, but also the fact that they are predicted to be only stable in a dynamic configuration. So they're not actually predicted to be stable in a static configuration. However, of course, we have observed them statically here in our sample. So the next question was, well, can we understand why these structures are stable? We went on to look if we could see more of these structures within the bulk of our pillar. And indeed we saw a few of them, as you can see here, each with their own circulating vorticity. And we're able to determine, let's see, by looking in more detail and trying to understand that it's actually some kind of static interaction that's responsible for the stability of these structures. So again, without this 3D magnetic imaging technique, we would not have been able to observe these structures. But also this has given us a lot more understanding of the physics behind three dimensional magnetic configurations. So hopefully with these couple of examples, I've shown you that magnetic tomography has already given us a lot of insight into 3D magnetic systems. But of course, let's see, a couple of years ago, we achieved magnetic tomography. We didn't want to stop there. We knew that there was a number of different, let's say, advances in experimental capabilities that we still wanted to see, or a number of directions that we still wanted to kind of make advances along. So we have three main, let's say, regimes in which we would like to improve our capabilities. First of all was going to more flexible experimental geometries to be able to look at, let's say, a wider variety of samples. Secondly was going to the fourth dimension. So we knew that a lot of the most interesting physics of 3D magnetic systems would actually involve their dynamic behavior. So of course going to higher spatial resolution, so could we push down the lens skills that we were actually able to image the magnetization on. So first of all, the more flexible experimental geometries. The first question may be, why do we need more flexible experimental geometries and why is tomography not a one size fits all technique. Well, the point with tomography is that we have tomography is a non-destructive imaging technique for 3D imaging. And it is particularly well suited for cylindrical samples. However, when we have a non-cylindrical sample, so a flatter extended sample as you see with the silicon nitric membrane here. At certain direct, so certain orientations of the sample when we rotate it, we actually block the beam, meaning that we have a loss of information at certain angles, and therefore lose or introduce some artifacts into our reconstruction. Now an alternative imaging technique that gets around this problem is laminography. We're here as opposed to tomography where it's very much, let's see, characterised by the rotation axis being perpendicular to the X-ray beam. With the laminography, we have actually our rotation axis tilted towards the beam at a non perpendicular angle, meaning that for different orientations of the sample with respect to the beam, we actually have a consistent amount of material, meaning that we can look at flat extended systems. And of course, before we could go on to immediately 3D magnetic laminography, what we needed to do was actually upgrade our reconstruction algorithm. So what we've done is we've essentially upgraded it, meaning that all projections measured at all different sample orientations are just combined in a single step, and that the tomographic geometry is no longer assumed in our reconstruction algorithm. Now this has actually led to substantial increases in construction. And with the recent implementation of GPU code, it has meant that it's a lot faster as well. So it's really helped a lot in terms of the flexibility and the speed of our reconstructions. And if anyone's interested in making use of this, it's available on open access online, and of course, if anyone wants to collaborate, then you're more than welcome to get in touch or ask questions. So we have our reconstruction algorithm. The next thing we needed was a setup, and we're lucky for us. The high-resolution tachographic laminography was being pioneered at the C-Sax beamline at the Swiss light source at the same time. So in here what I'm showing you is a video from Mirko, where they looked at an integrated circuit with, again, tachographic laminography. And as you can see, it's very impressive. They go from really these large scales with these large extended samples, and they can zoom in and look at the nanostructure of the circuits with the sub-20 nanometer spatial resolution. So it's a really highly effective, let's say, stable setup for laminography image. So we then go on to make use of this setup for magnetic laminography. And again, another advantage of laminography for magnetic imaging is that this time, because we now have our rotation axis at a sort of non-right angle to the x-rays, we actually probe all three components of the magnetization with one rotation axis, meaning that we only need one data set to one rotation, or projections around one rotation axis to actually recover all three components of the magnetization. And we've confirmed this with simulations of magnetic laminography. So the sample that we're looking at here is a 1.2 micrometer thick gadolinium cobalt film into which we've patterned a disk of five micrometers diameter. And again, we take a dichroic dichography to have a look at the 2D projections of the magnetic structure. As you can see, again, the sample is magnetic, which is great. And we have a very clear magnetic signal where we do see some change in the magnetic structure through the thickness of the disk. We measure 144 of these XMCD images around 360 degrees and for laminography. And we then use our reconstruction algorithm to reconstruct the internal magnetic configuration where we're able to observe that we have the change in the magnetic anisotropy through the thickness of the film, which leads to this transition between a single domain state at the top and a double vortex domain mode state at the bottom, showing that we have a very good reconstruction or very high resolution, effective reconstruction of our 3D magnetic structure that is again mounted on these extended sample holders. So this takes me on to the second point on our to-do list, which is going to the fourth dimension. And it's actually with this laminography or the development of magnetic laminography was a key step in making this possible. Specifically, because we now are able to probe flat extended samples, such as silicon hydride membranes with laminography, we're able to pattern contacts onto the surface of our sample. And in this way we perform essentially a pump probe measurement where we pass an AC current through our strip line, which is frequency and phase matched to the time structure of the synchrotron, so 500 megahertz. And essentially what we do is we measure a laminography data set for many different time delays of the excitation with respect to the X-rays. So we are able to obtain four-dimensional magnetic information. So what we can first of all do is we can have a look to see what this means. So what does 4D data mean when it comes to the magnetization? Well, we can first of all look at the lower half of our sample where we have vortex domain walls. And we see here what I'm showing you is a difference image between a reference state. So we can see that the vortex domain walls are actually oscillating from one side to the next of this white reference position. And indeed when we track the position of the vortex domain walls, we see indeed that we have a kind of breathing mode of the central domain, which all makes sense from a magnetic point of view. It's a really nice demonstration of the fact that within the bulk of our system, we're able to track the position of topological structures essentially. So domain walls in this case with high accuracy. But it's not only the tracking of structures that we can do. We can also perform Fourier analysis of our 4D data, or isolate or pick out the parts of our systems that correspond to the rotation of the magnetization at 500 megahertz. So we can see the frequency at which we're exciting our sample. And in this way we can identify coherent rotation modes of the magnetization that we see are very closely linked to the 3D magnetic structure with them. Let's see the rotation or the modes limited to kind of edge modes in the upper half of the sample, but of course very much in the vicinity of these vortex domain walls in the lower half. And we have this work featured on the cover of Nature Nano earlier last year. So now that we've developed magnetic laminography, and we've taken first steps to actually imaging 3D magnetization dynamics, and the last point on our list was of course going to higher spatial resolutions. And as I'm sure many of you in the audience are very aware, for coherent active imaging techniques, we have a very exciting time that could say in the next few years when it comes to pushing the spatial resolution of our techniques. So when we think about smaller length scales we of course know that we need higher spatial resolution or higher signal to noise ratio essentially in our data. So there's two main ways that we can do this. Firstly is going to higher coherent flux. So with the next day in the next few years we expect, or there's already let's say, many upgrades, either in planning or actually in progress at the moment. So that will provide orders of magnitude more coherent flux. And of course we've got the already the next generation of synchrotrons as well such as Max4 in Sweden and Sirius in Brazil. And with these let's say three orders of magnitude more flux for these techniques, we can expect to really push our spatial resolution down to very interesting length scales for the magnetization. Let's say approaching what's known as the magnetic exchange length. So on the order of 20 nanometers or even sub 20 nanometers where our understanding of the magnetic structures and how they manifest themselves is starting, you know, it becomes a little bit more limited. Now at the moment we don't yet have access to data sets that we can make use of this higher coherent flux. So we've gone in another direction in the last couple of years. And that is going to increase our signal to noise ratio by going to stronger signals in the first place and this is with soft dexterities. And where again, as I mentioned at the top of my talk, we have a much higher XMTD signal, where it's going to be up to 100% of the absorption of our magnetic material. So in the last couple of minutes of my talk, I'll give a quick intro into what we've been doing on the soft dexterities point of view with 3D magnetic imaging. We've not been using a coherent imaging technique, unfortunately, but we've been, we have been able to implement laminography at the Pollux beamline, this with slight source, which meets the use of scanning transmission X-ray microscopy. And as you can imagine, when the soft dexterity regime, everything's a bit tighter, everything's obviously in vacuum as well, but Katarina Witte, a postdoc at PSI, did a really great job of implementing this rotation stage with the, as you can see, the optics and the detector everything in place. And this allowed us to do our first sort of demonstration of 3D magnetic imaging with laminography at the Pollux beamline, who were able to map out the 3D magnetic structure of a target scourmillon. So you see essentially the blue and the red correspond to the magnetization pointing up and down and we have these ring like structures. So, what this shows us is that now by making use of the, let's say, higher sensitivity or the higher XMT signals of soft dexterities, we can now probe magnetic nanostructures and potentially, let's say in the next few years, go on to probing three dimensional magnetic nanostructures. And I think this is also an area where making use of coherent diffractive imaging techniques such as soft lecture typography will really help as well to push down these spatial resolutions to very interesting land scales. So, with that, I'd like to conclude. What I've shown you today is our work on applying coherent diffractive imaging techniques to three dimensional magnetic systems, specifically with our development of magnetic tomography where we're able to, for the first time observe these three dimensional or the 3D structure surrounding magnetic singularities. We've been able to through new types of data analysis, observe vortex rings in the magnetization. And with the development of magnetic lamina more recently, we've been able to map out the magnetization dynamics in 3D. And also, let's say take first steps towards higher spatial resolutions and soft dexterities. So, we're looking forward in the next few years. And we're really looking forward to taking advantage of the higher flux at, or the higher coherent flux at the upgrades and the next generation sinkers will make a huge difference to the quality of the data and the spatial development scales that we can look at the magnetization on. And with that we'll be aiming to look at both the statics and dynamics of 3D magnetic systems, and also going on the hunt for let's say new types of topological magnetic structures. So, in the last second, I'd just like to mention that next year I'll be starting my own group at Max Planck Institute in Dresden in Germany. So I do have PhD positions available. So if anyone knows of anybody who's looking for a PhD, please feel free to put them in contact with me. So thank you very much. And I'd be more than happy to answer any questions that you have. Thank you so much, Claire, for this beautiful impressive talk. I think really this brings coherent applications to a new level. So it's very beautiful to see this. I opened the session for questions. There is already one couple, a couple of them from Ian Robinson. Please Ian, unmute yourself and ask the question. And for everybody else, either you can write them in the chat, or you can raise your hand and I will. I think in my experience it's more effective if you unmute yourself and then we start the discussion. It's nicer. Please Ian. Yes, well, thank you again Claire. Very beautiful work and very impressive to new results from just published last year that's really good. We've got three questions but I won't feed all of them to you right now. Maybe come back later on some of the other ones. But the most curious question is, what is the theoretical reason why the magnetic vortex rings are not expected to be stable? Because to me they're the same as dislocations in a normal crystal and those, okay they're perturbations but there's no particular reason why they should not be stable. And I'm wondering why a magnetic vortex ring would not be stable. So the reason for that, and this is something that we've realised, so the reason why they were not predicted to be stable was that in the theory work that was done in the 1990s predicting the presence of these structures, they mainly they essentially only take into account the exchange due to the fact that these are analytical models and the magnetostatic interaction which is a long range interaction is particularly difficult to incorporate. Now what they saw was that essentially what you need is a nonlinear interaction or effect in order to stabilise these structures. So what people have generally in the last few years have been sort of thinking is that therefore you need chiral interactions such as a gelatin scheme area interaction in order to have stable 3D sort of configurations such as these vortex rings or indeed these hot beyond structures. Now what we've seen in our data is of course that they are stable and we believe that this is due to the magnetostatic interaction that is not often taken into account is of course a nonlinear interaction or a nonlinear effect especially. And in our case this seems to be the reason why we see these structures. So without the DM interaction you still think they would not be stable because again I'm curious. So we don't have any DMI in our systems and that's why we were quite surprised actually to see such structures. These are topologically trivial structures. I didn't go into detail about that but they are not a hot beyond their topologically trivial. But it's really the combination of the exchange and magnetostatics that is leading to their stability and this was quite a surprise I think for the community. If I can continue into my second question I'll skip the third one. I was wondering because of the DMI you would expect that you would see an asymmetry between clockwise and counterclockwise versions of these things but you said there is no DMI here so I guess the answer is you see equal numbers of each chirality is that right? So yeah it's essentially because we don't see any preferred chirality. And I think in our system we have no DMI and that would be a direction we're particularly interested in pursuing is looking at systems that hopefully we can stabilize these structures or somehow stabilize them and therefore look for topologically non-trivial systems. So I believe that although of course we don't need the DMI in order to stabilize these structures probably for higher order textures the DMI would help a lot. So let's hope. Thanks. Yeah there is a question from Ash Thripati and he says maybe I misunderstood but the results you showed are absorption contrast. Did you go on the resonance or to a part of the resonant edge where you could see only phase or is this interested or not? Yeah I can show you a slide that, so yeah you're absolutely right that we are using the absorption contrast of our, sorry. So yeah we're using the absorption contrast and the reason for that is so when we go to, of course with ticography we have access to the full complex transmission function. We have access to both the phase part and the absorption part of the XMCD signal. So you can see in this earlier work when we were first developing 2D magnetic imaging with ticography, you see this quite clearly that we have this absorption in red which we have this peak at the absorption edge. But of course we also have this kind of phase contrast where we actually flip the contrast of the signal, let's say above and below. Now what we found for our essentially for high spatial resolution imaging of magnetic structures is that the absorption contrast essentially gives us higher signal to noise ratio and higher spatial resolution. So that's the reason why we choose to use this absorption contrast part of our magnetic, let's say projections. Now for this, of course, maybe seems a bit strange that we're throwing away part of our information. When we're measuring at the maximum absorption or maximum absorption contrast or the energy that corresponds to the maximum absorption contrast, we have almost zero magnetic signal in the face and that's the reason why we can't use a combination of both. But for example when we come to, let's say thicker systems that would be very highly absorbing and we're already looking at some systems where we're really at the limit of getting even harder x-rays through our samples. That's where the phase may be an advantage where we can measure slightly below the absorption edge and get a relatively high signal to noise ratio in our images. So it's a bit of a compromise in terms and what we've been really looking forward or looking for is optimizing the image quality rather than choosing a particular part. I hope that helps answer the question. Actually, the question following this, is it clear why we have a better resolution with the absorption rather than in phase? So we have looked into this and as far, a few years ago actually, as far as I remember the main reason is just the, let's say, imaginary part of the scattering factor is just a bit stronger in this case. So when it comes to these kind of resonant effects with the magnetization we do just have, we have a stronger, stronger scattering. But yeah, I can definitely look into that again and possibly come up with a better answer if you're interested in more details. Here's another question from me, Lee, concerning the slice of circular left and right data from magnetic tomography, how did you get this? Do you reconstruct the data with circular right and circular left? So that's a very good point. So when it comes to, let's see, when it comes to tomography, you can see or perhaps it makes sense here. For tomography, we have the case that C plus and C minus, no, zero and 180 degrees are essentially the same orientation. So what we actually do to avoid, so we're creating our circular right using a faceplate and to avoid moving the faceplate during the measurement, we essentially just measure with one circular polarization, but measure around 360 degrees. And this way we effectively get XMCD images around 300 or 180 degrees. Now for laminography, where we have this alternative geometry, we have the case that let's say zero and 360 degrees. No, zero and 180 degrees, sorry, are no longer equivalent. So we actually measure C plus and C minus around 360 degrees.  Hi Dina, hi Claire. I may have a very quick one if I do not take time from anybody else. So in your 3D system, I think you can assume that your incoming beam is constant, the property of your incoming beam is constant all along the 3D object that you are, it's not like in optics for instance where if you have a very the incoming field would be transformed and distorted as all along the beam path through the samples, right? Yeah, yeah, yeah, you're absolutely right. We just, we assume essentially, yeah, so we assume parallel illumination and we assume that it's constant. It doesn't change. Yes, that's cool. That's very nice. Thank you. Any other questions? I am sure. I have a sort of a general question because I work with some, I think probably work with some things that may be comparable in like the tomographic department with also with CSACs data with small angle x-ray scattering. I'm just a bit curious, like when you run your reconstruction algorithms on like these big data sets, what sort of time scales are we talking about for like whatever you consider a normal size data set or could you give me some examples of the computation resources and time? Yeah, so of course as you know this very much relies on or depends on the size of the data set, so which is directly related to the volume that we're looking at. The first thing I can say is that when we went to the, let's say the upgrade of our reconstruction algorithm, we went to the GPU, this made a huge difference.  So it's made a complete difference or a huge difference, which really means that we can kind of run reconstructions on the go at the beam line, which makes a big difference. Now for the, to give a couple of examples for the Laminography data set, which for this is a relatively small volume, it's, you know, just over a micrometer thick and a five micrometers in diameter. This takes probably about, I just have a few minutes to reconstruct the internal reconstruction or the internal configuration. More recently we were looking at a much larger system, which was like about 10 micrometers thick and really looking at about 20 micrometers in diameter of the area that we were reconstructing. And this was then taking again hours. So it is quite a computation heavy. Yeah, no, no, I have a similar situation here. So I was just curious. But it's definitely, yeah, it's, it's no more manageable, but I think there's a lot that we can do to. Yeah, as long as it's not like months or weeks. Exactly. Especially once you realize you've done something wrong and you need to repeat it. But yeah, it's, it's manageable. Definitely we're going to look into trying to improve these things. Any more questions from the audience. I will, I have a one, a silly one, so maybe that helps everybody else to bring up some more interesting question. We have a sense why you had this, you have a limitation on the accuracy for the determination of magnetic momentum and direction. Do you have a sense, what is this, what is this due to, what is this limitation is experimental. Yeah, exactly. So, so first thing I would say is the numbers that I showed in this slide so this 2% and 2% in the magnitude and I think it was like 15 degrees in the, in the, in the direction. When we use the new type of reconstruction algorithm where we combine all of the projections in one single step, this gets brought down really decreases a lot. So the main source of error is it is actually a fundamental one. Essentially, it comes from the fundamental thing that's that is to do with the X-ray magnetic circular dichroism so we're sent to do the component of the magnetization parallel to the X-ray beam. What this means is that, imagine if you had to have a hedgehog structure so a highly divergent structure, where we have something you know, things to things pointing in or two things pointing out the net magnetic mass that we get from that is zero. So, and, and of course you wouldn't be able to tell the difference in a projection between you and all in or an all out hedgehog, essentially. So, and indeed that's what we see we've done quite a lot of them, looking into what the limitations are and we essentially get our errors are very much correlated with the presence of divergent structures such as block points or textures in the magnetization. But saying that although there is this kind of fundamental limitation we see that it's still actually works surprisingly well so we'll get higher errors in the vicinity of really the center of these, for example the singularities. But the, and therefore, but that, when we get the error, it's mostly manifests in a decrease of the magnitude of the magnetization so the direction of the magnetization is surprisingly still reconstructed with a very high degree of accuracy. So that is a fundamental thing and we're actually looking at combining this, and let's say this, this type of contrast with other types of contrast to try and get around this, this limitation. So Richard Sunberg as requested. The result's really amazing. Sorry if I missed it. If you've already discussed it about the time resolved images, where you're doing the AC pumping. How often are you taking a tomograph or a lamina geography image there. Could you tell me a little bit about how many positions you're doing how many rotation angles for the time result. Essentially what we did, so we were exciting the sample at 500 megahertz. We were very exciting actually with the or stood field of our strip lines and not directly with the current, and we measured eight, eight time steps or snapshots. And this is every 250 pico seconds. And for each of those snapshots we took 144 or 288 projections so 144 different orientations of the sample, you know, around this 360 degrees. So it's a lot of a lot of data but due to the smaller volume of the, of the sample that we were looking at so this disk which is a bit smaller than the big micro pillar, we were able to squeeze this into the constraints of a beam time. And this is one of the, well, actually we got extra we got we were lucky enough to be given some in house beam time, as well as our, this the official beam time which allowed us to really measure this data. And I think this is one of the main restrictions at the moment is the time it takes to measure these, these data sets so this is something that's also with the increase in coherent flux is going to make a massive difference with feasibility. So that was more of a, if I understand it was more of a stroboscopic measurement it wasn't like single shots you were doing. No, no. The limitation with this that it has to be stroboscopic because we need to measure many different orientations and even for tomography we need to measure many different projections and for a single time stop so I don't think that the single shot technique would be. Would work. Would work. Yeah. Thanks. Thank you. So I see that there is no other people who are asking questions. I actually have one Claire and more generic kids, you know, you were mentioning the development of new sources at the increase of coherent flux, and you know there is a dramatic increase of coherent flux actually in the for obvious reasons. But then the 3d it's maybe not really compatible with it with a soft x-rays but then you're interested in nano structure so where do you see that actually increase dramatic increase or coherent flux in the soft. So actually you can actually help you in your research, considering the difficulty and considering that when you go to such a small structures, then maybe other techniques can be a bit more efficient. Yeah, yeah. So I think it's a really good. It's a really good point. So we have been doing as I showed we had, we have been doing some some soft x-rays or 3d magnetic imaging. And they are okay we're working at the politics in mind where it's a bending magnet so we're very much limited by the flux but the one of the difficulties difficulties that we've been having is that we have highly so when you go to these 3d structures and you have a lot of electronic contrast because it's really quite highly absorbing an increase in flux in any cases really we're really desperate for photons at this case. In terms of the dichography and soft x-rays I think if we want to really go down to interesting then skills and by that I mean even reaching towards sub 10 nanometers spatial resolution which would be really important for these 3d magnetic I think that dichography is the way to go and really rather than perhaps and stick some more or TXM and stuff and I think that's where these increases in coherent flux will allow us to go to higher spatial resolution to really push the magnetic imaging sub 10 nanometers, but also a little bit related to the previous question. And I think it will really help with the throughput of measurements so if we want to do time resolved or quasi static measurements you know where we where we change some parameters such as magnetic field or temperature and stuff and and really be able to measure 3d data sets for for multiple different configurations, you know in the time constraints of a beam time I think this is also that like the pure essentially the time taken for a measurement will really benefit from the from the increase in flux. So I do think that soft x-rays are are going to be equally as as useful when it comes to the upgrades as hard x-rays. I've seen the audience there are many beamline scientists we have a request. Yeah, and so I think having I mean having the the option to measure these. So essentially to measure with high high spatial resolution but also with the combination of for example Laminography or the thermal technology if we have that possibility and we have the reconstruction algorithms so if anyone is interested in, let's say trying out magnetic 3d magnetic imaging at the beamline and I've been more than happy to talk about speaking to people and getting things up and running and hopefully getting more people interested in the technique. Thank you so much Claire. Thank you very much.


Here we are in our QuickBooks online test company file using the accountant view as opposed to the business view you can toggle between the two views by going to the cog up top and switching the view down below. We're going to duplicate some tabs to put our major financial statement reports in that being the balance sheet and income statement which we will do basically every time right click on the tab up top to duplicate it right clicking on the duplicated tab to duplicate as the one to the right is thinking I'm going to tab to the middle and go to the reports on the left hand side open up one of the big favorite financials that being the balance sheet which should be in the favorites it's everybody's favorite report so it'll be in the favorites it should be if it's not put it there then we're going to go to the tab to the right and we're going to go down to the reports on the left hand side and this time the P and the L otherwise known as the profit and loss or income statement I'm going to close the hamburger up top we'll change the range then I'm going to go from 010123 to 123123 run it tapping to the left scrolling up closing the hamburger changing the range to the same range 010123 to 123123 and let's run that as well and then I'm going to tab to the left this is the setup process we will generally be going through every time this is the workflow I usually think of when working within QuickBooks Online having my data input here my reports open on the right we now want to think about the auto miles tracking options within QuickBooks Online mainly geared to help you with your tax preparation to be able to take the auto deduction using the standard mileage rate although you can think about other uses for this tool as well you might want to track your personal miles for example for your own budgeting purposes and it can be used for that purpose as well we'll talk about the way auto expenses are typically deducted for say a schedule see business a bit in future presentations so you can see how this system might fit into your overall system to help you with your tax preparation at the end of the year right now let's just take a look at an overview of where it is located so we're on the left hand side we're looking for the mileage this is in the accountant view where you have it located here under mileage note that if you're in the business view it'll be located under apps I'm going to go back up to the dashboard so we can see that and go to the cogs tab and i'm going to switch to the business view and then under the business view it's going to be down here under the apps now that could be a little bit confusing at first because it kind of leads you to think that you have to actually basically connect to the app before you're going to see this mileage item here and that's not the case in other words you might be thinking well that means that I have to go into this apps area and then search for the quickbooks online auto application that's not the case it'll generally be here just with the normal quickbooks online I believe the logic of putting it under the apps area is that then you could integrate this with an app on your phone so if you want to integrate it with an app on your phone then you do have to download the app on your phone and that can help automate the tracking of the miles which we'll talk a little bit about in future presentations I'm going to go back to the switching the view to the accountant view let's go back on into the accountant view and then I'm going to go to the mileage on the left hand side so this is what the screen looks like when you just first go into it says track mileage automatically and get point six five five dollars a mile that's 65 and a half cents a mile and don't forget that hey penny because it adds up when you have a lot of miles in any case where do they come up with that point six five five in essence they're taking that from the tax code for auto deductions if you're using a mileage method generally geared towards an aimed at sole proprietor types of businesses that report their taxes with the help and use of a schedule c so that's kind of a primary target for this tool we'll talk more about how to deduct automobile expenses for a sole proprietorship in future presentations because I think that'll help us see how we might integrate this system into our bookkeeping system that might help us to make our tax preparation a little bit more easy at the end of the year but you can also use this tool for other purposes as well you might want to track your personal trips so that you can get a better idea of the personal costs and habits and so on on the personal trips and it does that as well so it says here get the free quickbooks mobile app point your device's camera at the code and a link will pop up so here's where the application comes into play remember this here I didn't I didn't add an application to get to this on in quickbooks we're just going into quickbooks in order to see this but if you want to link and integrate this onto the phone then you're going to have to have the app on the phone that will integrate with your quickbooks and of course the quickbooks is on the cloud so you can get into quickbooks either on the phone or on some other device such as a desktop so me I would imagine using this type of system having the integration on the phone and then and then tracking the miles and then on the desktop typically when doing the bookkeeping I would manage the miles and then allocate the trips to either business trips or personal trips so in essence if you have the app on the phone then the phone can kind of automatically track your miles and track where where you are going and then you can either on the phone or in your desktop computer now that it is integrated go into your system here and allocate all of your trips as business or personal now that's pretty neat pretty cool that it can it can do that because then it's going to track all of the places that you've gone and you can basically allocate those out although it's also can be a little bit weird when you're not used to that because it's like it's tracking basically everywhere you go