lectures. So the first speaker of today is Vishweshwa Guttal, who is giving the second lecture on Pistability and Socasticity in Ecological Layoffs. So please Vishu, share the screen when you are ready. I don't see the screen. Do you see my, okay, hold on. I think I made a mistake one second. Is it fine now? Can you see my slides? Excellent. Thank you. So welcome back everyone. So yesterday Simon gave a very broad overview that incidentally included ideas of by stability, tipping points, and also early warning signals. So I'm sort of going to continue on those themes today. As I had mentioned in the first talk, so I have this, this is the plan for the three talks I have. So I have sort of talked about basic by stable dynamics, resilience and tipping points, and how can we anticipate these using the ideas of early warning signals. And then today the main focus will be on spatial models, you know, everything I spoke on the last talk assume actually there was no reference to space. All the mathematical techniques I used was basically simple, ordinary differential equations with some noise superimposed on it, then I'd walk away. So but today, let us look at what happens if there is space. Now how do we understand by stable systems? Basically the one question that one can try to, which I try to focus on today would be, can spatial patterns in ecosystems be used to infer resilience of ecosystems? That's the main question I'm going to ask. So the last one, which I'm hoping will be as planned will be to look at, okay, so today I'll just do a brief recap. I'm going to go over this somewhat quickly before I move into some tipping points. So I give this example of large scale continental shift, that is a classic example. This is not the only one. There are many other examples of ecosystems for gradual changes in the driver. Okay. And of course this has been observed in many, many, many systems. Now to my own list of Simon added a whole bunch of other systems as the name is stock. So how do we, so here is the simple ecosystem model I demonstrated the first term in this ecosystem model where we represents the total biomass density in the system actually comprises the classic ecological model to logistic growth to which we add a grazing term which is sort of, you know, which could be intrinsic to the system could also be extrinsic, such as livestock grazing. Okay. So this is a nonlinear term and interestingly the ones you add this and for a whole range of parameter values you get a bistability. There is a region of this grazing rate for which two alternative stable states exist and which state current and there could be these switches, shifts, critical transitions, tipping points, abrupt changes at these two points which are critical points or the bifurcation points of this simple model. So the question, you know, the nice thing about this simple model was that we could think of the dynamics of ecosystems with bistability as a ball rolling in this landscape. So for example, the minima in these landscapes correspond to the stable branches in the bifurcation diagram. So depending on the initial condition, the system could be either in this state or this state. And this helps us understand concepts of basin of attraction and resilience. And this concept of potentials was not just for heuristics. It was also useful for arriving at quantitative metrics that helps us make some forecasts about tipping points. For example, if the system is far away from the critical point as in this, the leftmost point here, these potentials are symmetric. Whereas when you're very close to the tipping points, potentials are shallow with the low curvature and asymmetric. And this led to the phenomenon of critical slowing down and asymmetric fluctuations. Critical slowing down means that systems take no longer to return back to the equilibrium, they exhibit more fluctuations, and they also exhibit asymmetric fluctuations. Put these things together, we could come up with some metrics from the time series, and that could actually forecast. In this example, we found that if the system were to undergo a transition at this point, if we had this time series before the thousand time minutes, if we could, if I could calculate simple quantities like autocorrelation at lag 1, this measures the critical slow down, it's increasing with time as one is approaching a critical point, or the abrupt transition. Standard deviation and measure of fluctuation is increasing. The skewness, the strength of skewness, again, which is a measure of asymmetric fluctuation is also increasing. Now these metrics, if you had no, if you were somewhere around 800 or the 900th time minute, so these combined metrics give us a hint that the system might be going towards tipping point. So that's the summary of where we were. I also spoke to you about how there have been many empirical studies, experimental studies, field studies. Sometimes they work, sometimes they don't work. As I also showed you when there is huge amount of stochasticity, you know, some of these classic signatures can be masked. Okay, so now, so now of course, ecosystems are really spatial, right? Now they also exhibit really fascinating patterns. These are, you know, some of the classic examples of the fairy rings are formed in African deserts. And these are again, you know, patches of laboredentine patterns of vegetation. And, and then, you know, one can go on, there are more types of vegetation. Many of these vegetation patterns are often found in resource constrained systems or systems which actually have a relatively higher amount of ecological stress. So therefore, this sort of prompted many people to think, can these spatial patterns provide some signatures of abrupt regime shifts that might happen in the future? So this is an example of clustering in the muscles, muscles. And this is an example of clustering of vegetation on the sea bed. So there are many, many examples, plenty of examples. So now to understand these kind of state systems, there are three classic approaches. One is called, so the first two of them are actually both reaction diffusion systems. However, the distinction between the first and second comes from the fact that in the first system, there are no regular patterns, there are no patterning in the ecosystem. Systems sort of roughly appears homogeneous. There are second class of systems are regular patterning systems, and you may have heard of Turing patterns. Okay, and on the third class of systems are there are patterns, there is self organization, but there is no periodicity or regularity to these patterns. So there are these three types of spatial ways to think about ecosystem by stability. So I'm going to go one by one and see how we can, you know, do theory of these systems. How can we come up with these early warning indicators, followed by, you know, testing them systems as well. Reaction diffusion system and we think of spatial system, reaction diffusion system with no pattern. So what do I mean by that? Okay, by the way, before I go further, I want to exercise that just one second, my internet seems to be fluctuating a bit, I will see what happens. We show also the connection is a little bit disturbed, so. One second, I'll just, are you able to hear me clearly? Yeah, sometimes it, sometimes not. So perhaps it's better to remove the video. Okay, I will stop my video. Yeah, I'll stop. I have to unshade this for a second. Okay, now my connection, yeah, there's some, yeah, it does say it's a bit slow. Okay, I'll stop my video. I'll share the slide again. Okay. Okay. So, so some of the many of the points I'm going to make today, they are actually nicely summarized in this paper that many of us who work in this area came together and wrote a review article. So, so this is a reference you can refer to to get a summary of the theoretical principles behind spatial patterns and how we can use to use spatial patterns to infer resilience. Okay, so how do we go about this? Okay, let's go back to the same model I showed you. I showed you this model where there was this simple logistic growth term, followed by non-linear grazing term. So I'm going to assume the same term as a local reaction term, meaning in space locally exactly same processes are happening. There's a local carrying capacity in a local grazing rate. Of course, the grazing rate can have some stochasticity in it, which is represented by this eta C term as a Gaussian white noise. And then we add a spatial coupling term via the idea that you know typically see dispersal, which is a mechanism by which you know one of the key mechanisms by which spatial interactions happen is modeled by a simple diffusion term. So what diffusion term does basically intuitively is it spreads things out in space. So this is the model I'm going to use as you do know the mean field part of this. If there was no diffusion, if I did not have the diffusion, this system will show the same bifurcation diagram by stability. And for a, even when there is diffusion under a bunch of condition, this continues to be whole, this continues to hold true. But of course, you know there are some many certain aspects once we add space, I'm assuming those are not in play here. So this is what we showed using a combination of numerical simulations and also analytical calculations. So I'm not going to show analytical calculations. These are actually stochastic non-linear PDEs, right. There are methods borrowed from the statistical physics literature that we can use to compute the same things I'm going to show you today, but I'm going to focus only on the numerical simulations. So what we have that here is over a period of time, we run this simulations and then we sort of stress this ecosystem more and more over time by increasing this grazing parameter C. So by increasing this grazing parameter C slowly over time, we find that a vegetated system becomes a completely bare area. So that happens over a period of 52 years on the time scale that we chose in this model. So let's look at the top graph here. What this shows is the average biomass density. If you were to do a spatial mean of all the vegetation density, you find that it goes, it sort of gradually decays. And then by year 48 or so, it suddenly undergoes, sort of a rapid shift downwards and settle down to a very low biomass density region. So we plot spatial variance and spatial skewness for these spatial images. So what we basically do is for every, imagine every instant of time, we are computing spatial variance, which is basically variance of all the data available in a spatial image. Likewise, spatial skewness is the skewness of all the data available for a given image. So earlier it was computed over time. Now we are computing over space. So if you plot this, what you find interestingly is that even before this nonlinear shift in the mean value happens, there is a dramatic increase, sort of, you know, close to tenfold increase in the value of spatial variance. Likewise, the skewness actually increases from a value of close to zero, all the way to one, and even begins to turn downwards, even before the mean value has shown any significant trends. One can do these calculations again and show that even spatial correlation, the third plot here below also shows similar patterns. So basically the message here is that increase in spatial variance and spatial skewness, increase in spatial autocorrelations. And also what I have not shown you here is that even in the spectral properties with sort of, you know, relate to both correlation and the variance, they also increase. All of these quantities increase much more rapidly than the spatial mean value alone would increase. So therefore we can use these as indicators, early warning signals in spatial ecological systems which do not have spatial patterns. Okay, so that provides a theoretical background of, you know, how the same ideas of time series variance skewness autocorrelations can also be sort of, you know, nicely transformed into, you know, can be applied to spatial systems. Now that's a theory, you know, how do you test this in an empirical world? We know what do we need, especially if you have an empirical system that you really want to apply to a large scale ecosystem, how do you do this? So we need three things to be able to do that. One is that I need an ecosystem that has undergone a transition. Okay. And secondly, I need to have spatial data over time at sufficient spatial and temporal resolution for the system. Finally, it turns out that there are very few or I'm not aware of any such data available. At least, you know, five, five years ago when I was looking, there was no such clean data available. So what do we do? Okay, so here is an idea. You know, how do we test this theory, even when you don't have, you know, such an ecosystem that has undergone regime shift or abrupt transition over a period of time. We don't have such a data. What best can we do? You know, I told you the theory, right? You know, we have this state variable as a function of time. We need snapshots over time. And then we measure these metrics, for example. Imagine that instead of snapshots over time, I had snapshots over space. So the x-axis is not time anymore. It's now either space or the driver values. Okay. So this is actually an idea called space for time substitution. This is widely used in the ecology sort of field studies. For example, if you want to understand how shifting temperatures change species compositions, how do species ranges change? One idea that a lot of field ecologists use is, of course, you can't wait for 100 years for the climate change to happen. You can use or look along temperature gradients, altitudinal gradients, where you can find temperature gradients, and then use that space for time substitution to sort of transfer or forecast what might happen in the future if the temperature were to change. So we use this same idea. If we have an ecosystem that goes from one state to other state as a function of space, can I compute these indicators? Do they show expected patterns? So indeed, it turns out that there are such ecosystems. So this is an example of the very famous Serengeti Mara ecosystem in Kenya and Tanzania. And what you find in this ecosystem is the central area is sort of predominantly a grassland. However, the peripheral areas is actually a woodland ecosystem. So we asked the following question. If you now go from the central grassland areas towards the peripheral woodland areas, if you could think of this as space for time substitution, do you find signatures of these early warning signals as measured by spatial variance to sort of correlation and so on, as you go from one end to the other end of the ecosystem? Okay, so we chose this very high resolution data at 30 meters and then we classified each pixel of 30 meters as either wood or grass. And then remind you the scale here is some, you know, we are really talking about a few hundred kilometers by few hundred kilometers. It's really a huge data set. Okay, so what we do is find the relationship between vegetation and the rainfall in this entire landscape. We find that, you know, if we in this landscape, the grass cover sort of shows a non-linear relationship with a mean annual rainfall. You know, it is sort of expected from many savanna forest ecosystems, you know, Carla has spoken about this, Simon has mentioned this. So the data here again supports the same hypothesis. So we find that the grass cover shows this highly non-linear foundation as a function of mean annual rainfall. So what we now do is, let me remind you the theoretical expectation if the mean value of the state variable shows a non-linear transition. Then a spatial variance will increase even before the non-linearity in the mean begins. Secureness will again increase even before the mean will decrease, likewise correlation and the spectral properties. Okay, the black data here, black points here, just to show, you know, that, you know, we are not getting any statistical artifacts. So inside exactly as predicted, we find similar patterns in our data. So even before the non-linearity in the variance have been on the mean has begun, variance has increased quite dramatically. Secureness, spatial autocorrelation and low frequency spectra. And likewise, we find this across many other, many other concepts I showed you there. So sort of, you know, this provides an evidence that, you know, one can use these, you know, mathematical, you know, ideas derived from non-linear dynamical systems and models and apply it to messy real-world ecosystem. Okay, so that sort of, you know, gives one example of how we can use spatial models of ecosystem by stability in reaction diffusion systems, you know, patterns. So let me now move on to regular patterning systems. Regular patterning systems are also called Turing pattern systems. And here are some really beautiful examples. I'm not going to cover a whole lot of this. Again, I showed you some picture earlier. There are many, many parts of the natural world we have refined very nice regular periodic patterns. And these are often modeled by a mechanism called Turing mechanism where there is a very short range positive feedback. And then there is a, you know, an immediate long range negative feedback. So this combination of local positive, short range positive feedback and a longer range negative feedback. Causes these patterns to persist. And this paper in science argued that these patterns may actually provide some indication of a catastrophic shift. So look at this picture here. Look at this sort of, you know, diagram. So what this shows is there is a region of by stability here again, the region of by stability as you move along this act region of by stability. The spatial patterns are changing. So, so, Rick Kirk and co-authors argued that this changes in the, these spatial patterns may offer some hints about the resilience of ecosystem. However, there are other studies that sort of contest this to show that there are so many types of these patterns and the, and the nonlinearity and stochasticity can sort of influence and you know, confirmed of interpretations. Nevertheless, but this is a very interesting idea that spatial pattern can actually offer some signatures of resilience. So all the third type of spatial patterns are not are slightly different. Look at these pictures. So if you look at these pictures, you know, these two have some regularity in the spacing between vegetation, likewise this, however, if you look at this, you know, this cluster is much bigger than this cluster than this cluster and then this cluster. So what you basically see it is see here is that there are a, there's a whole range of vegetation sizes plus sizes that are possible. And this basically gave led to a whole class of new models and new studies that found some very interesting results. In this paper, Scanlan et al including Simon Levin, they show, they found that if you quantify these patch sizes, vegetation patch sizes, and if you look at the probability density functions, they show a power law. The power law basically is a very interesting pattern because power law often indicates that there is no well defined mean and variance, which in other words, what this means that you can probably find really, really large values of clusters, which are impossible in simple coding like models. And of course it's not only in vegetation that people have found such patterns. There are also examples of such power law clusters in muscles, saudras, cigars, and scrubs. Okay, of course, you know, there is a, let me caution, let me add a cautionary tale here by saying that there are many, many studies that also very strongly argue that in a lot of these studies, the statistical evidence for existence of power law is really weak. There's something to keep in mind, a very important point. Okay. And, you know, in, in, you know, early, you know, there was, there has been quite a bit of research on understanding where do these power laws come from because you know, when you have a power law nature of any quantity. And when the power law exponent belongs to certain ranges, especially if the, if that exponent is between one and two, there is the mean value is theoretically infinitely large. Okay, and so is the variance.  So, so in physics, there has been a lot of work, trying to understand our laws and physics in physics. The basic idea in physics is that whenever there is a phase transition, look at the figure see here, whenever there's a phase transition from one state to other state, at the point of phase transition, like what's also called critical point, you see certain universal features. As Simon was pointing out, this is a, you know, irrespective of the complexity of the system, otherwise, at the phase transition, the number of degrees of freedom are often, often very low and so a lot of very different types of systems happen to show very similar properties. And one such property is the existence of power loss. So, there has been a lot of speculation in complex systems whether whenever the power loss that we observe in complex systems such as the foundation system, ecological systems and so on, are the indicative of criticality. And this is a whole field in itself and I'm not going to really touch upon it. I encourage you to sort of read critically on this topic, very interesting topic. So, what I'm going to now focus more on the mechanisms. How is the some vegetation ecosystems show irregular patterns, meaning the cluster sizes are not a well defined average value. On the other hand, there are some other ecosystems where the cluster sizes show very clear periodic pattern, just during patterns. So what's the mechanism that makes them so different. So, how do you serve that to, hello, can you still hear me. Yes. Because my network set the net collection lost. I'm sorry. Yes, on the. Okay. So the question I was trying to address here was, you know, how is that ecosystems of similar types show rather different patterns, spatial patterns. So one way to understand that is to look at the net interaction strength. So here a positive value means a positive feedback, positive feedback means that the presence of, for example, a presence of a tree will facilitate the presence of another tree nearby. So there is a local positive feedback, followed by no net feedback after a distance. So if you have only a local positive feedback what you often find these are these irregular shaped patterns. On the other hand, if you had a local positive feedback immediately followed by a short range negative feedback. Okay, this difference leads to highly regular patterns which are also called during patterns. So therefore, as Simon was pointing out yesterday, when we try to understand spatial patterns mechanisms become really crucially important. So what are the biological processes, and often these are integrated with many geophysical processes such as water that flows in the landscape. So therefore eco hydrology plays a very important role in shaping these feedback as well. So, so moving on from these you know irregular. So let's go back to the original questions that I set out, which is, can we look at these spatial patterns and then make some inferences about stability. So the paper by Sonia Caffee and co authors, they made this following claim.  On the other hand, if you observed a, if you observed as, I was trying to use mine. On the other hand, if you observe that the, if you observe that the cluster sizes are not proper law but if they're exponential, then they are more likely to be less resilient. So basically the argument was that you can use the cluster size properties to infer something about the resilience of ecosystem. So to make that point again, what you're seeing here is a level of low, low, low stress system. This is to high stress ecosystem. And what you're seeing here is this power law is bending away bending away meaning, you know, this is not a power law anymore. So, so these, these parts are likely to represent more stable ecosystem, whenever you see a power law or a heavy tear distribution. If you find a exponential distribution, this could be an case of a highly resilient ecosystem. So, you know, so sort of summarize, you know, this idea of how one can use spatial patterns as signatures of tipping points. So I want to emphasize there are three types, you know, first is that of no spatial pattern, right? When there are no spatial patterns, I discussed, I also showed you empirical evidence. And then when you have these periodic patterns, okay, and then you have scale free patterns. So when you have this no patterning system, you can use the what we call generic early warning signals such as you know, variance, skewness and correlations. Those provide early warning signal. When you have periodic pattern, the very presence of the nature of the periodicity and this, you know, usually this spotted patterns, they are often thought to be maybe an indicator that we are very close to critical transitions. On the other hand, when you have systems with irregular patterns, as you move from scale free pattern to, you know, you know, you know, not so fact that a thin tailed distributions. Okay, then, then you infer that those systems are less resilient. That's a summary of various theoretical models. So so far in my, in my understanding, there is a reasonably good evidence that these sorts of indicators work well in real ecosystems. There's quite a bit of debate about these two. And there are, there have not been too many empirical studies that look at these two. So now let me, let me sort of provide a twist or spin here. Basically, to sort of show that these results are a lot more tricky and complicated. So for example, in this paper that was led by my PhD students Sumitra Shankaran, what she showed was that this sort of claim that cluster size distributions are the patch size distributions to provide early warning signal actually have nothing to do with this phenomenon of critical slowing down, which I have already sort of summarized. And in fact, the claim that loss of power law clustering is an indicator is not true. So basically in my this loss of power law clustering is not a generic indicator of ecosystem resilience. So in fact, there is a quite a bit of, you know, depending on the model that one uses, and the mechanism that one incorporates, we can actually show sort of, you know, test the limitations of some of these metrics. So how do we go about doing this, let me, let me sort of try to describe how we build these simple models. So these are very different type of models, these are not reaction diffusion systems.  So in these cellular automata models, you have just one second. So you have, so you sort of assume that the space is divided into a whole large grid like in the central, central figure here. Okay, and different cells either can be occupied by a, for example, a tree or it could be a muscle bed. So tree is only a representative organism here. And it could also be empty. So it could basically be one, you know, we represent occupied cells as one, and others as zero. So you sort of implement certain stochastic update rules. For example, let's say if we choose this, this pair of a tree and an unoccupied area next to each other. So two possibilities happen. So one is that of death. So there is a probability of death here. And then there's a probability of birth here. For example, you can see that in this case, if this arrow is chosen in the simulation, this original tree has been is now dead. On the other hand, if the birth was chosen, you know, there is now an addition of three here. So there could be a birth event or a death event. Likewise, there could be additional complex interactions. So these are called facilitation or positive feedback interaction. For example, if we choose to update for a pair of trees which are next to each other, two things can happen. One of them can die like this happened here. So of the two here, one of them has died. On the other hand, the two together will facilitate birth of another tree nearby. Okay, and they happen with another set of probabilities. Okay, so now we can convert all these sort of intuitive rules of how birth and death happens in probabilistic terms, and depending on the neighborhood. Okay, so and so and in these type of models, typically, there are many, many, many parameters. For example, in many of the papers I was showing you earlier, often there are five to 10 parameter values, and those large number of parameter values make it very hard to understand what parameter is causing what effect. In contrast, in this model what we have done is we have chosen a very simple model inspired by statistical physics that has only two parameter values. One is P. P represents basically local birth rate as I demonstrated here, or even local death rate. P controls the baseline, the production and death rate. Q controls the strength of facilitation, how a plant will influence the birth and death of plants nearby. There are two parameters and therefore, because there are just two parameters in this simple model, one can sort of do an extensive set of simulations and find out what happens. So what we then have done with these type of models is do simulates, simulates them for a very large amount of time. So for example, I'm just showing you two representative simulations here. On the left side you're seeing a simulation for, I don't remember the exact parameter values, no they're probably low P and the low Q. Okay, on the other hand, I, if I'm right here on the right side we have kept the value of P which is the baseline birth rate, same as the previous one. However, we have a much higher value of Q, which is high positive feedback. So, so now we can very easily control two parameter values, and then see the effect. So you can already see very clearly in this simple simulation that all else being equal, increasing positive feedback increases clustering in these ecosystems. Okay, so therefore one can study how the clustering properties change as a function of positive feedback values. So here is the classic phase diagram. So what we do here in this case is consider two cases, Q is equal to zero represents a case when there is no, no, no, no, no, no facilitation. So in this case you find that as you vary this driver value P which is the baseline birth rate, the system undergoes a phase transition from a bare steady state which means everyone is dead on the entire spatial landscape. And there's a continuous phase transition to a vegetated state are also called active phase in the, in the physics literature. And the crucial point here is this phase transition is a continuous phase transition. On the other hand, look at the value with large value of positive feedback. You find that the response of the ecosystem to reducing value of the driver values highly nonlinear. There is a very small range of P the steady state density drops fairly nonlinearly sharply.  So this shows an example of how positive feedback in space affects the abrupt regime shifts. So unlike the sort of you know, phenomenological model I showed you in the previous talk. This is an example of a spatially explicit model where one can incorporate some realistic features and mimic features of by stability. Again, this would be the region of seen this model the region of by stability would be roughly as much as we saw very clearly shown here. So let's change this model what we do is the following you know we do simulations. And then you know from the simulations like this. We calculate at steady state, what are all the different clusters, what are the customer sizes, and what are the statistics of cutter sizes. So I'm going to show you one result from that right now. So what we have done here is you know just assume that we have chosen a value of P, which is in the middle of this phase diagram continuous phase transition, which is low positive feedback. We have chosen a system far from the critical point zero here. And then you find that at this point there is a power loss in the class sizes. Okay, so this much simpler model than the previous ones can also reproduce existence of power law in the ecosystems. And he said when the, when the positive feedback is high. You can find this power loss, even at the point of critical threshold here so this is I know, so this is the parameter value for this graph here corresponds to the exact parameter value with the system will abruptly collapse, and you find that you find a power law there. This basically means is some of the previous claims, such as cluster size distribution can be used as a how far or how resilient the ecosystem is really not robust for example, I'm finding the same power law distribution of course the exponents are different. They are originally experiments are different. And yet, this in this case, the system is really far from the threshold, right. However, in this case, this time is quite close to the show. So one can find the same cluster size distribution is irrespective of how far or how close you are to ecosystem. And what really matters is the positive feedback. The positive feedback is important mechanisms are important. So depending on the values of the server with my slides spent away. So depending on the value of positive feedback, we can find my, my, my tablet is behaving a bit awkwardly. What is this, there must be some option to raise. Yeah, I guess it's not the annotation of zoom, otherwise you have to go to annotate clear. It's called. Okay, I'll come back. So, you know, power law in the cluster sizes, therefore, is not a good measure. However, you know, there are other types of power loss that do emerge at the, you know, at the, at the point of phase transition. Unfortunately, the resolution of this figure is a bit unsatisfactory. But what you're really seeing here is a measure of correlations, spatial correlations. Basically, what this means is that, you know, how perturbations in space are correlated across the entire landscape, what we find is that typically, at the critical thresholds, correlations have, there are very, very long range correlations in ecosystems. And, and this manifests often as a power law in the correlation function, or the power spectrum. Therefore, those could be used as indicators of proximity to critical points. So in fact, we now have a manuscript that is currently being written up where we find some empirical evidence, some supporting evidence I wouldn't say very conclusive, but something consistent with this theory. Okay, so basically sort of, you know, if I have to sort of summarize this patient patterns are fascinating mechanisms matter. Therefore, however, the interpretation of the resilience from the patterns alone are certain one cannot naively use the patterns to make interpretations so the. So, for example, if they're one by by either by looking at the nature of patchiness or the question size distributions, we have shown in our papers that some of the previous simulation studies were probably finding a set of parameters where it seems to have worked but it's not really a general result. So, so this, so with that sort of, you know, demonstration of various simulational results, let me sort of briefly allude to what kind of analytical techniques are can be used in these studies. So, unfortunately, I'm not going to go into much detail. So, for example, we can take the space the cellular automata model I have described, one can write down a mean field approximation, and the mean field approximation makes a very nice set of predictions of the existence of critical, you know, critical points, whether the phase transition is continuous or discontinuous, it often underestimates the values of positive feedback, one needs to find a discontinuous phase one can also do something called a stochastic demographic approximation. Again, I'm not going to go into these details, I'm just going to mention to you, and you know, I would, if any of you are interested more in this, feel free to get in touch with me, I will be happy to share some of our own labs as well as more general manuscripts that sort of describes these methods. So basically there are a whole variety of methods one can use so classically the idea of a mean field approximation is that we have a well connected system, and I'm looking at a deterministic limit where in the number of sites are infinitely large number of individuals are infinitely large. However, we know that real ecosystems have finite numbers. How can we know the effect of those finite numbers so to do that something called a finite cell expansion, it's a very powerful technique. And there are methods of methods called focal plant equation Langevin equation, using which one can find the steady state distributions. Okay, so often in this approximation, you don't have a deterministic equation of this type, what you have is a stochastic differential equation of this type. And the stochastic differential equation would then need to be solved using the methods of focal plant equation on Langevin equations. And in some cases, the stochastic differential equations can also capture the effect of the system sizes that you are considering. So I'm not going to go into any further details of this. So I'm coming to sort of end of my talk so a lot of the work I presented from my lab today was done by these two PhD students they have finished their PhDs now. Really, very, very fabulous work done by them. And then also, many, many collaborators in particular Sonya Kefi, and her students Alex and Miguel. And of course, you know, there are many, many more collaborators and funding that has made this work possible. In particular, Amit Ashwin and Stephanie and it option they were all involved in some of the work I presented today. And so finally, before, before I take any question as I had mentioned, so I'm going to talk about intrinsic noise and by stability in collective so that's the sort of you know, prelude to tomorrow's talk how we can actually assess of noise and by stability and and how noise has some very counterintuitive effects. When we study collective sort of plants and trees, but instead of, you know, animals. So I'm now happy to take question I think we have quite a bit of time so I'm happy to go to details of anything that has sort of skipped over. A few questions in the chat, which I read for you. I just remind that if anyone wants to ask a question please use the quite a bit of I should have seen this midway through. Sorry. He doesn't pop up on my window when somebody chats. Okay, so go ahead with the questions please. Yes, yes. So I was just saying that if anyone wants to ask a question about can use the raise and tool. So, I'm going to start reading the question so the one question from to one is, so there is no universality for specially correlated systems found in ecology in general. So is there no universality for specially correlated stuff question.  See clearly, you know, there are many common principles and common patterns right you know you look at zebra code patterns are these some of the patterns I showed you in the beginning right, for example, sorry, I can, for example, sorry on this. Look at look at these patterns right you know some of these patterns, or even the code patterns in zebra, you know, we now know that the code patterns in many animals, and on this kind of vegetation can both be explained by mechanism such as during instability during patterns. So there is lot of there is their generality, and there is universality in the spatial pattern formation. But, but there are some. Also, there are also some details that are important you know, you know certain additional parameters like strong positive feedback and the scale and the strength of positive feedback can confirm these results therefore I think one has to use a combination of these mathematical general mathematical theories, together with the mechanistic approach I think one has to use a combination to sort of understand the limitations of universality here. I don't know if I answered your question right. Well there is no sign from. Yes. Thanks for the answer. So there is a question from Miguel Rodriguez, please. Yeah, I, I am thinking a little bit of the lack of data sets that you mentioned to test the this this principles and I was thinking if maybe land covers super pose like land cover maps super pose with carbon sequestration maps could be used or that's just two cores. So I think there are a resolution, because for both of them there are contemporary distribution and also historical distributions around. So, so, so I think for the, so I spoke about three types of special patterns like one is the first one being where you course crane so much that you don't know the special patterns anymore. Right. So the second one is there are very fine scale special patterns you know those images I showed you those were patches over tens of meters of approximately those scales. So the same with third one as the regular patterns they're also need to be observed on those case is the first one can be done using some of the data sets we mentioned. So those you know Landsat kind of data sets, right, which we are, which we are currently working on as well we are using a whole bunch of satellite based vegetation metrics to not only look at the patterns of various spatial metrics, but also can we construct model from data, can we derive, you know model from data as we are also looking at those questions but if you want to look at these you know fine scales patient tuning like patterns, I could be totally wrong but you know, I think that the data sets that clearly show evidence for the theory are lacking right now. Thank you. There are more questions on the chat box actually I can see that. Yeah, there were a few questions about the new model. Yeah. What is what is the model one without by stability is that's right for the model. So I don't know at what instant you asked me this question. So I think you are maybe referring to the model in a had in one of those slides. For example, what one can do is imagine that the density, the, let's say there is a huge spatial landscape, and you find that 40% of the area is covered by trees. Right. So 60% is background right. So, now how do I know it's driven by positive feedback. Okay, so what one can do is, we can create a null model which maintains the same cover in the landscape 40% but it's randomized the distribution of the entire trees. So the clusters that will be formed in the randomized data set will be entirely not because of the interactions in ecology. They're entirely because of the density itself. So that's one way to arrive at null models for some of these kind of questions. So it will not have by stability. So it's just entirely, I made up the data right so the second there's a question on what causes the sharp negative feedback. I think it's the steering system said so you find that there's a positive feedback for short range, which becomes negative feedback for longer range. So what happens in these systems is that, so for example if these are clusters of trees. So that is, they draw water from neighboring regions. So the neighborhood of trees will have higher water retention. What that also means is that the slightly farther away from this cluster will be devoid of water. So the water is sort of conserved, if you were to think of water as conserved on very short timescales. So the rainfall falls homogenous in the landscape. So there is a cluster of trees, they not only retain locally well they also draw water from the neighbors local neighborhood. And because of which are slightly larger distances, there will be a lesser amount of water than the, than the average. So that causes the negative feedback that this slightly longer distances. Oh, somebody has answered the questions. Yes, this is the beauty of the job. Yeah. Another question by Zoray, who is asking which, I mean, what does feedback bifurcation mean ecology, ecological modeling. I don't think I understood the question. What was the positive feedback can cause new types of bifurcations. So when we have a week by when we have weak positive feedback, you have typically have continuous phase transitions or continuous transition from one state to other states. On the other hand, when you have strong positive feedback, the transition can become abrupt. So that was what I was saying. I was not sure if I use the word feedback bifurcation though. Great. So we have, if there are no more questions, I don't see any hand raised. Great. So there will be the last lecture by visual on Thursday. So today's from now. Yeah, I think you will have opportunity to ask a further question. Now.


North Korean people 김정은, like a god 안녕하세요, 여러분 안녕하세요, 여러분 안녕하세요, 여러분 안녕하세요, 여러분 안녕하세요, 여러분 안녕하세요, 여러분 안녕하세요, 여러분 안녕하세요, 여러분 Where are you from? I'm from North Korea And I'm born there And I speak from all the way to North Korea to America And now I'm American As she said, she was born in North Korea And moved to America And now she came to Korea That's very interesting So I want to ask you some few questions So is it okay? Yeah, of course Go ahead Then why did you escape from North Korea? I always have dream of escaping through North Korea to China Because China is the only country that we can see So I don't know about America or South Korea So I watched a lot of Chinese movies In North Korea, we don't have enough lights 24시간, electricity wasn't running That's why I want to go to China to see the beautiful lights And then everything is wealthy So how was your childhood? My childhood was normal My house was wealthy enough Because my mom was a business woman So she made a lot of money from China to North Korea North Korea to China So I had a South Korean brand of dress Always snack was enough And food was enough for us But other houses like other families Or like having struggle Time with the like starving And you know dying from hunger How did you escape from North Korea? So I first escaped from North Korea to China border first And then I used to like be container of bus It looks like bed inside So there's like several bed like on the top And it's kind of bunk bed So I was on the top And I used on there I ride the bus China to Ross It was mountain And I walked on the mountain Three or four hours That's the border too That's one of the border So it's a second border So Ross to Thailand will be the third border So we used narrow boat Boat? Like a canoe Yes narrow boat You can not sit next to it It's very narrow and very like small And like only one body fit on it Like you can not sit next to it Yeah it was so dangerous It's very thin boat And I ever see that time So I was so scared Scary like it was so scary Because there was I mean alligators Alligator Alligators Yeah I know And then you know the circle things in the water I was so scared But finally I arrived Ross to Thailand Using the narrow boat That's how I crossed the three borders How long does it take to go there? It takes a month Actually it wasn't take a month But we have to stay several places Safe Make sure we safe to move Because we don't have passport or city license So we have to be escape secretly So after I got into Thailand And I was in present camp Actually I was looking for the policemen first Because Thailand police Thailand government close to South Korean government So we were looking for the Thailand government And that way they can rescue us And I was stay there Small president So you was in prison Yes I was in prison first How long? 10 months 10 months? In prison? Yes And I had a free American interview One for Korean interview Korean government interview So after that I was under 18 So I was 10 years old I need a rigor guardian So I had an American foster family Who they can taking care of us So I was staying there with them Like 3 years Yeah So that's how you come to America? Yes that's how I come to America How long does it take?  American life is totally different North Korea life Life in North Korea Because especially the high school is different The uniform Like in North Korea We always wear uniform In the morning And then afternoon We don't have to wear uniform Because we have to work Volunteer work always They don't pay nothing So we have to volunteer Like in school in North Korea In America There isn't any volunteer It's your choice High school If they force that That's not called volunteer No No It's just like I don't know how you call that But That's funny So like in America You don't have to wear uniform Always Just like You can wear this Anything you want It's just like very free And Free skin shape No free skin shape in North Korea Of course not There isn't any free skin shape If you do skin shape in the public place You will Go present You won't go present But like You can catch from Policeman Like stop Stop doing that So When did you come to Korea? March 11 How's it There's a big difference Like North Korea and South Korea Of course There's always big difference North Korea is totally different More than any other countries So South Korea It's like A lot of buildings Like very high And tall buildings Letters everywhere And I have one more question Like In South Korea We have the freedom of religion Like If you are Christian If you're Buddhism And even I'm Muslim I can go mosque I can pray Whenever There's freedom But How is it in North Korea? There isn't any choice For the religion Really North Korean religion Aren't you American?  Of course I'm sure I'm watching the news About this It's not acting They're sincerely they cry It's not acting I wasn't acting too I wasn't cry about this too actually It's our god Okay, so Thank you for interview Actually, I always want to talk about When I was a soldier I was always educated that North Korean is bad North Koreans are bad But when I meet North Korean Like Nara And you I'm Evelyn Evelyn Don't forget And they're so kind Very nice It's very confused I think North Koreans Are just like Our friends Yes We're normal people Yeah, right So I hope It would be Peace country Like I want to travel North Korea someday Yes Insha'Allah That's what I want to say Thank you for watching my video Thank you for watching my video Thank you Thank you Bye Bye Thank you Thank you Hello everyone So I have a YouTube channel Called Evelyn Jong And you can surf chat And I I work on Like YouTube channel I don't work on YouTube channel that much But Please subscribe My YouTube videos And then Subscribe And thumbs up My videos Thank you Bye


Right now Sophie have we got any questions on our slide or does everybody just want to go home? No, we do have some questions on our slide. Oh So the one at the very very top that has two upvotes Is how do you try and change slash influence grumpy front line staff to smile and greet parents and children? That's how do you okay, um, oh poor front line staff I have to say Generally speaking I find front line stuff to be brilliant They are often quite overwhelmed in their role and what I would suggest here is actually stepping into their shoes and try and understand What is it that is making them feel less than delighted in their role right now? So it can be sometimes really simple things like we sometimes find that front line stuff I've got really horrible working conditions that they're sitting constantly in a draft And that this is really unpleasant or that they're expected to deal with all the difficult stuff That's coming in but all the nice stuff gets cherry picked off by someone else So just putting ourselves into their shoes. I think is a really good starting point there But then also having quite an open and honest discussion with them about their role about how what they feel that they can they can bring I'm making sure that they feel that they're being I was gonna say fully utilized but that I think Sounds a little bit wrong. I guess making sure that we're playing to their strengths really and understanding what they they feel that they They bring and then giving them reason to smile making sure their surroundings are good And that they're appreciated that we stop and we say thank you to them And I put that out as a challenge to all of you really and do you have? Great front line staff in your school And if you do when was the last time that you told them that you think that they're doing a great job? And if it comes to your mind that that wasn't very recently Could you just write them a card or drop them an email or pick up the phone to them and let them know that you think that They're doing a great job because they don't hear it very often what they hear more of is the problems and the difficulties It's not an easy job So, yeah, that would be my advice there Brilliant, so we have another question next popular Which is what is the best to measure how a student is at the starting point to use as a guideline to measure progress? Strengthen difficulties or something else So and I Have sent you a link Sophie to the well-being toolkit from the Anna Freud Center Which is usually where I would look to try and decide what's the best tool for measuring kind of anything to do with Children's well-being There's a whole range of different tools and actually what the Anna Freud Center's well-being toolkit does is it kind of Outlines them all and lets you know what the strengths are of each of those different tools So that you can make a really good decision about which one will work best for you The thing I would say though is that whilst validated tools and measures are a really good thing And I'm a scientist and I love science and I love to measure stuff Sometimes the best thing to do is just to stop and work out What do you actually want to know because you can end up implementing some really long-winded tool? And you might find out loads of stuff, but not actually answer the question that you're interested in knowing the answer to So creating something yourself That's really short and really simple and actually asks the question that you want to know the answer to Might sometimes be a better way of doing it than using a validated measure It depends on what you're you're trying to achieve I think definitely trying to measure things in some way is good because we can see progress and often it can Help us to make good decisions But don't assume that a validated tool will always meet your needs You might want to create your own and it's just a question of saying well, what do I want to know? How would I know that this has exceeded what would that look like and then asking questions around that? Brilliant. Someone's just popped into the chat. I work with autistic children Do you have some advice for when we go back into the building in September? Also, do you have any suggestions for good social fun time with kids on the spectrum? So what we can do is send everybody Sophie the notes from the course about Supporting autistic children to return to school and we will be running that course again over the summer for anybody Who wants to come so we could send a link to that as well And anyone who wanted to come to that we've changed how you book on to those courses So you can now come as part of a premium membership to the site, which means you pay 17 pound 50 for the month and then you can come to as many as you want So you used to pay 20 pounds a session and I just pay for as you pay once and you come to as many as you like But in terms of simple things and I would generally be thinking always about how can I help this child to succeed? So I would be thinking and this would be true for autistic children or children who are school avoidant I'd be trying to think what's going to motivate to get this child to come into school Why do they want to come and it's not for us to judge their reasons because their reasons might not make sense to us It might be that they really missed Lego club or you know That there's a particular place that makes them feel comfortable and we might have much loftier aspirations for why they should be here But it's about what matters to them and seeing it from their point of view So trying to find a hook there about why they might want to attend And then thinking how can we create a series of eye cans for this child? So how can we help them to succeed? So what will often happen is that there's lots of I can'ts we see all the things that they can't do and instead It's about going really sort of macro and saying what are the successes that we can have here So it's not about saying this child failed to attend school. They couldn't stay in all day It's about do you know what this child managed across the threshold today and that was really great So we're looking for the successes that we can we can build so we can build on a series of eye cans and Then in terms of the other bit of that was around sort of positive social times I think for children who are autistic and I would be driven by the child And I would be trying to tap into their special interest is often a really good starting point So our autistic children will generally have one or more special Interest things which they want to talk about and do endlessly which might not make sense to the people around them But if we're looking to build relationships with that child Either stepping into their world and actually giving them inviting them to tell us about the thing They care so much about and to really engage with them and help them to teach us about it Can really help or pairing them up with other children who might share that special interest to Generally speaking we find that for our autistic children creating structured activities that have got clear rules of engagement will work really really well Whether or not that engages their special interest and things like Lego clubs and Lego therapy and can work really well here And there's there's lots of really really good ideas about there about that out there I'll send you a link to a book about Lego therapy whose title I've completely forgotten off the top of my head But that's very good Brilliant just making a note of that And so the next question is what different methods of parent communication are used by different providers, which they find effective oh That's probably one to put out there Is anyone got any good practice? They would like to share about what they found to be effective in terms of working with parents. Okay collect I Do a lot of texting Texting yeah lots of texting don't do video don't do anything like that a lot of texting and Obviously telephone communication, but a lot of texting and any letters that come out from the school I Will always follow up with the text not the full letter Just what they need to know and that is humongous brilliant for the the parents to say yeah I understand what's going on. I like that because I think as well text is so immediate and it's really sort of It's not very scary as a means of communication I think is it so things like letters can sometimes feel quite formal can't they and actually many of us struggle with the phone But a text. Yeah, yeah much more manageable. Yeah. Yeah any other thoughts on how people are engaging with their parents So one thing I would say here is Which I think someone did share earlier is about the sharing of good news So actually trying to change that conversation between school and home So often it can be that you fall into a cycle of only communicating with home when there's a problem And we get to a point where certainly I've been in this Role as a parent in the past where when I see the school's number flashing up on my phone I get that sinking feeling of oh no, what's gone wrong now? And actually if instead you could create a situation that when your school's number came up on a parent or careless phone They thought are brilliant. Why are they in touch? That's really what we want We want to have positive communications with home in particular where you've got children who have fallen into a bit of a cycle of Difficulty and challenging behavior if you're able to hunt for the good there and actually pick up the phone or drop a line home When something really positive has happened that can completely change the tenet of that relationship with with home And can make parents and carers much more ready to engage with you And it can also change the sort of narrative around school at home because instead of when the child gets home Hearing yet again that they're a disappointment that they've done this wrong that they've done that wrong that the other has gone Wrong if instead they hear I heard that you worked really hard in math today And you were able to sit and through the whole lesson and you you actively participated. I'm really proud of you That's a whole different thing to be happening Sometimes you've got to hunt quite hard to find that good But where you've got children who you're not making progress with actually hunting out those good things and communicating home with them Can be a really really positive thing to do We've been sent the right and Friday think good videos So they're all the recorded in school and then the children have been sent tell me that have been at home Have been sending in their recordings of what they've been up to that week as well And at the beginning there was wasn't very many and now everybody's starting to take part in and it is lovely Each picture each week takes a turn to do it And then they'll have special music to it this week is dedicated to the year six leavers But it's that has been a brilliant way of communication That's brilliant. And did you say you were using a specific tool for that or it's good Okay, I don't know that one. So I've had a class dojo I don't know if anyone else is using that but I think there are a few different tools out there Aren't they that are meant for communicating between school and home and some of those and it can be used really really positively and I think again This is always about just keeping a check on making sure that this is driven by the genuine needs of your school Community that it's being used in a positive way and that it's not putting too much onus on staff What we don't want is to create a situation where we're using something like say class dojo And that becomes another big administrative burden for already overburdened staff But rather that it's a positive means of communicating home. That's not too too heavy Next Sophie How can we support staff who are reluctant to ask for help how can it So how can we empower them to their own self-care plan? Yeah So the first thing I would say here where we've got staff who are more reluctant to seek help It's about thinking what is it about our culture here that means that some staff are Reluctant and is there anything we can do to change there and this has to absolutely be led from the top and I would be looking at What is the Kind of example that's being set by our senior leaders and we certainly do have a role there for our leaders for our governors of Making it clear that it's okay to be accessing help And then I'd be looking at things as well like the staff room culture Do we have a staff room where people feel able to ask or support of each other? Where we are supportive of each other when things are challenging and Then we can think finally if we've got someone who is is Reluctant to ask for help and we don't really feel like we're able to engage there I would do two things one is thinking more generally about how we can promote positive Well-being because that can feel a bit less difficult for people to engage with rather than tackling the difficulties So you might think about more generally more universal approaches to promoting positive well-being And then also thinking about whether there are any sources of support that we can highlight for those staff Which are anonymous so we do this for children too sometimes Where if they're not yet ready to confide in someone face-to-face and having these conversations with a known entity feels too hard We might be highlighting things like Childline or Samaritans and for staff We might be highlighting things like the education support partnership where a member of staff can go completely anonymously and get support and guidance with Any difficulties that they're facing and that can feel a lot less hard than having to talk to a member of Staff who you're gonna have to face every day And you might just not feel comfortable letting them know about the issues that you're facing and asking for help that way Brilliant. Someone's asked how do I access other courses? Great question. Did you plant that one Sophie? No, there's someone's actually and it's been upvoted as well Okay, so we can send through information about how you access the site, but very briefly So we've been working quite hard On on this and so we were a face-to-face training company And then COVID happened and so the plans which we'd had to deliver online training for many years that haven't actioned Have all now come to fruition or they haven't all come to fruition, but it's happening So since Easter we've had a website where you can access on-demand training And we've got now well over a hundred on-demand training courses and lots more in the pipeline Which are series of videos, so they're really short accessible bite-sized courses And you can access those by signing up to the site either as an organization So if you have a team and you would like your whole team to be able to access all of the courses We can do a four-week free trial for you and then it costs 750 pounds for the whole year for all of your staff to access all the on-demand training or as an individual you can Access those on-demand courses for five pounds a month And we also make every week a different course free for a week So there's a few free courses and again safer you can send a link through to those so our kind of COVID specific courses There's about five of them They're all free and always have been and always will be and then we make a different course free each week So last week it was about writing a well-being action plan for yourself this week You can access a free course on emotionally based school avoidance and another one about pathological demand avoidance Which I'm really excited about that one because this is a Condition that is not very well understood. It's part of the autism spectrum And it's really misunderstood and it's the kind of course We could never have run in the past because we couldn't have made it work We couldn't have you know We wouldn't have been able to get staff out of school for a whole day To go on that kind of training But by providing a course that takes less than an hour to complete and making it free to people for the week this Week we've had hundreds and hundreds of people complete that course who never would have known about this and they wouldn't have known How to meet the needs of those kinds of students and what we know about pathological demand avoidance is that it is a Kind of subset of autism, but when we try to treat it as autism Then often we make things worse for those children and things can spiral quite quickly for them And these are often the kinds of kids who will struggle with school based anxiety and might become School avoidance, but there are simple things that we can do to really help them So yes, in short, you can you can sign up So if he will send all the all the links through there and now in addition to being able to access the on-demand training We do also have our premium membership for people who want to be able to access the face-to-face No, the live online Opportunities as well of which we're going to provide at least four per month But we will be led by you as to what topics you want and how frequent they should be and that kind of thing And we'll be providing other opportunities as things arise and the other thing you could send through Sophie is a Link to the suggested course page on the website because again I'm I'm doing all the commissioning and I'm being led by what you tell me you need So a course that I'm in the process of commissioning at the moment is one on Mutism because I've been asked about that. So again, tell me what you want And I'll I'll do my best to to meet those needs I think I think I've told you everything you need to know about accessing our courses now So if you'll send through links and do just keep feeding back to us We're learning all the time and and it's been incredible the number of people who have engaged with our courses We've had and our bereavement course had over 25,000 people did it in a week, which is amazing So yeah, please do do join up and we will make sure that you all get added to the Mail list for the free courses as well. If you weren't now, I think most of you will probably already on it Okay, any any any more for any more. So there's quite a few questions. There's one about certificates For the courses, but I'll acknowledge that in my email What do you do if you're displaying work from all ability levels? But it is it's clearly causing bullying as children and parents compare work. Oh I Don't know the answer to that one. Sorry if anyone's got a good idea about that I mean, I think that's a wider culture question, isn't it? So the question was about if we're looking to display Work and sort of success at every level But that if pupils or parents are comparing the work of some students to others and it might cause kind of teasing or bullying Because what is successful when people might not be successful another. Can I just say that we we Don't ever put a child's name on a piece of work. That's Shoulders I have a lot of children who are in care and We can't afford the risk of identifying that they are At school with us. So the children's work is up That child has a photo of the work being up to take home for their carers or Parents or whoever they live with but you can't walk around the school and see whose work is Whose what you can do is see that that is year to work Because it's on a year to war or it's a year one work and within year one. There are children who are Making marks and there are children who are writing form sentences, but we we have to we have to anonymize Everything so that everything is equal We can't take the risk of having children's names on boards it it just And also we have children who come and go so quickly that it would be very difficult You know, we just try to make sure that we have a really good range up So we have something from everybody is has to go on the wall within a term But there are no names no Thank you, Leslie. That's really helpful. So just you know what we do. Yeah No, but I think that's the thing That's why it's always nice to come together because actually what is completely standard practice in one school is Something that's completely new and really helpful to another. So thank you for sharing that. That's really helpful So There is a question about the Lego Club that you were talking about earlier How do we run clubs like Lego when only one child can touch it before it needs to be sanitized? Yeah, how how we do that in this current moment is a bit more challenging What some of the schools I've been working with of doing have been kind of making up kits for each individual people So that they will have a bag with their Lego in and that each child plays with their own Individual Lego and then the Lego goes back into the bag and lots of special schools that I've been working with Have been working on that basis so that each child essentially has a set of resources that will be going around with them And it's difficult and lots of the schools I'm working with are having to invest in more resources And they would do normally in order to have enough for each child to have their own set Which might not be how they would usually do things but that's something that they're building into into their budgets And if anyone has different or better ideas then do do do share them But that's that's what I've heard of happening at the moment Brilliant Could a well-being action plan and a pupil profile be merged together or is it better to keep them separate a? Well-being action plan and a pupil profile good idea So okay So well-being action plans really briefly for anyone who hasn't done the training on that a well-being action plan is basically a really simple Framework for well-being where we think about what's in our well-being toolbox What the things we do to kind of keep ourselves happy and well What are the things that are included in our daily routine that we do each day in order to be well and stay well thinking about our Physical and our emotional well-being what are the things that we avoid because we know that those are things that kind of bring Us down or make us feel less good and then also thinking about What are the warning signs that things might be going less well for us? And what do we do next if we see those warning signs and who who and what is in our support network? So that's well-being action plan in like 30 seconds So Could that be combined with a pupil profile? Yes, it could I think and this is all really about doing what works for you And for the people so well-being action plans are a great framework for working with an individual people if you want a really easy simple framework for Generating discussion and understanding what might work for that people and as a starting point and a pupil profile Assuming that I'm thinking of the the right thing and people sometimes use the same words for different things But I'm thinking of something here that might go round with a pupil so that different members of staff might know how to support that People and meet their needs and so what you might do might be to create for example a one-page Passport or pupil profile based on what you learn from doing a well-being action plan and have that move around with the people so that Adults knew quite quickly what they might be able to do to support that People again in the notes will send through to you about supporting autistic children to return to school And I did put together a very simple one-page profile that a pupil could complete So that different adults knew what they could do in order to support that people and help them to emotionally regulate and Manage within the classroom and you might adapt that Another resource that I must highlight for you Is the Head Start Kerno well-being action plan website which will send a link through to you So the kids in Cornwall worked with us to create an online version of the well-being action plan where It's pre that there's basically loads of ideas from the young people themselves about how you might populate that plan And you can create an online version that you can then Either just keep online or you can kind of print off and it's it's it's a really really neat tool It's still in development and will I think get better and better But based on the needs right now and it was brought forward More quickly and published more quickly than it might have done and so that it could help to start meet It could start to meet need more quickly and running out of words now But it's really really great and we're really proud of it And just generally and the the kids in Cornwall have done some really fab work So do look up generally the Head Start Kerno work and you'll find all sorts there to inspire you and all sorts of resources You can use okay last couple of ones and so because I'm aware we've kept everyone a really long time It's just one last question Would it be beneficial to have a well well-being care plan for all students in your class thinking about supply teachers cover staff? Etc. Yeah, so well-being action plans and those sorts of frameworks I think are useful for everybody and it would be a really useful things for students to do as they're Transitioning back into school after the holiday because for everybody this is going to look difficult and challenging often I would recommend Putting together a well-being action plan in the run-up to holidays for staff and for students And at any time of transition when things might change and we just need to take a little bit more care of ourselves And certainly I think that having these kinds of plans and developing them with all students would be a really positive start to the New term thinking about how we're gonna keep ourselves well thinking about the ways in which we can support each other as well And helping friends to recognize the things that they can do to help on another because there's often a real will to do that And absolutely we might share a simplified version of those plans particularly for our more vulnerable students With the various different adults that might be involved in their care So often if we can find simple ways to communicate so that people can recognize when things are going less well and Really importantly what they might do next. It's incredibly helpful. So you might have a student for example who might have Developed a sign a symbol to say I'm struggling right now They might have a red card or it might be that they take the green felt pen out of their pencil case And they put it on their table and that indicates I need your help right now And that we might have a time of calm agreed with that student that when they put that green felt pen on the table in Front of them then what they need is an adult to come and check in with them Or to be given permission to go and leave the room and to do some breathing exercises or to go to a safe space that they have Within the classroom or within the wider school. It's about planning at times of calm about how we'll manage those moments of distress So that's all the questions Hooray. Well, thank you everybody and Thank you for coming. Thank you more widely for the absolutely remarkable work that you're all doing I've been quite it's been quite an emotional kind of term and a half and Every time I think about what you're all doing every day I get quite sort of choked up thinking about it because it's incredible you're incredible and Please do keep talking to us about how we can best help you to support the children in your care and your staff and the families as well But the one thing I would ask of you above everything else right now is please have a think about what you will do for yourself And how you will make sure that you get some form of rest some form of relaxation and some decent self-care Over the summer holiday because what you're doing is incredible But you need to stop at some point and look after yourself. Otherwise, you can't be the adult that your children need whatever Thank you ever so much. We will close there Everyone so may hope I get a break too. Yeah. Yeah, I'll try I'll try try and leave by example And yeah, thank you ever so much for all that you're doing and do take care Do be in touch and I'm sure I'll see many of you over the summer on the various courses that we've got running But have a lovely evening now.  Thank you and thank you to Sophie


What are you gonna make me a? Negroni would you like one so Stanley Tucci made a Negroni and the internet lost its mind Let's check it out. So a Negroni, but we're gonna make a Negroni. I Love up drinks as much as the next guy, but drinks with high sugar content And yes, the Negroni qualifies our unpleasant once they warm up and should always be served on the rocks unless drinking out Of a coupe makes you feel fancy in which case proceed So a fair amount of ice in a shaker and use your hands just it's the most hygienic way The tuch is absolutely correct here. Always touch the ice with your hands. I'm serious What you want is a double shot of gin. If you don't like gin you can use vodka There's no such thing as a Negroni with vodka If you want vodka sweet for muth and kumpari by all means drink it but don't call it a Negroni Also building the drink over ice as a no-no the ingredients will dilute unevenly a shot of Sweet for muth. I see he's not doing equal parts. I actually have no problem with this. Everybody has their preferred margarita spec I don't know why some bartenders are so legalistic about Negronis good on him for making it the way he likes Also being a man of culture the tuch must know that for muth is kept in the fridge So I'm assuming you pulled the bottle out right before his wife started shooting this video next and use a good sweet If you can find a good sweet that's great If you can find a good sweet for muth good for muth is ubiquitous dude. Welcome to the party Martini You know that brand martini? Martini is not good. I love martini and I do this for a living in fact I prefer it over carpano and most cocktails carpano is great stuff But as a tendency to walk over anything you mix it with it's great on the rocks, but in a Negroni I'll stick with martini. Thanks a single shot of kumpari kumpari correct, sir Never shake a Negroni if you think I'm being a snob try it both ways you'll see that I'm right put it in a coupe like that You can put it in a martini glass Any glass with a martini in it is a martini glass let that sink in you just held up two cocktail glasses you want to Garnish it with a slice of orange You want to put a little bit of the juice in I would never garnish a Negroni like this But this is one of those areas where in my opinion people may differ if you want your Negroni with an orange slice And a bit of juice squeezed in be my guest You want it? That will never happen That's good now this part of the recipe He really knocks out of the park toy with your spouse before you give them the drink make them beg and always try what you made before handing It off to make sure it isn't poison. Okay real talk This is how you make a Negroni grab your mixing glass out of the freezer add equal parts gin sweet vermouth and kumpari If you want to use more gin do it I won't tell stir with the biggest ice you have and strain into a chilled glass over the biggest ice You have get yourself an orange peel express it over the surface of the drink and garnish and all seriousness Mr. Tucci's video didn't go viral because he made the perfect Negroni It went viral because he's total class a handsome older man making a tasty drink while wearing an actual shirt tucked into actual pants For comparison, I made this video in Gryffindor pajamas and at the end of the day isn't the only opinion that really matters his wife's I mean the drink was for her. He'll probably never see this But mr. Tucci, please keep making and explaining cocktails in effortless fashion You're great to watch and we could all use a stiff drink right now I hope you wander into my bar someday so I can take care of your alcoholic needs.  Tucci's Negroni or this video leave it in the comments stay safe all the advice professionals, and I'll see you tomorrow


A college basketball bombshell Jay Wright retiring from Villanova and he shared out a statement last night John and maybe it's me being a skeptic maybe it's me seeing Tom Brady retire this past offseason in unretire but in the statement he released on behalf of Villanova that you shared out he never utters the word retire you do not see retire in this statement do you think Jay Wright is ultimately done coaching college basketball forever I do and you know one of the things that Jay has shared with me over the last 10 or 15 years is that he would love to take other jobs in college basketball but he also would not want to leave Villanova to take another job he would love to take other jobs in the NBA but he wouldn't want to leave Villanova to take another job I know from spending time with Jay this past season that he was burnt out dealing with running Villanova's program last summer to going then and doing the Olympics in the Far East with Team USA basketball and trying to juggle both and look I mean you know I think we're seeing too and you know you and I talk about this a little bit in our burgeoning friendship right here that there are other things in life besides work I mean Jay Wright again at 60 years old has gotten into the Hall of Fame has been a part of a staff that's won an Olympic gold medal has went to four final fours obviously he's won multiple national championships I mean I'm sure he made he's made more money than he knows what to do with he obviously is going to have the opportunity now to enjoy life to enjoy his family I'm sure that he will have a plethora of offers to get into the broadcasting world so he'll live life now on his own terms at the age of 60


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