OK, shall we start again? Today's second speaker is Professor Henry Park at T.S. Please welcome him. Thanks for the introduction. And I know all your tangents. I learned a lot about stochastic somodynamics from Professor Chesson Lee last week. I think there are some new faces here. So maybe didn't learn. He taught you from the very basics to the very recent hot topics like TUR and speed limit. My talk is also about one example, using the stochastic thermodynamics to resolve the very longstanding issue for controversial problems raised in the conventional thermodynamics. Basically, I'm going to talk about the heat engine, even though the title looks horrible. It's very long and on saga or whatever. But it's a very simple problem. You know, the heat engine. What do you want to do with the heat engine? Usually, you want to increase the performance, make a better performance. What is better? Better is power. You want to increase the power. Or so you want to increase the efficiency of the engine. So you have to, you want to increase both of the power and efficiency. But is it possible to do that? Is there any kind of trade-off relation? If you increase the power, then you have to sacrifice your efficiency or not. Those kind of questions. So I'm trying to answer to this question in this talk. So starting from the very basic heat engine, you can find in the freshman textbook. You have an engine, a two-terminal lead, you have a two-terminal two reservoirs connected to the engine. Hot reservoir and cold reservoir. And hot reservoir will release some energy in the form of heat to the engine. And you can use part of this energy to the useful work. And remaining energy is going to be dumped into the cold reservoir. That's the basic thing. What is going on in this? Cyclic engine or the steady-state engine or whatever heat engine. Analytics is obvious. This is energy conservation. Coming in should be same as coming out. Interesting thing is thermodynamics. Because we know all the thermodynamics second law must be satisfied. So you have to capture total entry production. But engine is in a cyclic state or the steady-state. Engine does not have any contribution to the entropy increase. Only the two reservoirs. But these reservoirs lose some energy. And this is in equilibrium always. So entropy change can be written in terms of Claus's form, which was found very long time ago by Clausius. So this reservoir loses some entropy. But this guy, because you have an energy increase, increase of total entropy. So if you add up all these, they must be positive. This is second law. And one important thing is efficiency. Efficiency is something like how much you can do with some input energy. So W divided by the input energy. Put these things into here. These two occasions, usually these two occasions you can easily find. Efficiency has an upper bound, which is called Carnot efficiency given by the 1 minus temperature difference. This is all in the freshman textbook in general physics. It's a little bit more useful to rewrite this equation in terms of Carnot efficiency and enterprise production and the work. So I get rid of these all heat energy terms. Then you can easily find you can rewrite whole thing in this way. By looking at this, then you can easily see how to get to the Carnot efficiency. So this is usually for the cyclic engine. For the steady state engine, instead of this guy, you can use the enterprise production rate and work rate. This work rate is basically power. OK. In order to reach the Carnot efficiency, obviously this is 0 if eta goes to eta. See? In order to make that, what is the requirement for that? It's almost only s star equals 0. If s star equals 0, then this is 0. This is usually not OK. Enterprise production rate is 0, means usually we are thinking about the quasi-static process, which we learn as a freshman. But this power, w dot, doesn't have to be 0. If it is 0, then sometimes it can cause more problems because 0 divided by 0. So basically, some of the acetylene does not prohibit finite power engine with Carnot efficiency. So you can have a finite power in principle. It's not banned by the thermo acetylene. This engine with Carnot efficiency and finite power people usually call this a dream engine because people thought if you have a Carnot efficiency, then somehow you are thinking you cannot have the power. Then that's a useless engine because you have no power. But even if you have a maximum efficiency but with a finite power, then it's going to be a very useful engine. So this is a kind of dream. All the recent debates started from this paper by Benetti Saito and Cassati in Pierre about 11 years ago. They really calculate the efficiency and power in the frame of linear irreversible thermodynamics. Looks, sounds terrible, but it's basically linear response theory. It's something like you have again a hot or cold reservoir and you have a channel. So then the energy can flow from hot to cold. But if you also add a potential gradient like a chemical potential gradient, then particles also move. If particles move, then you can say you have some kind of work coming out because you move something from here to there. So you have a particle flux and you can have a free heat flux in the linear response regime. It must be linearly depend on this external force. External people call this thermodynamic force. We have some coefficient like that. OK? So of course, there is no gradient and there is no current. This is equilibrium situation. But if there is a gradient, then there is a current. One of the amazing discovery by Onsaga, the so-called Onsaga reciprocal symmetry, is these off-damer elements are symmetric. They are same each other. Onsaga got the Nobel Prize in chemistry by this work. This is, I'm not going to derive the whole these things here, but this Onsaga reciprocal symmetry is based on the time reversal symmetry in microscopic dynamics, if you follow his derivation. However, Kasimir, the later, he found when you apply the magnetic field for the electronic system, the magnetic field obviously breaks the time reversal symmetry. So if you break the time reversal symmetry, then Onsaga symmetry doesn't have to be satisfied in general. However, he found interesting symmetry. If you change the magnetic field upside down, then you have this kind of symmetry. So this B field is up for example. This B field is down. So these two equalities, these coefficients are for the different system. One is magnetic field up, one is magnetic field down. Whatever he found interesting symmetry, this symmetry, Onsaga symmetry is broken for a given system. Using knowing all these things, they try to found from this linear response theory, they try to find the efficiency and power and all kinds of stuff. And I'm not going to tell you the derivation, derivation is rather simple, but this is the result. This is a normalized efficiency, normalized against the current efficiency. Here is so-called asymmetric factor, the symmetry between these two of them on an element. And forget about this red dashed line, I don't know how to get rid of these things because I got these things from their paper. This blue line is the maximum efficiency you can get for a system with some S, with a system with some H symmetry in general. And they found this flat line, along this flat line, obviously this is one, so this is current efficiency, and this flat line and the production rate is zero. But more importantly they found along this line, power is given by this, as a function of S. So what this means? When S equal to one, this line, this is usual microscopic term of symmetry, then this is the maximum point you can have, so current efficiency can be reached, but unfortunately on S equal to one, the power is zero. That's why we could not find anything with current efficiency with finite power before. But their suggestion is if you break the time with a symmetry, then you can go to this symmetric factor to not equal to one, then this is maximum efficiency, still current efficiency, and the production rate is zero, but work is finite. So there is a way to get the dream engine. This publication triggers many, many further studies to find really the dream engine is possible or not. How can you make the dream engine explicitly? So they do the same calculations, for example, so-called two terminal transport problem, which is temperature difference and chemical potential difference, electron transport in the classical limit, the magnetic field region. Then following this theory, on the Saga Symmetry theory, this on Saga Symmetry possibly broken there. But however, explain calculation show this on Saga Symmetry is not broken. This on Saga Symmetry result does not disallow the symmetric coefficient. They only say these two guys are same. So for example, if coefficients is even function of B, then these two guys must be the same. So unfortunately the could not find the asymmetric on Saga coefficient, where you can find the dream engine like that. So they went for a little more complicated system, so-called three terminal transport. We have two terminal, but you put the one terminal in between so you can control another, whatever parameter system parameters and try to find whether, and where the magnetic field is all there, then on Saga Symmetry does not have to be conserved. So they really found on Saga Symmetry is broken, is L is the matrix of this coefficient. So in this three terminal cases, L is three by three matrix. They found this. Wow, it's great. However, in this linear universal formulaic formulation, anthropocernical zero is not allowed in their calculation. So this is group, this is back. So again, you cannot find the dream engine at all. Right after that, inspired by the symmetric uncertainty relation, which you learn lasted for, I think more than two hours from Professor Jason Lee, this is based on the stock test of thermodynamics. So people try to calculate, is there any kind of similar trade-off relations between the power and efficiency? Indeed, they succeeded. Yeah, you see that this is only by one year later after T-wall was reported. They found so-called power efficiency trade-off relation is expressed in this way. You see left side is power, and right side is this, and theta by some kind of system, detail dependent constant.  That means W dot cannot be positive finite. So they concluded probably there is no dream engine, not in the linear response regime and whatever, in general framework. But they calculate based on some kind of Hamiltonian systems. So it is not real general, general all different type of non-equilibrium systems. So later on, the same side, same side part, using the his uncertainty relation and derive this kind of trade-off relation. It's the same thing, but only the coefficient is a little bit different. This coefficient is basically work fluctuation rate. If this is not diverging, usually not diverging, then this is finite. So again, you cannot have a dream engine. However, I think you learned last week, this T-wall, standard T-wall only satisfied only for the overdamped systems. But in the same year a little later, another group, Decent and Sasser, derive much simpler looking trade-off relation, which is given by this. The car is also some kind of constant depending on the details of system. Using not T-wall, but another kind of trade-off relation is so-called entropic bound on currents. So when Eta was at the sea, he sees also you cannot have a finite positive power. This system is basically can be applied to the, this result can be applied to the under-damped, general under-damped and over-damped long-term dynamics, even with magnetic field. So story must be closed because they found even magnetic field, you cannot have a dream engine. But the problem is, then what is this, this guy's result about Benentie and Saito and Kasati. Magnetic field is on, then you can have unsurpassable coefficient can be possibly asymmetric. And some people found in the complicated structure you have really, Gonzaga symmetry is broken. Then what is the, so basically two results are not consistent to each other. So what is the problem? So this is the question you are asking. Two-terminal heat engine, because three-terminal, we know that your entropy, zero entropy production rate cannot be reached. Still we are looking at two-terminal engine with broken unsurpassed symmetry. So is it impossible? That's the one possibility, but maybe it's possible. So the remanding can be really there because their calculation is also only applied to the discontinuum dynamics with magnetic field. So you may have something else. Or this is still possible, broken unsurpassed symmetry possible, but the remanding is not realized due to some other reasons. So that's the question you are trying to answer in our paper and I'm trying to answer to you today. Answer is of course this. So the conclusion is unfortunately you cannot have a dream engine, whatever you do. But there is some other ways. So we are only talking about the magnetic field here. Okay, let's go. And so to show that we are going into the exactly solvable model, which is something is nonlinear, you cannot solve in general. So you go to the linear Brownian particle engine, so-called, is under that system V is the velocity vector. And this is linear potential, harmonic potential case, whatever, stiffness matrix in general. You can have a non-conservative force like a torque inside of the system and magnetic field, Lorentz force. And the friction term is gamma in the friction matrix and psi is noise, noise can be noise for each component of the loss vector. You can think of each component of the loss vector as a velocity for the given particle. Well, v1 is, you can think of about vx, v2 is vui, but also you can think about v1 is first particle velocity and v2 is second particle velocity. But anyway, they are in a different temperature. You know, to make a two terminal engine, you have to have a temperature gradient. Okay, this is a simple system because even though this is linear, it's difficult to solve. So we go to the most simple system, two particle system or the two-dimensional system. So you have X1 and X2, one is T1 and one is T2, one particle is here, the other particle is here, and these particles are only doing the one-dimensional motion and they are all inside of this harmonic potential or harmonically interacting, whatever. So I'm thinking about this kind of system. So concretely, K is given by this. Non-conservative force is asymmetric of the element, it's generating a torque. And between these, of course, low-range force and this patient is just taking a simple identity matrix. You will solve this. Well, I'm not gonna show you the derivation, but you need the stochastic thermodynamics tools or technique to calculate the heat and all that in this calculation. So unfortunately, you learn all these stochastic thermodynamics tools last week, so you can do that by yourself. This is exactly so, Bobu. And you know, this guy, the Onsaga-Kashimi symmetry must be satisfied. Well, unfortunately, this is even function only. So Onsaga symmetry is restored even with the magnetic field as I advertised in the previous page. So no dremensin at all. Then one of the, my poster got an idea, go to the three-dimension.  However, there is a way to escape out of that problem. That problem, we take three-dimension, or a stiffness coefficient here, same, and this is torque. So basically one, two, three-dimension, torque is around this way, a magnetic field in general. But main thing is we take this gamma only two-dimensional. The one guy is zero. And I'll take this temperature matrix, T1 is zero. What that means, what that means is this. This second particle is here, first third particle here, but first particle is outside of a reservoir because first particle is not connected to this because this is zero and T1 is zero, it is basically deterministic. So we have two terminals still and three-particle system. Is it clear? No? No, you have a third terminal that I just cut. Cut link to the third terminal means third reservoir. System is one, two, three-particle, okay? So this means this first particle, system is composed of three-particle, but this guy is connected to the low temperature, this guy is connected to high temperature, but this guy is outside of two reservoirs, okay? Then terminal means reservoirs, connection, okay? So this is the situation. We try to solve this thing analytically. It's horrible calculation. It will be three-by-three, exactly solvable. We succeeded in that and I'll show the one coefficient. For general B is too much complicated, so we take the BX equals zero, then we calculate L12 and L21. This is often an element of one side of the matrix. It looks horrible and this inside of this, here the C is also given by that, but if you look at, really carefully, then this C is all even function in B, so this C is all even function. Only thing is, oops, only thing is you have this guy and that guy. You see that this is just a minus sign in each other. This is all the function, so it is also where what, Casimir symmetry is conserved here, but also what symmetry is broken. This guy is different from that guy because of this BZ component, okay? So we found two-terminal engine and on-service symmetry is broken. Then what do you expect? Deneity, Saito, and Kasati theory in the linear irreversible thermodynamics, you can have a dream engine. You can have a finite power with current efficiency. On the other hand, then what about Dechen, the Sasa? He said, his derivation is also very simple. He showed the under-damped along the way, even with magnetic field, power should be given by this, so dream engine is impossible. So these two theories are contradicted to each other. What is the problem? It's a very simple problem. The stability of the steady state. Even though the K here is positive definite, torque force is there. It is still okay, we torque force solely, but you have a Lorentz force here. They combine each other, sometimes system can get out of the stable steady state, which has been known, the, this kind of stability has been known only two or three years ago. People thought B field doesn't do nothing, so you have always a stable Boltzmann distribution. But as soon as you add the torque, B field is a combination of effect on the system, and system can be out of the stable non-nuclear steady state. Linear irreversible thermodynamic, they do not think about the stable steady state or unstable steady state. They just think about, okay, you had a single is a steady state, stable, then there it is going on, okay? So we checked the stability of this thing. In some cases, analytically some cases, too complicated, we go into the numerical test to find out the stability analysis, stability region. You see coming back to the first page of this guy, this is Eta, Eta C, WDadiq, the positive along this line, and of course in our system, as is once I estimate the broken, so we are somewhere here.  Where is the stable region? Immaculately, it's all unstable. And stable, on a single one, the stable region going up to reach the top plateau. No other reasons going in. So controversy between this resistance of dream engine of these old walls from the Onsaka symmetry and all that is not really a controversy. If we consider the stability condition, if stability condition is there, then there is extra constraint, then you're gonna have no dream engine is possible. How much time? Yeah, I'm good. This is my last speech. So this was the question you are asking at the beginning. And so is this. Two-tone heat engine with broken Onsaka symmetry can be realized. However, stability requirement make the dream engine realize, make dream engine not realize, impossible. That's our result. And this trade-off relation by power and efficiency by especially Deton and Sasa is working. It's really solid result, even with magnetic field, so impossible. But there is a way, we know, we work very long. You know, to break the Onsaka symmetry, which gonna basically prohibit the dream engine, you can use some other non-magnetic field. So using some other external force to break the time-reversed symmetry, then you may have a dream engine. So one example is velocity-dependent force. Broken, of course, it's a time-reversed symmetry. Broken, which can be realized by active reservoir, which is very popular, I guess maybe next speaker wanna talk about it. And it's a first cooling in the plasmus, cold damping, many where a phenomenological velocity dependent force is really present. So in there, if you use that kind of things, you can realize the dream engine possible. Also, Deton and Sasa's result about this power-efficient trade-off is only for the under-damped long-jabang dynamics with white noise. You can have non-mocovian noise. Basically, this active reservoir is also considered as a non-mocovian active reservoir, memory, or nobody will look at the discrete dynamics. We don't know whether there the dream engine is possible or not. That's the still open question. Thank you for your attention. Any questions? So how would you define the dream engine for discrete dynamics? Carbon efficiency or the maximum efficiency with finite power? But I mean, it would stay at the delta W over delta S state. There's no W dot and S dot. No, S dot can be zero. If S dot is zero, then you have a carbon efficiency. The double dot is finite. Discrete system? Yeah, yeah, yeah, that's right. How come I know? I don't know about the discrete system. We tried for the, you know, the quantum heat engine problem is basically because the state is discrete in the system. You can think about this here, the jumping system. Right. But that's an example. Example-wise, if you solve it, you cannot find a dream engine. However, there is no general proof like a Dacheng and Sasa for the continuous dynamics. That's the only thing I say. If you go to the new quantum system, coherence factor also change a lot so carbon efficiency can be overcome. So that's all different problems for the quantum case. Another question? So you've been only talking about the steady state autonomous heat engine. So is there still not possible for the periodic heat engine? Cyclic engine. Yeah. Cyclic engine is also can be included by in the Dacheng and Sasa formulation. So even in the cyclic engine, you know, at least if you follow the Dacheng and Sasa, you cannot have a dream engine. Maybe I missed it in the three particle system. How this temperature was zero in the particle one. Are we set to zero? For example. By a steady state or something? You know, you have particles interacting each other. Then these particles inside the one reservoir. That is T1 and T2. T1 and T2. And they are totally connected, these two particles. Yeah. And the particle in the middle. Middle can have T1 minus T2 kind of, I don't know. No, we can interact. But this guy does not inside of the reservoir. It's something like, it's a very simple form of heat transport in the long chain. One end particle is in the reservoir T1. The other end you have T2. But the other particle between is not in the reservoir. Temperature is zero of that product. We set the temperature is zero because it is outside. Temperature zero is nothing but there is no interaction between the, there is no interaction between the stock that's reservoir. That's all. Okay. Other questions? Only thing because, just one mention. Because this is life science workshop, I did nothing about the life here. I think Professor Shen already talked about a lot of life. But heat engine is, can be connected to the biological engine, you know, the many ways. Especially information engine. That guy just have talked about the last week. The virus is sensing something, taking information and going to the that direction type of information engine. But information engine genetically can be converted to the heat engine. One-ton mapping is possible. So if you learn something about the heat engine, then you can also learn about the information engine. Through that bridge, you can reach the life science. Okay. Okay. Let's thank Professor Park.


Good afternoon everybody and welcome to this webinar with the Institute for International and European Affairs. My name is Dario Kallig and I'm the chair of the UK group in the Institute and it really is a great pleasure for me to welcome Tommy Gorman. Tommy as you know has been the RTE man in Belfast for 20 years where he played a central and essential role in explaining in a very profound and complete way to people listening to him. Pop was happening in Northern Ireland before that of course he was in Brussels where he played an equally important role just before the end of the 20th century in explaining to people in Ireland what was happening in Europe so it's a great pleasure to welcome Tommy. He will speak to us on the future for Northern Ireland and the relations on these islands. Tommy you're most welcome the floor is yours. Thank you very much Dahi and it's lovely to be talking to people at this really important time in our history. I retired from RTE earlier this year I had 41 wonderful years there but you don't retire your temptation to watch things to analyze and to try and see where things are going so I'm glad that in recent days I started working with colleagues in a publication or in a website called A Currency and I intend to be providing two long reads there once a month for a start. So on a day like this when we live in such uncertain times it's it's I suppose it's a very human reaction to look somewhere for a ballast and to look for inspiration. So I think back to the day in 19 sorry in 2008 May 2008 when Tony Blair gambled correctly on like a rack on the Northern Ireland peace process when Bertie Hearn was also about to have his role and possibly what was the greatest achievement of his political career. That's the the the contribution they made to the restoration of devolved government in Stormont and I suppose it was extremely novel because it brought together the two opposites Shane Fain and the DUP at the head of that government and on that day Ian Paisley walked down those marvell steps in the Stormont chamber and he quoted Ecclesiastes tree he said there's a time for everything a season for every activity under the heavens a time to be born and a time to die a time to plant and a time to uproot a time to kill and a time to heal a time to tear down and a time to build and as I see it we are now in the era one that can't be avoided of a number of reckonings and we discuss the reckonings that I'm referring to in detail later in this conversation but first of all I think it's important to take into account about Ian Paisley that he even though he was the all-powerful leader of the DUP helped in a great way by the chief strategist of the DUP Peter Robinson Ian Paisley had to look over his shoulder within his own party too I think back to a time in November 2006 they had come back from Saint Andrews where there had been a political breakthrough and Ian Paisley gathered his troops in Stormont early in late November November the 24th 2006 and on that day Ian Paisley was attempting to deal with I suppose an upsurge of opposition within his own party they were called the 12 apostles and they were very very wary about the direction he was about to take about the signal that he was about to give that he was prepared to go into government and miraculously on that day from left field Michael Stone a loyalist paramilitary out on prison on out from prison on license attempted to get into Stormont it was a huge security rampus the building had to be evacuated and that managed to buy time for Ian Paisley the devolutionary refer to earlier was in 2007 not in 2008 excuse me so then the following year 2007 Paisley led the DUP into power sharing May 2007 within a year he was gone moved to one side moved to one side because he was in his 80s and the difficulties of being at the dispatch box once a week dealing with questions on his flow on the floor of the house in Stormont also some of the reluctance within his own party that he was pursuing this chocolate brother's relationship chocolate brother's a phrase coined by Jerry Moriarty of the Irish Times this chocolate brother relationship with Mark McGinnis that was causing some dissension in his ranks too so Peter Robinson took over as leader of the DUP that was 2008 just a year Ian Paisley had he had a year as leader and first minister then Robinson took over and Robinson in turn even though he was a very very able strategist he too had his difficulties you'll remember when he went to Florida on holidays was it in August 2013 and he dispatched that letter from Florida which really irked the Martin McGinnis and shame fame because he was withdrawing from some of the commitments that he had made including plans for developments and what was decided the old may his prison that was called a letter from Florida Robinson continued in power sharing the relationship and remember it's a unique relationship this mandatory coalition model was far from perfect as it was attempting to find its feet we always have to remind ourselves that it's a unique relationship in Western Europe this mandatory coalition model so Robinson in 2015 was still in power and one day he was due to go down to address a meeting in Dublin of all places and he had health issues an ambulance was sent for and he was subsequently told that having continued with his travels he might well have been dead by the time he reached Newry Peter Robinson required stents uh it forced I suppose or it encouraged a revaluation of his life and at the end of that year Peter Robinson stepped aside that was the end of 2015 and he came into 2016 so now there's a new leader and this is Arlene Foster Arlene Foster who has moved earlier in her career from the Ulster Unionist with Jeffrey Donaldson to the DUP one of the hammer blows against David Trimble and the Ulster Unionist party one of the factors in the growth of the DUP so Arlene Foster is in but she too had to look over her shoulder I remember she was at the Euros with Martin McGinnis in France in 2016 McGinnis was pushing her to go to an Ireland match and a Northern Ireland match as a symbol of a united power sharing administration Arlene Foster was reluctant to do so remember to in her first year um August in that summer of 2016 the Brexit referendum took place. Brexit referendum that had Arlene Foster and Martin McGinnis scurrying around to see what sort of a response they could have that would try to keep their show on the road despite this decision about Brexit and they spent over a week drafting a two-page letter it included in a clause we need to retain as far as possible the ease with which we trade with EU member states that was a Northern Ireland response that was the summer of 2016 and then if you look at what happened towards the end of 2016 George Bush became president of the United States Martin McGinnis was diagnosed with cancer and towards the end of 2016 Arlene Foster was now a year in his first minister the difficulties about the renewable heat incentive controversy began to emerge in a very dramatic way so before the year was out Martin McGinnis's health had worsened Arlene Foster was under such pressure that Sheen Thane was was preparing to withdraw from government and power sharing collapsed so that was the start of 2016 there was no power sharing administration you look at what happened since you had the efforts by the British and Irish governments to get devolved a government up and running again Jerry Adams before he left as Sheen Thane leader before he retired from that position he made one final effort to broker a solution with the DUP to reflow power sharing that didn't work and it took the efforts of Simon Coveney and Julian Smith on behalf of the British and Irish governments and the pressure I think from the electorate to get power sharing up and running after three years down so now you have Arlene Foster weakened by her experience of the RHI you have Brexit up and running plans for it and then the next thing that comes along just weeks after that administration was in place you have the pandemic Northern Ireland new administration trying to find its feet sadly with this pandemic which I suppose no administration in the civilized world has found fully effective fully efficient way of dealing with the pandemic Northern Ireland was no stranger to it I suppose its greatest bounce in relation to the pandemic came when the British Prime Minister Boris Johnson who was under pressure gambled in relation to a vaccines policy that was ahead of most other places the United States and certainly the European Union included and Northern Ireland got a bounce from that but the entire 12 months of that new administration in Northern Ireland was spent dealing with the pandemic there was no opportunity to develop the kind of synergies and the kind of progress and the kind of relationships on other policy areas that would give out a signal of a fully effective government you look at some of the problems they had north south relations were damaged over who's going where where is the pandemic the greater the greater threat and so on you look at say the policy they had of giving grants to golf clubs of giving grants to businesses there was a Sinn Fein office that caught up got caught up in say that imperfect that imperfect policy that came from the storm and executive so you've had the storm and executive wobbling on so many fronts over the years exacerbated by Brexit certainly not helped by the pandemic and I think it was those circumstances including the fact that the dup was this party that always had difficulties adapting to power sharing through paisley's time through robinson's time and now through ironing fosters time that all those factors were bubbling below the surface so I think that's what has happened in recent times and that's why I say we're into a season of reckonings we've talked about the dup and we can say that that was inevitable let's talk about Brexit because it is the background problem to all of the political instability that we're seeing now let's talk about how it happened in northern Ireland I remember David Cameron throwing it out there to appease his own critics within his own party he made that promise in in relation in the run-up to the 2015 election the brexit referendum was held then in 2016 Theresa May was one of the few British government ministers who came to north she was home secretary at the time I think she came to northern Ireland immediately before the brexit vote there was no sense within conservative party politics and indeed in the debate that was taking place across the water there was no sense that northern Ireland was going to be the most vulnerable part of the United Kingdom because if brexit was actually carried if the decision was taken to withdraw from the European Union there was absolutely no understanding throughout the brexit debate of the role that Europe had played in northern Ireland's peace process in recent times we've quite rightly heard the role the Americans had buy-in from the Americans in the United States but I think any fair analysis of what happened in terms of the good fight agreement in the peace process would see the impact being a member of the European Parliament had on John Hume because I walked with him many of those nights in Strasbourg when you know he'd go and he'd look and he'd see neighbouring Germany and he'd talk about how Europe was this great example of compromise and reconciliation and Hume was inspired by what he saw in Europe and he in many respects he encouraged the two administrations and indeed the Americans to European European eyes Ireland's problem the northern Irish situation and it was ingenious in that respect because it actually built on the fact that we were all part of something bigger and that's something bigger had been quite a positive force in the reconciliation that took place in British and Irish relations in the 1970s the 1980s the 1990s and in more recent times Dahi who's chairing the session today was a diplomat in the Department of Foreign Affairs he saw at first hand what happened when Irish and British diplomats went and sat around that European table when we realized how much we had in common it was a positive factor in say the relationship with Margaret Thatcher and with success of British Prime Ministers throughout that line that continued right up to the present time with Boris Johnson it say it had an impact on John Major's time it had a huge impact on Tony Blair's time so there was in many respects there was a Europeanization of the Irish situation in the Brexit agreement and Hume who's I always say provided so much of the ideology for the Good Friday Agreement recognize that and when Brexit took place that very important supportive part of the architecture of the Good Friday Agreement was removed so as I see it now when people talk about the Northern Ireland protocol challenging and in some respects contradicting the Good Friday Agreement I say that's a very very valid point but it also has to go back to where the actual Brexit process began and it has to question whether that European dimension was taken into account in the Brexit debate in the United Kingdom and my conclusion is and I think the evidence is there to support it that the proper weight the proper understanding was not given to it I think it's also worth noting and these sessions I think in these times we should always try to be honest with ourselves and with others the DUP was the party in Northern Ireland that gave most support to Brexit there were elements in the Ulster Unionist party that were quietly supportive of it there weren't certainly elements in the in the Ulster Unionist party that were against Brexit that wanted to remain in the in say within the that wanted Northern Ireland to remain in the EU but certainly the DUP was the most committed party in favour of Brexit it actually helped that they had a number of members in the Westminster Parliament ten at one stage down to eight in more recent times but they were actually playing a role in the Brexit discussions their natural allies over the years were the Brexit tears just as the Brexit tears match and match your ally in the Brussels press corps I belong to in the 90s was Boris Johnson so the DUP were an important contributor to the Brexit debate at Westminster I think it's also worth pointing out that in the final days of the Brexit process when the Brexit campaign required further resources that they used a vehicle of money being given to the DUP and the DUP's finances as a party that was based in Northern Ireland the DUP were able to return those finances to providing the funding for some of the important material that was distributed in to large numbers of people in the days and in a very effective way immediately before the Brexit debate took place so I think it's always very important discussions like this for us to acknowledge that the DUP was consistently a pro-Brexit party the only one in Northern Ireland to do so and I think it's it's also relevant to state that Arlene Foster has made a number of very eloquent speeches in recent times including one in the storm at the chamber two days ago but she did state in the course of her contribution in storming Monday that she continues to support Brexit so Arlene Foster has shown no sign of saying well maybe we didn't give full consideration to the deeper consequences and the profound consequences of Brexit she remains loyal to her party position that Brexit was the right thing did the DUP expect that the vote would be carried in favour of the leaving the European Union I certainly know many senior significant figures in the DUP who did not think that would take place we all know David Cameron believed it would not take place and I think it should also be acknowledged that Theresa May as the British Prime Minister who showed a lack of awareness of the possible implications of Brexit when she came and she did that interview with Mark Devonport in I think it was probably May 2016 in Northern Ireland that as Prime Minister I think Theresa May began to grasp the more potentially profound consequences of Brexit on Northern Ireland when she became Prime Minister and I think some of her advisors at that time at that time were helpful in getting her to that position Theresa May was the person who wanted a softer Brexit that would have prevented a lot of the practical issues we are now seeing that flow from the Northern Ireland protocol and that has to be said to be fair to her but the DUP was one of the parties that went along with Boris Johnson in pushing for the harder Brexit all to think that when we're looking back at Boris Johnson's behaviour and I see now the suggestion that oh they had no idea that you know that the Northern Ireland protocol was going to be affecting people in such a meaningful way Boris Johnson in the last few weeks before he had to make his big move in relation to reaching a Brexit compromise with the British government he and his officials had several important conversations with Irish ministers with the Taoiseach at the time and with Irish officials you know I'm thinking of the likes of say from an Irish perspective the likes of Martin Fraser and John Kalman, Brian Murphy, James Darcy and on the British side you had the likes of Eddie Leicester, Mark Sedwell who was a Cabinet Secretary at the time always showed an awareness of Irish issues but I think that has changed and changed dramatically on the watch of Lord David Frost and I think that's where a lot of the current difficulties arise so now let's come to the modern, let's come to today and where I think things are at and the reckoning is that we're that are unavoidable. The first reckoning is this debate within the Democratic Unionist Party. Is it party of traditionalists? Is it a more hardline party? Is it a party that's heading towards the centre and believes in pragmatism? Robinson was a pragmatist, Arlene Foster was a pragmatist, Edwin Putes has been on the traditional wing of the party. As I see it the most important members in the DUP at the moment are Edwin Putes, his nominee for First Minister Paul Given, the economy minister Paul Frew was a very very difficult position, challenges on so many fronts and it's going to have to do some very fast learning and I think of the Westminster MPs by far the most influential at the moment is Ian Paisley Jr. So I think that debate is going to be had in the DUP, it's a reckoning that can't be avoided and I think in many respects because it has been there for so many years I take an attitude of I think bring it on and let it happen. I think the second reckoning that's going to take place is you look at say the numbers in the Northern Ireland Assembly at the moment, the DUP has 28 Assembly members, Sinn Féin has 27, the DUP lost several members in the last Assembly elections and you've always had this possibility of Sinn Féin becoming the largest party and that cannot be avoided. At the very latest the Assembly elections are due in May, if storm collapses before then the British government has the option of allowing elections before then it can take a number of emergency measures to prevent it for a couple of months for several months but at the latest you're going to have Assembly elections in May. Even before the Arlene Foster situation arose when she was removed there were some in the DUP wondering should we go to opposition and try and regroup there? It was only the beginning of a conversation but they were already thinking what happens if we are not the largest party? Will we go into government which Sinn Féin? And I think there's a very real possibility that the Good Friday Agreement model of a mandatory coalition, that that model is certainly up for review and you may have some parties who will be pushing for a more traditional model of government and opposition. I've always felt that it was unfair on the Northern Ireland Assembly that they've had no place to look to that they could say well this is how they do it here and these are the mistakes they make. They've had to find their own chemistry in this situation. They look at the Royal Ireland's government and opposition, okay coalition governments, single party governments, you have those models but you don't have this mandatory coalition, they don't have that in Westminster and if they're looking for examples it's usually a government and opposition model and that's the lonely place to be in to be trying to make new history. So I think those important elections are coming as well. The next question I think that we cannot avoid is the question of United Ireland. I think that debate is underway now. The question of a border poll, when will it take place, how will it take place, what would be the best circumstances for it to take place and I think that Brexit has contributed to that in some respects it has destabilised matters and I think it has accelerated the push for a border poll and I do believe that train has left the station I don't know when it's going to reach its destination, it's hard to predict that but I think it has left the station and that is definitely on the political agenda. All to think it's really important that at a forum like this we recognise what's happening with Sinn Fein. I look back at that picture of Ian Paisley and his party and Gerry Adams and Martin McGinnis and Sinn Fein sitting around the table in Stormont before they formed power sharing and that was a well moment because it signalled change. Can you look at where the DUP has travelled since then and gone backwards in some respects and what has happened to Sinn Fein? I remember was it 2011 Gerry Adams made the decision to go down south because he was afraid and his party was afraid that they had maybe hit that last ceiling they had five TDs at the time they were afraid they might step back to four I think was it Arthur Morgan was not going to stand and loud that's where Gerry Adams stood and you look at what has happened to Sinn Fein since you look at Sinn Fein at the time of the Good Friday Agreement the SDLP provided an awful lot of the ideology Sinn Fein grew to be the largest voice of nationalism stroke republicanism. Sinn Fein is now in that position and it's in that position even though it has seven members in Westminster who do not take their seats yet they still get a mandate you look at what has happened down south you look at opinion polls last week and I think it's very very clear that Sinn Fein is fast getting to the situation where it could well be the largest party in Northern Ireland after next May's elections and whatever may follow from those and it's at the very least in line to be the junior partner at least in a coalition government down south so that's an extraordinary journey now part of me says that journey has been going on for almost a hundred years that we have the centenary of Northern Ireland but if you look at the Sinn Fein story you look at its relationship with Fina Fawle you look at Michael Collins what was his policy when he was a senior figure in the IRA and his you know his links with Fina Gail you look at the round between Fina Fawle and Sinn Fein you look at the way Sinn Fein has got rid of smaller parties eaten them up one by one pushed them aside pushed its way to the centre you look at the pressure it's now placing a not just Fina Fawle and Fina Gail so I think that reckoning is coming south of the border as well the next reckoning that I think is taking is is is inevitable is one on Brexit what is Boris Johnson going to do in the next few weeks how are they going to handle the Northern Ireland protocol how is David Frost going to behave what is going to be the role of the Americans in terms of how they can impact on the British what I've seen in recent days is I've seen a British government that's currently under pressure over postponing its opening of society post post in the like in the pandemic circumstances and I see the greatest threat to Boris Johnson at the moment is not coming from Kirstam or under Labour or indeed from the SNP the greatest threat to Boris Johnson I think a short medium and probably long term is from within his own party and you can see that he will do things at times to appease his own party and I think if Boris Johnson remains under pressure over the pandemic and his policy there that he's quite likely to consider using the Northern Ireland protocol to appease some of his own back benchers and the DUP members included so I think it's coming to a reckoning in relation to Brexit in the in the next few weeks because some of these measures have either to be renewed or the British have to go on their own way oh there's a part of me that feels that the pressure from the Americans and the willingness of the Europeans who have been weakened by their vaccine strategy the willingness of the Europeans to always seek a compromise because it's from their very nature the optimist in me says that they will find a way to sort out the difficulties in the Northern Ireland protocol situation that you might bring some element of political stability to Northern Ireland but I think that reckoning is coming as well just a final point on I'm following matters over the last 48 hours I noticed Brandon Lewis on his feet today in relation to the Irish language row that's taking place in Stormont where do I see that going? Brandon Lewis in his conversations with Mary Lou MacDonald it seems it did make some offer that the British government would provide legislation on the Irish language if the DUP were not prepared to do so in Stormont fascinating that Shane Fain and the DBSD LP whose members take their seats in Westminster that they are looking on the possibility of using Westminster to solve a problem that Northern Ireland's Assembly itself is not able to resolve that these two nationalist parties United Ireland parties are looking to Westminster to do that the irony that is interesting my concern if Brandon Lewis does that is I think the next obvious move that will come there is you would have the likes of Nigel Dodds and Sammy Wilson in Westminster in the House of Lords and in the House of Commons saying if you are prepared to get involved on Irish language issues that Stormont cannot resolve well we are expecting you to do the very same in relation to the Northern Ireland protocol and I think if you bear in mind that the DUP have votes in Westminster that they take their seats in Westminster that they have important alliances in Westminster I think that could become a factor in British thinking that if they give the Sprat of the Irish language to the SDLP and Shane Fain that it would be well within their capacity to give the salmon deeper moves in relation to the Northern Ireland protocol to the DUP and to their own backbenchers so for those reasons I think we're in quite a volatile situation I think we're in a quite an interesting situation but the final thought I leave with you in this session of our discussions is one of the most profound changes I've noticed in Northern Ireland over the past 10, 15 years is the absence of any sort of grassroots support for the use of violence. Violence plagued our lives for 30, 40 years the utterly unnecessary taking of human life the awful effect that had on thousands upon thousands of people and I think that explains a lot of the visceral dislike people have of any party who would have any association with the use of force in our politics and while there have been examples in recent years of street protest of rioting and that is not off the table in current times nowhere have I seen any convincing evidence to suggest that there would be support for killing and shooting and burning like we saw throughout the troubles. I think there's no public appetite for that and one of the great advantages of this big brother society we live in of how you can put a little marker into your phone and you're going to meet somebody on your WhatsApp and they can see where you are on the road. I think this whole big brother society we live in where technology has moved to such a place I think and it brings me great joy to say this I don't see how even people who would have the intent to carry out a campaign of killing and trying to antagonize their neighbors I don't think the possibilities to do so exists in our modern society. Thank you.


YouTube made some policy changes back in November of last year that they are seemingly enforcing right now out of nowhere. Most of these changes without warning YouTubers and some of these changes specifically involving gaming YouTube channels such as myself. You probably have heard a little bit about the situation or at least seen various videos pop up because many content creators have talked about it. Not only live streamers but even some of us news channels have at least covered this story. I think it's interesting because it puts YouTube in this really weird situation where they don't want you making content for kids but then they also want your content to be friendly for kids. And all of this really stems from the fact that what YouTube is trying to do is at least maintain its ability to, you know, keep the money flowing, right? All of these changes are always about pleasing advertisers and you might go, why do they care so much about that?  In fact, if you actually dig through the financials for YouTube, you'll find out that YouTube for the most part just breaks even. So if there's anything happening that's going to cause them to lose advertisers, then eventually they stop breaking even and YouTube becomes a loss leader. Now I don't think that that means YouTube would go away. They're owned by Google. Who's owned by Alphabet. They are one of the largest and richest companies in the world. And YouTube is literally the number two most visited website and platform on the entire planet right behind Google.com. And then obviously in terms of applications, I think TikTok is now more downloaded and more used than YouTube, but YouTube is still right up there. They're not going to just stop supporting YouTube because it's not making money, but they clearly want to make moves that are going to ensure YouTube's longevity and doing things and making policy changes to ensure that they can continue that ad revenue coming in is well to the benefit of YouTube and arguably to the benefit of us creators because hey, if we're able to get bigger and better companies buying ads on YouTube, that should lead to us making more money. At least that's sort of the idea. The problem YouTube obviously has is two fold. You can't say don't make content for kids. Meanwhile, make your content friendly for kids. Those are two contradicting points and YouTube does a very poor job communicating these changes and then making us understand how these changes will actually affect videos with real world examples. They pretty much never do that. And what's interesting is when there is something important that they want to note to creators, they literally put it in the back end. This is something they put in the back end today that addresses a view issue I was having yesterday with my content where they acknowledge, hey, you know what, this is a known problem. You know what you should also put back here? Nome policy changes that may affect my channel, but they don't do that. They hide everything on their blog. Now it's known by some of us that they do put these policy changes on their blog, but still it's not always the easiest blog to follow. It's like a Q&A blog and unless you're looking for specific things, you're probably not likely to find it. And this is just fundamental to YouTube's bad communication with those content creators. So this is what the update said back in November of 2022. We've updated our guidelines to include both clear language and specific guideline changes and changes to add suitabilities. See below for impacted guidelines as well as non exhaustive examples of what is changing.  So they're not getting rid of your videos, but no ads. In my experience, videos not having ads leads to a significantly less views because YouTube is less incentivized to push that content.  Audiences remain unchanged and may receive ad revenue. So there's going to be a lot of discretion applied. Most of this for the most part has nothing to do with us as like video game content creators. So we're going to kind of let that policy go. Sort of makes sense.  And next thing you know, advertisers will pull out significantly. Next up, violence. Non graphic dead bodies presented without any context. Game violence directed at real named persons or acts that are manufactured to create shocking experiences such as brutal mass killing, you could argue games that call a duty sort of push that implied moment of death, such as bombing a building with people inside. Again, video games have that it's especially in all of the military shooters may not receive ad revenue. Standard gameplay or gory injuries are present after the first eight seconds. Non graphic strategies after their aftermath such as footage of a town flooded or police seizures as part of a law enforcement may receive ad revenue. So as long as you stay out of some mystery eight second window, you can have some stuff, but there's also limitations because it can't represent the idea of mass killing of people, which is something that does exist in several military games. All right, harmful or dangerous acts. The dangerous acts where minors are participants or victims, such as minors participating in experiments or challenging of all stunts unsuitable for kids may not receive ad revenue. Again, really strange because you're saying not suitable for kids. When you told us we can't make content for kids, or we also don't receive ads. What is it YouTube? Can we make content that isn't for children and receive ads? Or does all of our content need to be targeted to children? And then we have to tell you it's not for kids when there's actually a checkbox when we upload our videos, or we have to select if our video is intended for children or not. If our content is not intended for children, we can receive ad revenue. If it is intended for children, we cannot receive ad revenue and we cannot have comments on our videos. And yet you put a policy in place right here. Challenges involving stunts unsuitable for kids may not receive ad revenue. But in order to get ad revenue, you need to be making content that isn't for children in the first place. Do you see the conundrum here? YouTube's trying to please advertisers making your content more kid friendly, but we're not supposed to make our content for kids. It's a really weird catch 22 situation, in my opinion. Sensitive events. We're going to kind of skip over that. That has to do more with politics and news and religion and all that. In appropriate language, though, this is one that's getting a lot of people right now. Our approach to profanity is changing. All varieties of profanity are now treated equally, meaning they are not differentiated based on levels of severity. For example, light, moderate, strong or extreme.  Well, thanks.  Anyways, therefore, profanity used in the title thumbnails or in the titles for seven seconds or used consistently throughout the video may not receive ad revenue. Of course, they have no examples of what consistently means. How many times do you have to use it? If you have a swear word once every minute, is that too much? Again, they don't really explain it. Profanities used after the first eight seconds may receive ad revenue. Our position on not monetizing content with profanity throughout or compromise the majority of the video is not changing. Again, they don't really explain it.  For the most part, I've had a lot of their older content unmonetized because they are blanket applying this to previous content, which happened under other policies. And you know, this is where people are looking forward and wondering what's next. What's YouTube going to do? YouTube's in this weird place. As I said, they're trying to please advertisers while also trying to please governing bodies who do not want YouTube to be targeting children, but yet they want your content to be friendly towards children. They basically want family friendly content intended for older than age 13 audiences will also be in friendly to people under age 13 on the off chance that someone younger than 13 sees your video. And that all makes it friendly to advertisers. Now, what I don't understand is why YouTube won't just let us rate our channels or have YouTube rate our channels for us as it's sort of like the ESRB rating or the TV rating right for everybody T for teen M for mature and allow advertisers to buy ads in various categories of family friendly to teens to news content to whatever. Look, these policy changes aren't going to affect me. You guys know already, I barely swear as it is in my normal video content. And I feel like I swear infrequently enough during live streams that I probably won't get dinged. I guess I can't guarantee it. I obviously don't participate in most of these violent acts. I guess it's arguable. Certain games I live stream once in a blue moon might be impacted, but I don't live stream enough of those games often enough to really be that concerned. I just think YouTube is stuck between a rock and a hard place. They're trying to avoid government interference and they're also trying to please advertisers and they're they're kind of two separate ideals when I feel like again the obvious answer is to just age rate our channels to certain groups and you don't base how you spread your videos on that. You base that on the age of the actual user. So as an example, if I rate my channel for T and above, then you should be targeting my videos towards people that according to the profiles anyways are 13 and older. If it is a channel that is for children and families, obviously maybe you brought in that to all age groups. Look, none of this is ideal, of course, because then you're limiting audience reach and some YouTubers will be mad about that as well. So there isn't really an ideal situation here other than maybe just being more transparent. Look, if you want YouTube to be a place that basically doesn't have profanity, I'm okay with that. I think when it comes to creating content or doing live reactions or all this stuff, there are ways to express ourselves in very serious tones where we don't have to swear even if that's common off of YouTube, but I also think that we need to keep in mind that YouTube is trying to maintain profitability of some level and also help support us creators by ensuring that we continue to have high quality ads which will lead to higher CPM, which lead to more money per video. So I am not YouTube. I don't care what YouTube does for the most part. Most of our policy changes don't affect us while we are targeted as an older audience. In fact, our primary age groups are between this ages of 18 and 45. It's a pretty wide range age group there, but that's literally where 90% of our audience resides. So we're already reaching an older audience as it is. But also I don't create the sort of content that I feel like YouTube policies ever really end up hurting. I just want them to communicate better. These policy changes were not even made aware to us. They were not presented on the back end. They never warned us. They just started demonetizing videos.  They have all of our emails. They could tell us on the back end. There are so many different ways. I mean, some of us have MCNs. Our MCNs were unaware of these policy changes. That's crazy to me that literal people that are job to keep their content creators updated weren't aware of made aware of these policy changes. So look, YouTube, you need to get on top of this and just communicate better and give actual examples instead of saying, oh, if there's some profanity, but if there's too much profanity, show videos, have video examples of this is okay and this is not okay. Give better example. Don't just give us words. Give us real video examples of what's okay and what's not okay so we can better understand the policies. That's another thing I would suggest YouTube to do as well. Anyways, it's not going to affect my channel too much. It might affect yours. It might affect some of your favorite content creators and live streamers. Not really going to affect us. We're going to keep on trucking. In fact, we have another live stream going up tonight here in like two, three hours anyways. So anyways, I'll catch you guys there. Otherwise, I'll also see you tomorrow at our podcast and yet more video content during this rather dry news cycle. We don't have a lot of news here to kick off January, which is pretty typical from the big Nintendo. Thank you guys and I'll catch you later.


Ana, I don't even want to introduce you, you've been everything. So Ana Palacio, over to you. Well, you know, I had an idea to say a few things that I'm not going to say, because I think that, thank you, Hubert. You have really presented what there is there for us. So I will make three comments. The first comment, I will go take the lens back from the sit-in. In my opinion, what is more puzzling with our citizens, which has a repercussion in our system, in our political system, there's this growth of the illiberals, is that Europe is the place of rationality. Rationality comes from the Enlightenment, and we are supposed to make choices based on the interest. What we see today is the invasion everywhere of the irrationality, of the emotional, and this we have to analyze. And all our instruments are geared, because in the end, we are a legal construction. All our system is a legal construction. And legality is about predictability, and it's about certainty. And the opposed to predictability and certainty is emotions. And so this is, for me, one issue in which we have to reflect and reflect deeply. If I take the lens a bit further, I think that we have, and I won't go into it in our governance, national, because we still are states. Even if some of us would like to be somewhere else, we are states. In our states, we have this challenge on how to transform classical party systems that are classical agendas and that comes from the first challenge. But of course, when we go to the European level, I agree with Mr. Bervedrin, we should, this is in our interest, create une Europe puissance. Absolutely clear. But honestly, we have to realize that our citizens do not follow on this idea of building more Europe. And you know what? We are in an intergovernmental moment in the European Union. The crisis in the commission is many things. First of them is the reflect of this intergovernmental moment when groups, the PPP, the group, the PSC group, the classical groups that made it forward, that by agreeing, by having a big discipline, are completely splintered. My third comment, taking the lens, is honestly, this is not any longer a world and it's difficult to adapt it. I mean, it's not a European, it's not a Western world. And you know, we say this, but we haven't interiorized this. So we have either the panic reaction or the overreaction. But I mean, Kevin, I think that we have to have clear eyes of what's coming. And what's coming is exactly what you have said. So our dependence on the United States, our transatlantic links, all this we have to rationally, and I will just end by this comment, which is a bit contradictory to what I rationally address. Thank you very much.  But I always think, protège from what exactly? I mean, who I understand, but what's from what is confusing?


Hello and welcome to the session. Today I will help you with the following question. The question says, construct the following quadrilateral. Quadrilateral dEaR where dE is 4 cm, eA is 5 cm, ar is 4.5 cm, angle E is 60 degrees and angle A is 90 degrees. Now before drawing the actual figure, first let's see the rough sketch of this quadrilateral. This is dEaR where dE is 4 cm, eA is 5 cm, ar is 4.5 cm, angle E is 60 degrees and angle A is 90 degrees. Now let's move on to the solution. Now we draw the figure step by step. Now visualizing the rough sketch of the quadrilateral dEaR we can say that our first step can be draw a line segment eA equal to 5 cm. So we have taken a line segment eA equal to 5 cm. Now as you can see in the figure angle E is 60 degrees and angle A is 90 degrees. So next step can be make angles of 60 degrees and 90 degrees at e and a respectively. So we have made angle of 60 degrees at e and angle of 90 degrees at a. Now our next step would be to locate the point r where ar is 4.5 cm. To do this what we do is with a as the centre and radius 4.5 cm we make an arc on the ray ax. So we have made an arc of radius 4.5 cm on the ray ax. Now let's mark this point as ar is 4.5 cm. Now our next step is to locate the point d where dE is 4 cm. So we can write with e as the centre and radius 4 cm mark an arc on the ray Ey. So as you can see we have made an arc of radius 4 cm on the ray Ey. Now let's mark this point as d. Now in the next step we will join the points d and r in order to obtain the required quadrilateral. So lastly we join the points d and r so as to get the required quadrilateral dE ar. On joining the points d and r we get the quadrilateral dE ar with dE 4 cm, eA 5 cm, ar 4.5 cm, angle E 60 degrees and angle A 90 degrees. So hope you enjoyed the session. Have a good day.


Scientists love to put stars and bars on their plots to indicate what comparisons or what treatment groups are significantly different from each other. I've talked before about why you don't need to put five stars next to one of these comparisons to indicate that it's super duper significant. No, you really just need a single star. Anyway, one of the challenges is, you know, how do you put those bars and stars onto the plot if when you're creating the plot from the beginning, you don't know how many comparisons you're going to have and you don't know where exactly you want to put those stars and bars. Well, we'll figure that out in today's episode of Code Club. Hey, folks, I'm Pat Schloss. In recent episodes of Code Club, we've been building up a figure to display the differences in relative abundance of bacterial populations that are found in patients that have varying disease statuses. And these data are coming from a paper that my lab published a number of years ago, looking for biomarkers associated with Clostridioides difficile infections or C. diff infections. Right. As you can see in this plot, healthy individuals are indicated by the gray points and lines. Those that have diarrhea, but no C. difficile infection are blue. And those that have diarrhea and C. difficile are red. Now, in that original study, one of the things we found was that it was really difficult to differentiate between people with diarrhea plus and minus C. difficile piece of cake to differentiate between people that were healthy and people with diarrhea. But within the diarrhea between people with and without C. diff was a lot harder. Well, what we've been developing in the recent episodes of Code Club is this plot. Again, the ball indicates the median relative abundance across maybe close to 100 individuals for each of these three groups. And the line indicates the range of the interquartile range. Because there are so many points in the dataset, we thought it was just way too busy to show all the data. And so we're substituting that making the compromise by putting in the range of the interquartile range. Now, when we look at this, I naturally want to see that there are significant differences in the data, right? So if I look at this Bactroides OTU two, I'm pretty confident that the healthy individuals are significantly different from the diarrhea, the people with diarrhea, right? But are these two are diarrhea samples that with and without C. diff? Are they significantly different from each other? We don't know. Well, in the last episode, we ran a set of statistical tests where we use non parametric Kruskal-Wallis test. And then on the comparisons that were significant, we then did a pairwise Wilcoxon test. What I'd like to do is take that information and put it onto this plot, so that we can then draw lines between different disease status groups for each of our bacterial taxa to indicate what comparisons are significant. Let's head over to our studio where we'll get going working on today's code. We've got a lot to do today. If you want to get this code that I'm starting with, please, please, please do that. Down below in the description, there's a link to a blog post where you can grab this code. Also across the top, as you probably know by now, there's a video where if you haven't installed our studio or the tidyverse or gotten this data, you can go there and get that. So you can be following along. And that is so important that you follow along, do what I'm doing, and then take it and adapt it to your own data. So you can really make it your own. And you can really just, you know, flourish in your skills with R. Anyway, as we've seen before, we load all these different libraries, we get our metadata, O2 counts, we figure out the number of sequences we have per sample so we can calculate a limit of detection, we process our taxonomy data, we get our O2 relative abundances, we pool things, pool O2Us where the maximum median for any of the three disease status groups for that taxon is less than half a percent. Anything lower than that, then you're really kind of looking, you know, looking at medians that are based on only a handful or a couple of reads. We then pull it all together and we come up with this O2 disease relabund data frame that has for all the subjects, their disease status, each O2U that's in them, as well as the relative abundance of that O2U and its taxonomy. Then in the last episode, we went ahead and we calculated the experiment-wide significance for each O2U using the Crosco-Wallis test. We did that test on each O2U to figure out which O2Us were significantly different across the three disease status groups. And if we look at experiment significance, we find that we have this data frame of our taxa, our data, and our P experiment. Now, something that came up after I published the video is that some eagle-eyed observer noticed that this line here where I calculate P experiment using P adjust didn't actually do anything.  So to show what they saw, I'm going to do P.value in this select. And I want to run all these lines to show you what they saw. And I should have noticed that my P value, which was the raw P value out of the Crosco-Wallis, is the same as what I thought was the P adjusted. The other thing that you perhaps notice is that this data frame is still grouped by taxa. P adjust was working. It just works within groups, right? So if my data are grouped, then it's adjusting within the group. And because there's only one P value in that group, then it doesn't really do anything. So what I could have done was after unnest, I could do ungroup and then pipe that in. And so now if I give this another run, now I see that my P values are different from the raw P value and the adjusted P value. If I didn't want to have to do the ungroup, and perhaps what I should have actually done was I could get rid of this group by taxon, and then I could say nest data equals minus taxon. And so that means nest in the data column, everything but the taxon column. And so if we run this, we now see that again, everything but the taxon column is grouped within the data column. And if I then go ahead and rerun down to that select, I again see that my P values are different, showing that it worked. I'm going to go ahead and get rid of that P value because I don't care about it so much. And update this to look at experiment significance. And we get our updated data frame. Now, for this example, that didn't matter, right? Nothing changed, nothing was significant that should have been significant, and so forth. So I'm not so worried about it. But you never know down the road, you might have some borderline P values where that P adjust actually matters. And so you want to make sure that your data are not grouped before you do P dot adjust. The next step in the pipeline then was to take experiment significance. And for those ot us that were significantly different that has significant difference among the three groups, you then we then ran a pairwise Wilcox test. And we could then run this to figure out what comparisons were significantly different, right? And so this builds in a correction for multiple comparisons in both the experiment wide as well as the pairwise, we used BH as our P adjust method, which is short for Benjamin Hatchberg. So we're in good shape there. Now again, what I want to do is I want to take this testing data and use that to map on to our plot, our bars and our stars. Before I can do that, though, I need to clean up my code because I kind of left it in a bit of a mess from the last episode. So I'm going to grab all this testing data. And I actually don't need that final ungroup. So I'm going to delete that. Because again, the data was ungrouped. And I'm going to throw that down here at the end. And I'm going to save it. And what I want to do, because I kind of moved things around, is I'm going to take this O2 disease relevant, and I'm going to put this back as part of my pipeline to build the plot. And we'll make sure that it works and looks good. And that this is then what we're going to add on to. Excellent. This is the plot I had hoped to generate. And so we've got our code back to working. I'm going to come back in here to my code. And I'm going to save this as my O2 you plot. And what we're going to do is we're going to use O2 plot. And we're going to add on to O2 plot our stars and bars, right? So I'm going to go ahead and grab gg save and move that to the very end, because I like to have that at the end for what we're, you know, incorporating all the changes to the figure. So we've got our experiment significance here, as we've seen, and we now have our experiment significance going into the pairwise test. So I will call this pairwise test. And so now I have the variable or the data frame that we'll call pairwise test. And again, we have our pairwise comparisons for each O2, we have group one and group two, and the associated p value. And these p values are all significant, they're all less than point zero five. And so I'd feel comfortable drawing a line between say the non diaryl control or the healthy, and the case, which is the seat of positive, and then putting a star next to it because the p value again is quite small. So how are we going to do this? I'm going to do O2 you plot. And I'm going to add to it, right? So I've got the plot saved as a variable. And just like I've added lines, you know, like I added back up here, like theme classic and the theme and the labs and all that other stuff, I can keep adding stuff onto it. And so that's what I'm going to do. I'm going to add on extra geomes and extra styling to add those bars and the stars to indicate significance. And what we'll do is we'll do a geome segment. And geome segment, we will give it data. And that data that it's going to use is my pairwise test. And I'll have an AES for aesthetics. And we will say, we'll have to give it x equals something x and equals something y equals something and y and equals something, right. And so those are the required aesthetics for geome segment. So we're basically giving it coordinates that we want to draw a segment between. To get started, I'm going to put x and x and as let's do 90. And then my y and y and I need to figure that out, because I'm going to put that in my pairwise test as a data frame. So I'm going to put y and y and and I'm going to create those columns now in pairwise test.  And tax on position is going to be the y axis position that the label for that tax on is being plotted at. So to show you if I do as dot numeric on tax on so tax on is a factor. And so a factor is a vector special vector that is numbered and has orders and has names or labels associated with those numbers. I see that tax on position has these numbers. So my bloudia is at position two, and back droidies at position 11. If I go back to my plot, I see bloudia is at y position two. And back droidies is up here at 11 and 12, I think, right. And so that is going to be the position that I am drawing my segments from using tax on position. I need to program in the dodge that I was getting out of position dodge before when I did the stat summary with the ball and the lines. That's not going to be that hard. So we'll go ahead and do why because I need a column for y and y and for the coordinates to draw the line between. And I would do if else. And so if else group one equals equals, and I'll say non diaryl control. So if the group one is non diaryl control and again to show you what that looks like, then that's going to be the gray bar right the gray line. And so then my y position should be tax on position. And I'll say plus 0.2. Otherwise, I'm going to do tax on a position minus 0.2. And you know what, I'm just going to call it pause, because this is getting too long. All right. And so then I need y and which will be if else group one equals equals. And that's going to be a diaryl control. And that will be pause. So if that's true, then we want to use that position. And actually come to think of it, I want this position to be just the position right. So if it's if group one isn't non diaryl control, then it's going to be diaryl control. And again, the ordering is non diaryl control, diaryl control and then case. And so that line needs to start at up above bump for not for the healthy at the tax on position for non diaryl control. And then and then it needs to go if it's to diaryl control, it's going to go to position. And if it's case group of group two, rather, not group one, if group two is diaryl control, it's going to end at the position. And if it's false, then it's going to be case. And then I want it to be position minus 0.2. Okay, so that gets me my y my y end. Let's go ahead and run this and see what we get. So I'm getting an error message that object disease stat not found. And that is happening, because it's inheriting the AES from the original ggplot command, right? So I can do inherit dot AES equals false. And now what I see is I have a vertical line at position 90. And of course, there are three lines or two lines overlapping here. And so I need to dodge those apart on my x axis. So to dodge the lines horizontally along the x axis, I need to add an x and x and column. So x is the special one x and will be the same as x because it's a vertical line. So to do this, we're going to do something like if else, but it's called case when. So do case when. And so case when you can give it a logical question. And if it's true, then you you then give it the value to use if it's true. If it's false, it then goes to the next logical question, right? So we'll do case when group one equals equals non diaryl control and group two equals equals diaryl control, right? So if that's the case, then we'll do a tilde. I'll then say 60. And then we'll repeat this, right? Because we have other groups, right? So non diaryl control case, I will then make that 75. And then non diaryl control should be diaryl control for the third line to case. And I'll make that 90. Okay. And so then that is good. And so again, what's going to happen is it evaluates this first question. If it's true, we get 60. If it's false, then it evaluates this next question of is group one non diaryl control and case. If that's true, it returns 75. Otherwise, it comes down and does diaryl control in case. And that's 90.  And so we'll go there. And then we'll do x and equals x. So I'll save that. And now I'm going to change x to the x and x and to the x and lucky there, we've got two lines indicating the comparison between healthy and diaryl, seed of negative and healthy and diarrhea seed of positive for our all of our ot us. The LS stippies shows a significant comparison between the two diaryl samples, which is interesting. So that's good. The next thing I want to do is be able to put in a star next to those lines to indicate that it is in fact significant to do that. I need to again modify my my pair wise test data frame. And where we're going is I'm going to add a geome text. And so that is going to take again data equals pair wise test. And I need AES and I'm going to have x equals x star and y equals y star. And so those are the two aesthetics. And I will then have label equals star. And again, I don't want to forget that I want to do inherit dot AES equals false. So now I need to get those x star and y star variables. And so I'll go ahead in here into this mutate statement, my x star is going I'm going to say x star equals let's do 1.1 times x. I think that should be good. I should bump it to the right, like 10%. We've got these weird logarithms. I'm not totally sure how that will look. We also need then y star. So for y star, I'm going to borrow this case when statement down. And for if group one is non diaryl control, the diaryl control, that again is going to go from up point to to the right to the position. So that's going to be position plus 0.1. Because I want to start to be in the center of that vertical line. For the non diaryl control case, that is going to be right at pause. And then for diaryl control case, that's going to be ultra pause minus 0.1. And I'm picking 0.1 as my increment for the star, because that's half the length of the line. Let's go ahead and see what this looks like. And there we go. We've got our stars. Actually, the stars are, I think there must be some space underneath the star, the vertical justification. That's okay. I'm going to go ahead and bump it down just a smidge. And so maybe instead of 0.1, I'll do 0.05. And then the position will also have to be dropped down 0.05. And then this will have to go down another 0.05. So I'm pretty happy with the way this looks. One thing, as you've heard me say that I worry about a little bit, is hopefully it's clear that this bar is the comparison between the healthy and the diarylcid of neg. And this bar is between the healthy and the diarylcid of positive. We'll see. Maybe we'll do some focus groups and figure that out. One thing I don't like about this, though, is I don't like having this column of stars and bars. I would rather have this column be adjusted over to the left. So it's kind of hugging the data. To do that, what I'd like to do is increment it to perhaps 10% to the right of the largest 75th percentile. So again, these whiskers or the line segments indicate the intra-cortile range. So if I can figure out what is the largest 75th percentile for all of the taxa across all three disease status groups, then I can use that value and increment it by 10, 20, 30%. And that is then what I can use as my exposition for drawing those lines and the stars. So I need to calculate the 75th percentile for each of those disease status groups for each taxa, and then return the largest 75th percentile for each taxa. So I'm going to do that using a map function. And again, I'll kind of rough in the code to do mutate max, quartile equals, and I'll say map, and then dot x equals data. And then the formula that I need to use is get max quartile. And we will then give it dot x, and then we'll pipe that into the rest of the pipeline. But I may need to make this get max quartile. So get max quartile will be a function, right? And so we give it an argument x, and we've got the function body here in the braces. And then I will pipe x into group by, and it's already coming in data is chunked by O2. So I'll group by disease stat. And then I will pipe that to summarize. And I will do third q as quantile. And I will give it the relabund column. So I'm taking all the relative abundances for each disease status group in this taxon, and prob equals 0.75. Okay. So that's going to get me the three quartile values, I'll say dot groups equals quote drop. And then we will pipe that and do a summarize and do a max quartile. And that then will be the max of the third q. And I then will pull max quartile as the output from get max quartile. So I forgot the function keyword. So we'll do function all that. And so that loads it. And so now if I run these first two lines, so we get a column for max quartile. And this is a list of type double, right? So there's a special map function we can use, which would be map underscore DBL. And so now if we use max double, then we should have a column with the actual value for the maximum quartile. So now as this pipes through, we get down to here where we're defining x. And what I want to put in here is max quartile, and I'll just say times 1.1. And here I'll do the same thing, perhaps times 1.3. And here perhaps I'll do times 1.5. So it's complaining that it can't find object max quartile. And I wonder if I don't have a select function up here. Yeah, so I forgot to bring in the max quartile. So I'll go ahead and put that in. And that looks pretty good. We've got the stars and bars closer to our data. You know what, maybe I'll increment the value a little bit more. So it's not so on top of each other. And so I'll come back up and maybe I'll make this 1.3, this 1.5, maybe 1.6, let's say, and then 1.9. So I think that looks good and gives a decent amount of space. If you've watched any number of these videos, you know, I can spend all day just kind of futzing with the position of things in my plots. And so I think that looks pretty good. Again, the thing that I just kind of wrestle with is whether or not it's clear that the bar represents the comparison between the groups that the that the line is connecting. I hope so. You know, we could put that information in the legend. If we had to, maybe we could go ahead and use like the same approach to put little whiskers on the on the bars here. I don't really want to do that. An alternative approach could be over here in the margin just to the right of the y-axis. I could put like abc. So, you know, for like, for right, for coca cola, I could put like a for healthy and then bb for the two diarrheal samples to kind of indicate significant scripts to say that like a is distinct from b, right? And then down here where we have for alastepis, the three different would be like abc. I don't really like that either. Let me know down below in the comments what you think of this. Maybe I'm overthinking things too much. I'm kind of happy with the way this looks. Ultimately, you know, I think these data are pretty clear about what's significant just by eyeballing it without even having to really look at a p value. The one thing we know is not significant are these other categories where we pulled together those otus. So I'm pretty happy with the way this looks. And I think I think it turned out pretty well. Again, the nice thing that we've done is use the data itself to determine the positioning of our bars, the length and span of the bars and the position of those stars to give it that nice dynamic look. Again, I could change the amount that I'm pooling the data by and then it should work. So I'm going to go ahead and try that as just kind of my final hurrah for today's episode. And I will come all the way back up to the top where we did pool. And I'm going to change this to 1%. And so changing it to a 1% pooling worked perfectly. Everything adjusted without me having to go into the code and muck with anything. So I'm really happy about how that worked. And I think that looks that looks really good. So again, let me know down below in the comments what you would do to make it more clear what's going on in the comparisons. Is this clear enough? Or would you do something else to clarify it? Again, we could maybe put little whiskers on it, but I don't want to mess with that. I think that would just kind of make everything look all the more busy. Alternatively, we could put letters indicating the significance groups. I think that also just kind of makes things look messy and kind of confusing. So I think this is good. I'm pretty happy with it. And I'll leave it here for now. Anyway, I really hope you found this interesting. Again, there's a lot of different things going on here. You know, if I had to boil it down to what did we cover? Well, we talked about adding other layers onto an existing plot. We talked about building out a data frame and adding columns, where we're using if else, as well as case when both of those are really powerful functions for conditionally creating other data, right? We created new columns based on the values in other columns. And so the ability to use those conditional values is really awesome. Anyway, I hope you found this interesting.  Keep practicing with this. I think it's really valuable to see concepts in other contexts. And that really helps you to reinforce the skills that you're learning. Please tell your friends about what we're doing here in Code Club. I've got some exciting episodes coming up here in the next few days and weeks. And I want you to be tuned in. So be sure that you're subscribed and you're getting notifications about what's going on. Thanks for coming along and spending your time with me today. I really hope you've gotten something out of this and we'll see you next time for another episode of Code Club.