 I'm happy to have to hear what you guys have done for me. I'm happy that they agreed to give us a seminar. We're going to come in here in 1990, but also it was really online. I can see getting a lot of colleagues connected. So I would start presenting Professor Cephe Consolini, who is the Senior Scientist at the Prophetic National Institute, who is 17 years old. His field of study is Space Plasma, in particular complexity and turbulence in Space Plasma. In 2000, he won the Dr. Cephe Borja Foundation Prize for his studies on the typical nature of electromagnetic dynamics in the substance. And he's lectured at the University of Tolbergata in Rome in plasma physics and advanced statistics and it's also more than 220%. So Professor Consolini, in this next 30 minutes, we'll share with us a review of the most relevant details of the dynamics of the air manifestors in terms of complexity. So please welcome Professor Cephe Consolini. Thank you, everybody. I would like to thank you to invite me here and to give me the opportunity to present some mini-review, let me say, about these things dealing with the complexity and why we need complexity and when we would like to discuss the near-earth plasma dynamics. Now, this is the table of contents of my talk and I would like just to start with the lexicon because it is necessary that to... someone is calling me. And it is necessary just to fix some words and how we use these words in our context before proceeding in the next discussion. So I will show you some results in the past. Then I would like to discuss some results dealing with the complexity and criticality in the matter of say dynamics. And I would like just to present some very recent results that we have published very recently, last year. And then I would like just to leave you with some open questions dealing with this topic. Now, lexicon. So in my talk, I will use two words and these words are essentially chaos and criticality. So what's the meaning of chaos and what's the meaning of criticality and how we use this terminology. So chaos is something that is typical for a dynamical system when at least one lexicon of exponent is positive and it is a chaos. You can observe chaos also in a system dealing with a few degrees of freedom. Completely different. This is the, for instance, a non-map when you can observe chaotic behavior when some parameters overcome some fixed values. And conversely criticality is something that occurs generally in the limit of many degrees of freedom in the infinite number of degrees of freedom. So this is the difference. You can find this definition in a beautiful paper that appears in Jensen, a journal of physical complex system. And one distinct features of criticality is the emergence of a longer-range correlation. This is typical, for instance, in the case of Isil model or things like this one where you have essentially a term which is an algebraic term that extends for many orders of models, essentially. Now, the other words that I will use in my presentation were complexity. Now, this is a very critical word because complexity sometimes assume different meanings depending on the field we are using these things. So I have just collected some definition and some, let me say, yes, different meaning of the words of complexity depending on different fields. Now, a complex system is a system which consists of many interacting elements that give rise to an emergent phenomenon. What is an emergent phenomenon? Something that can be directly surmised from the equation dealing with the evolution of the subunits, essentially. All complexity arises from competition between randomness and order. And this is another definition and that the underlying topology of a complex system is inherently related to a certain amount of randomness. Randomness in the interaction, in the network of interaction between the different elements. Another definition from Lou is following one complex system are formed by many agents interacting with each other. So it's mainly similar to the previous one. But in this case, they use also the word non-linear ways. So non-linear is another element of a complex system. And summarising, we could say that a complex system is a system whose phenomenological laws that describe the global behavior of the system are not necessarily directly related to the elemental laws that regulate the evolution of its elementary part. This is fundamental. And this is the emerging behavior sometimes as, let me say, a universal character. So it means that completely different physical systems. So systems that are essentially regulated by different kind of microscopic equations sometimes at a certain level of description, they show a similar behavior, a universal behavior. Complexity does the emergence of non-trivial behavior due to the interaction of the units, the platform itself. And let me conclude with the sentence that was on complex system on one special feature of complex system from Giorgio Parisi. An interest in physical complex system is the existence of a large amount of different equilibrium states. So it means metastability in many situations. So now we have just some definitions and I would like to introduce the topic of my book. The linear space is extremely complex. It's a region of space which is a consistent of many different units in terms of currents internal region of plasma characterized by different features and which responds essentially to the external driver. So to the, let me say, to the solar wind in a way that it is not always the same. So we, now we have not a completely understanding of the details of the interaction between the solar wind and this system. Now you can just give a look to this picture. You can see that, okay, this is a non-equilibrium system. It is sometimes in a stationary condition but this is not the equilibrium because the magnetic field, the geomagnetic field tends to be a more or less a depolar structure. So in this case it's completely asymmetric because the interaction with the solar wind just essentially elongate the system and also the fact that it is a non-equilibrium is demonstrated by the presence of a large amount of currents. So this means dissipation. And in terms of the prerogine dissipation these are dissipative structures and these are typical for systems that have to survive outside of equilibrium. Now, the dynamics of this system is extremely complex. So you can see here, for instance, a geomagnetic storm and this is the famous Bastille event that occurs in 2000 on the most larger storm that we observed in the last 20 years. And you can see how the response of the system depending on the latitude and also depending on which kind of currents we are monitoring using this geomagnetic index. So the plasma in this system behaves in completely different ways. The high-latitude phenomena are characterized by a very Bastille dynamics. The low-latitude show a more regular behavior even if this was regular. It's something that we have to take care because it's not exactly this one. Now, the study, let me say, in the past, in the early 90s, there was the first attempt to try to investigate the complex dynamics of the magnetospheric plasma using a different approach. For instance, one of the most famous paper that appeared, and that was the first paper, let me say, that demonstrated there is a nonlinear response of the magnetosphere to the solar wind driver, was the paper from Syltan in 1919. And in this paper, it was clearly showed that the ratio between the power spectral density of the driver, which is the solar wind, in this case it is the southward component of the magnetic field, is essentially, below a certain characteristic scale, the dynamics is not one to one. So there is a sort of a filtering effect. At the time they were talking about a filtering effect, but mostly one or two years later, essentially one or two years later, they realized that, okay, this is not a filtering effect, but the dynamics of this system, for instance, during the geomagnetic storm, is characterized by chaos. And this is one of the first paper by Cleimas in 1996, where they attempt to reconstruct their tractor, a keratical tractor, in the case of the DST index. So the essentially is the phase space that they reconstruct using the DST index and a delayed version of this. And they found that, essentially, you can reconstruct an attractor, which is very similar to some attractor that we have already seen in other motivation. However, they realized that we cannot describe all the physics, the area of the system in terms of autonomous system, but we need other models. Now, the main problem deals with the fact that, okay, the dynamics, the short time scale dynamics, is extremely rich. And we are not able with the simple model, analog model, to reproduce the real spectral features. So there should be some more that we are missing when we deal with the simple model. Simple model means a simple equation, essentially, dynamical equations relating with macroscopic dynamics of the system. So macroscopic variables. And so there should be much more. And we need to understand. I used to talk about the globality, the macronosphere, the ionosphere, because when we deal with, for instance, highlighted the geomagnetic indexes, we are including also the effect of the aurora ion sphere. And so we are including also the effect of the plasma in the ion sphere. So we realize that what is the origin of this difference? There should be more. It could be, it could come, for instance, from two blocks inside this medium, okay? And the point was the following. In 1992 and 1996, a pre-challenge price realized that, okay, we should have some stochastic elements in the dynamics of the response of this plasma system. They talk about stochastic elements. Later, me and some co-authors demonstrate that the character of the dynamics of this system is better described in terms of a multi-fractal dynamics. So it means that essentially the energy is this signal is a multi-fractal signal. And so this means that essentially we have much more degree of freedoms that the degrees of freedom that there's a small sector that they put in analog models. So, and the dynamics resembles, for instance, the dynamics of the two blocks. And so this was the element. In details, this is the IA index. This is the time derivative of the IA index. You can construct the measure and then you can start the how is distributed the release of the energy in a role during substance. And you can find that this measure is a multi-fractal measure, which means that you have a lot, a huge amount of singularities essentially in the system. So this behavior has a singular character in some sense. But the more we realize that, okay, if we take the IA index, for instance, and we do a local internet analysis approach, what this means that we are essentially computing the wavelength spectrum and we are extracting only the part of the spectrum that exceeds the oceanic condition. So you can expect that if you are observing a stochastic noise, you should have just some spotty behavior all of the frequencies. In this case, we found a coherent structure here. So in space time, you have that the energy increases in a coherent manner. So these are coherent structure. And we call this coherent structure as avalanche. So the character of the dynamics of the magnetospheric energy released during the course of magnetic subson is characterized by what we call punctuated, punctuated and avalanche dynamics. And another important point is that the avalanche does not seem to have a characteristic scale. So you can find very small avalanches here and the biggest one. And they are spreading over time and scales. This is scale because frequency in this case corresponds to time scales. Another evidence is the following. Okay. One element that seems to emerge from this analysis in the past was the fact that we have essentially two different kind of dynamics. A fast dynamics that occurs on time scale smaller than 100 minutes of the plasma and a long time scale dynamics that occurs on scale longer. These two dynamics can be different. Inside the magnetosphere we have two main processes during a magnetic storm. The announcement of convection that is completely driven by the changes of the condition of the magnetic field and also internal energy release that occurs as a reconnection process, let me say, in the plasma sheet of the region. And so one is very fast and the other one is very long in time. And so we can try to separate these two. And if we separate these two, we can try to reconstruct what is called the state function. Essentially this is constructed using, for instance, the statistics of the long time scale situation and the statistics of the short time scale using a Langevin approach. And when we do this, we see that the fast dynamics is a single well. So it means that this is not inside a single well structure while the slow dynamics show the formation of the metastable states like this one. So you just push from the gradient part on the metastable states, then you stay in that region and then you relax energy returning to the original configuration. This was something that it was extremely interesting but also you can see that during the storm and this was the period of the larger storm. If you look in time, we see how, for instance, the slow dynamics changes the state function, which means that we are generating a more complex fitness space if you want. If you want to use this term. Now, another property, as I was saying, is the football character. And football is a common feature that you can find inside the plasma both in the magnetosphere and in the ionosphere. This is, for instance, a peculiar phenomenon that occurs in the region which is called the current disruption. The current disruption is connected with the disruption of the cross-state currents in the tail region of the plasma sheet. And the current is wrapped and you observe the formation of field-aligned currents that tends to transport essentially plasma into the aurora regions. And during this phenomenon, you have a depolarization phenomenon because the tail of the magnetosphere relaxes. In this phenomenon, you can see that there are a huge amount of fluctuations whose features are generally captured by power-low spectra, which are very well in agreement with what is affecting its turbulence in many different regions. This is the spectrum for the current disruption. This is below the ion-cylidron frequency. Above you have a minus five-third or minus one. This is the spectrum that you observe in the cluster. This is the spectrum that you observe in the case of electric field in the aurora region as crossed by CSIS satellite. So you have different situations, but you have still, let me say, the emergence of power-low scaling for the fluctuations over a wide range of scales. In this case, these are more than two orders of magnitude. Then you have more than nearly four orders of magnitude. Here we cannot go in this part because the time interval is short, but so turbulence is something that is essentially constitutive elements of the dynamics of both the ion-sphere and magnetic-sphere plasma. Now let me move to another argument complex. In the early 90s, Tom Chan suggested that the dynamics of this complex system is better described by an infinite-dimensional nonlinear system near critical. So what does it mean? It means that we should observe the state invariant processes in the energy relaxation. So later, there were some studies. Originally, I think this connected with Tom Chan's view, where we attempt essentially to study what the similarities between the so-called self-organized critical system and the dynamics of the Earth's magnetic-sphere plasma. Now, one of the first evidence of the existence of scaling variance in the energy release was done just by studying the bus side of the I-index. In terms of, I would like to remind that the I-index is a measure of the rate of the energy deposition in the Rural region. And you can connect the direct with this I-index with the energy that is released during the Magnospheric Samson. And so essentially, by studying the distribution function of this bus by integrating, so bus by bus, what it was found is that essentially you can recover a power distribution over nearly three and a half orders of magnitude. So what does it mean? It means that you don't have a characteristic energy for the release of these energies, for the release of the energy from the Rituals. One of the models that was proposed at that time was the repeat-reforce model, essentially you are imagining like the drops of water that are more or less irregular with the Gaussian distribution. In this case, we are in completely different situations. So we have not a characteristic scaling. We have a lightning that creates a huge amount of small bus dynamics energy release and sometimes a very large one, the system-wide one. And also by comparing the results of the spectral features of the index with the simulations from the SEM-PAI models, by Cardard SEM-PAI models, we found that there was a very similar behavior. So this was one indication that perhaps the energy release during the magnetic-spheric substance is a scaling variant process. These evidence were later corroborated by other measurements. For instance, Angelopoulos in 1999 found that the scaling variant provided distribution function for the varsity bulk flows in the table. So it means that essentially the reconnection process that occurs in that region is not a massive one, but it's just a spotted dynamics with many reconnecting sites. And where the energy release depends on the structure that you are reconnecting, the structure that you are reconnecting. Later, also, Louis and Cardard SEM-PAI models found that the spatial energy distribution and side distribution of aurora is the luminosity and the Euliski space and features of aurora blobs. All these features are characterized by scaling variants. And so the existence of scaling variants in these different phenomena suggests that the dynamics of the plasma inside the magnetic-spheric and also in the spherical region can be related with the dynamics of a non-equilibrium system near a critical point. And they call for certain in step-organized criticality, this name was coined by Tom Chang in order to consider that, okay, we have a driving an external gradient, so a certain amount of tuning effect could be, could exist in this situation. These are some other results. For instance, by studying the aurora blobs as observed by polar UVI emerges in the ultraviolet, that they can reconstruct the energy deposited in every single blobs. And when they do their distribution function, they found that it's a nearly polar distribution function covering nearly six orders of magnitude. So this was really impressive. This is another example that essentially means that, okay, this is for auroral index, I index, this is what occurs in magnetic storms. So for the rule of magnitude, the magnetic index. So the behavior is similar. Now, what is the origin of this scale invariant behavior? Now, Freeman in 2000 anyway said, okay, but they can find similar results in 2.5 million as the solar wind. So what we are observing is essentially the same behavior that you have outside. But the situation is not so simple. Because if you look to the time of these events, these are not correlated one-on-one. So it means that, okay, the behavior could be similar, but we have different timing. Another point is this one. Essentially, if we look to the distribution of two quantities, which is the size at the, if I remember the duration, you can find that you have a spreading here in this cycle for the small scale, while for the large scale you have a correlation. And so, no, this is the outside. Sorry, this is the energy that is driven inside the minus sphere via the Perot-Argasso function. So the difference is essentially that, okay, the ear there is not a clear correlation. The correlation is only for the very large events when you have a massive transfer of energy and that kind of, in that situation the convection is the main phenomenon that drives all the magnetosphere. Another evidence of this double tension is just this one. Using wavelet and local frequency measure, we can separate the spotted dynamics from the directly driven. You can see here the relationship between this signal which is the index common place of the mean behavior that we extracted by removing the spotted dynamics and the BB sound. So this is the convection while this is the internal dynamics. So we have completely different aspects and this is extremely important because if you want to make a prediction, a forecasting for a space wavelength we have to join this information but we have to know the internal dynamics and this is something that at the moment we are not able to reproduce very well. So essentially we have these two processes and the internal dynamics is characterized by these scale-invariant features. However, as usual these results were clearly discussed with other results like the one that were found by Seath North Charm and Papadolos where they say, okay, during this you can recover, you can find a general shape. You have the expansion, the recovery and the growth like a complex manifold along a complex manifold and so you can see here the flow which is the expansion phase, then you go up and then you have the transition at the onset here which is just the jump from this manifold which is not just a flight but exactly the complex manifold. And they say, okay so the global we have also global long-dimensional dynamics that is observed both in Samson and in storms and in terms of the transition theory this is a first-order transition while there are some features like the previous that I have shown you before so this one which seems to be and also this related with the second-order phase transition so we have two processes that are joining during Samson and another step was done later just to understand if we can extract these two features so we use a different approach we extract the complex dynamics and we found that okay this seems to be something that is related with extreme statistics this is the distribution function the fresh distribution function which is something that is generally used to characterize extreme events statistics so what we can conclude from this analysis, okay we have two different processes that are here the first dynamics which is completely controlled by plasma features and the connection process occurring in the central part of the tail region which is characterized by scaling variance and that we can treat in terms of extreme events statistics and then we have the driven part which is the one that we are able to forecast using the external driver so using the solar wind condition we can reconstruct quite well a certain part of the external dynamics but we have we missed the fast fluctuations and the fast fluctuation is still important because for instance if you want to predict effects like the one that are related with the geomagnetic induced currents you need to predict very well the transient because this is really the the current that you can induce in this system and so in terms of prediction of forecasting is extremely important to get information about this dynamics so we can conclude this by saying that neither self-organize or self-organization model taken separately can explain the variety of the dynamic of the atmospheric activity on certain scales I would like to say that essentially the complex dynamics of this system is that there is also competing processes between dissipation and the fluctuating process, fluctuating process in the driver dissipation with the process occurring inside and now let me move to the recent results what we have done okay in the early 2000s some people tried to model the dynamics of plasma minus fatty plasma in terms of geomagnetic indices because these are the quantities how we can observe the global future the problem is that we are now we have not enough measurements to like let me say images of the plasma conditions inside the biosphere we have some spotting measurements while the global dynamics can be essentially monitored using geomagnetic indices with a certain level so they said okay we would like to model for instance a index using the stochastic dynamical process using a large equation and the first attempt were done by not they try to predict the fluctuations so the fluctuations and later Poolkin tried to predict the dynamics itself of the index and not of the fluctuating time the idea is that okay we can compute the the drift and the diffusion term they use this very simple expression and they computed the dependence of the drift and the diffusion term from the value of the index and but this was the prediction so again the results are very good that this is a real and this is the modeling away we are not convinced that this is enough and why because we believe that there should be something more and we try to essentially to see to verify if we can model these things using a simple equation using a drift diffusion equation essentially but to see to see this we need to essentially verify the condition on the Kramels-Moyal coefficients to see if we can stop our modeling just to get the evolution of the system in using just the terms to so the drift and the diffusion coefficient so the thing that we have done is just to taste the Chapman-Cormogorov equation the agreement between the the results of the observation and the one that we can construct a certain scale applying the Chapman-Cormogorov equation later we need to verify that the four order Kramels-Moyal coefficient is zero because if the four sort of Kramels-Moyal coefficient is zero we can essentially apply the so that we can reduce all our description in terms of the diffusion process but okay looking at the D1, D2 and D4 we notice that D4 is not zero so we cannot showcase the expansion for the Fokker-Pranck equation in terms of Fokker-Pranck operator and so we have just to consider that also terms of higher than four so the drift diffusion equation is not a good approximation and so if we do this a best description should be done in terms of diffusion that contains also Poissonian jump so you have a drift diffusion equation but you have some jumps that can be related to the Basti dynamics and this is an example of the real index, the model one and the characteristic of the power spectral features that are very similar now we are confident that we have to include also these Basti dynamics using Poisson jump process and so this means essentially the dynamics of this system is a complex dynamics consisting of many processes interacting with each other and this jump process can be related with the sporadic plasma enhancement and energy released in the central plasma machine and so these are the conclusions so essentially in this very drift review I have shown you that there are many features for the atmospheric plasma dynamics which are the nonlinear dynamics contrary to the equilibrium scaling variance non-equilibrium first and second of the phase transition fast as low dynamics Markovian character that can be bounded via a jump diffusion stochastic dynamics so I think that we have not to forget that we are dealing with an open system so in open system the situation we cannot relate with the equilibrium system near or close the equilibrium system or close the dynamic system and so the situation forces at some time separated from those producing the distribution and so this is something that can be the origin of this very complex behavior and now we we still have some open question and I think that these are the very critical issues that we would like to discuss in the future so in order to model to forecast the overall dynamics of this plasma system we need to essentially to identify the best type of variables because most of these studies have been done using geomagnetic states or by observing the situation of the magnetic field and other plasma dynamics locally but not globally another point is we would need to construct a real fitness landscape so how we can construct from this landscape so if you want to say the face space but this is not the face space landscape of the minimum of the systems how the system evolves in this complex landscape that reminds a landscape which is a complex instance you have a big but then you can have many other local like a year stable states and the last one is what are the relevant control parameters because we are the control parameters so the condition outside of the solar of the so the medium what these are extremely so what are the best control parameters that can be used to understand and model the different that we can find so let me say that I would like to thank and and thank you for your attention so this is thank you very much we have time for one short question and we are already invited to write down the questions with the cup we can also wait at the end to see the questions that you said let me check in the room the cup you usually do a question on the work we have thank you very much for my memory thank you I have only one question do you want to come back to like 7 I'm just curious about the one of the first very precise no no I'm curious about the trajectory of this this is GST right so this is a super of GST we can do the same with GST we have time to do this yes it's a reconstruction of GST using an analog model but even if we're using this analog model which is essentially a dynamic of system equation you have the evolution of GST that is related with the a driving term and the dissipation term essentially you have these two elements very simple depending on the changing of the external condition but the same can be observed with GST I even noticed that I have written GST but I forget to write the Surya D it was demonstrated that we are in presence of a stranger whose dimensionality is near 3 because they reconstructed the phase space and I noticed that the correlation dimension that you can compute by this is essentially a number in terms of about 2.5 or 2.7 and so this means that they face the motion occurs on a fractal structure in the phase space and when you observe you have a fractality this means that it is a stranger and so the behavior is chaotic because it was demonstrated that in the case of chaos you have a stranger that okay so this time again let's try again let's and okay you don't mind asking me to hold your presentation while I'm still yes if I am able to do it let's try okay to our second FBI so I have a special presentation for you she is working on 14th year she joined the C&R group for the National Research Center in Italy and in 2014 she entered the Institute for Complexity in the same time being involved in turbulence and plasma irregularity in the summer of nine she started to work on metriplexity formality so I think she will explain what this means what this means in 2014 she has been operating with biologics and all things were modeled so he will present also some formalities beautiful yes which he started in one thousand and one dynamic not that the second thank you thank you I want also to mention and thank very much both Bruno and Sandra more than other than Genka for inviting me and giving me the opportunity to speak to the audience here and connected from away so my key point of this presentation is a very short I wouldn't say review but rather spotty tasting of dynamics of course I will not bother you with the thousand and one dynamics where dynamics I mean a dynamical system so a set of variables describing a physical system and the equations describing the motion of these variables that we think are enough to describe the system then the comment not that F equals N times A was not enough underlines that to my understanding complexity is not in the main dynamics from complexity that you may find from complexity don't change the basic laws of physics that we are aware of like the beautiful laws that Stella has written on her on her shirt with the general view the grande but consider that all those laws were obtained focusing mainly on singular particles on single particles on very few degrees of freedom systems and now what we have to do is taking many many systems undergoing the fundamental laws and put them together to get what is finally actually complexity so these are the contents of the presentation I will define complexity as a property of many composite systems on a one hand I would say that complexity in a sense doesn't exist as anomalies don't exist because everything is complex the non-complex things are the exception and not the general rule we give three examples that are because these are the things in which I work so turbulent media as an example of complexity that is in situations of high local gradients or long distance interactions the parcels of fluid organize themselves in structures that are singular and coherent those structures Giuseppe Consolini was speaking about and this is for beyond smooth treatment that is the treatment of Zumbia art is better than with the variables that are not everywhere differentiable that are not everywhere deterministic or smooth I will speak about these metriplectic formalism another subject about dissipation dissipation like mechanical friction that transfers the energy from microscopic to microscopic very small scale while in the case of turbulence the energy transfer takes place between nearby scales mainly and last but not least I will invite you to peep into the world of quantitative life science speaking about networks of interactions that describe profit webs that is network like schemes describing ecosystems conceived like unique whole things described by the many very many variables necessary for those to be described complexity is what happens when the many or even few actually constituents of a composite system interact in such an important way that the collective behavior of the system results more than from the single characteristics of the single components from the characteristics of interactions among these components here I give you the example of the exceptional non-complex composite system that is the Maxwell gas a model in which a guest is represented as the collection of small particles rigid bending on the on the other meeting interacting only when they meet each other with point like interactions and in that case the non-complex case the behavior and the thermodynamics of the whole system may be rather easily inferred from the properties and the expression of the energy of the single particle because the interactions are point like they almost don't exist they almost never exist in case of much more properly complex and in this case non-complex systems I can say you know what they do they the subsystems as isolated ones that's it instead in complex properly complex system like colloidal systems particles interact with long range interaction they sense each other even from afar and what happens is that this determines the emergence of mesoscale structures that is aggregates of subsystems like this here and there in which that they have a scale that interpolate between the scale of the microscopic component and the scale of the whole system now this produces a hierarchy of aggregates between the single particle and the whole system scales giving rise to behavior that is not predictable a priori if you ignore interactions like instead in the case of much less so what one may say now is what they do as isolated ones you make them interact and everything changes and this is the essence of complexity the emergence of things that you couldn't expect if you didn't take into account the interactions so the first example of complexity is turbulence that has been long retreated by Consolini turbulence organizes the free evolution so that there are these features coherent structures may distinguish it that these groups of subsystems organize going together forming coherent structures and this happens on many scales like vortices in the classical turbulent theories the local quantities and this is very important like velocity, density kinetic energy or dissipation in non-ideal limits show mathematically irregular behavior if you describe them with local quantities these are non-differentiable almost everywhere they have spikes they are really wide like these like these plots I have reported of the velocity of the solar wind and of the temperature of it from this beautiful review of blue and carbon and the time series and space profiles appear as intermittent noisy signal it is clear here that I am speaking of noise in a possibly improper way for some one of you actually for me noise is something probabilistic okay not necessarily gaussian not necessarily wide not necessarily uncorrelated okay so what we introduce first of all is the so called stochastic approach that is I try to describe the system via equations in which I try to consider the nature, the probabilistic nature of fluctuations directly put in the equations some noise probabilistic terms these are basically works that I have been doing together with Gosolini SFD stays for stochastic field theory so you turn all the fluid equations and plasma equations into stochastic field theories that is local descriptions in which noises appear what are noises in this case okay for instance this is an HD okay written in suitably annoying formalism with all the indices of SO3 group okay basically this quantity is here like omelow the ratio between current and matter density and the ratio between the gradient of pressure and matter density is considered so why the so irregular to be better represented by noise so the MHD equations become longer than field equations that is field equations in which noise in which probabilistic terms like this these and that appear the same thing can be done and we have done it lately for equations in which instead of the local velocity and the magnetic field of MHD we used their gradients to stress the topological nature of the structures that we find besides this what I want to say is that if you have a system with noises in its equations what happens is that you don't have the initial condition problem like the Newton problem with the initial condition when defined and then the forces even for all the times later you have terms forces kicks that continuously time by time throw the dice so to speak so you will not have a system leaving only one life but statistically speaking leaving many many let's say histories together each weighted with a different statistical weight probability to take place depending on the shape of the dynamics that you have put there precisely like when pharma introduced these graphs the path integral so the history and the probability to behave like this or like that of these kind of units that are the turbulent such a this is just calculated via integrals what do I mean ok for instance this is a system that many of you may know the so-called equatorial let's say turbulence given by the E cross B effect in the ionosphere you have an interplay I will not go into the detail because it is not possible to explain it shortly for those who doesn't know who don't know and for those who already know it it is simply annoying but however it is an interplay between the geomagnetic field and the georectic field and the velocity of the plasma so that the equator the plasma of the ionosphere is pulled up by this combination and just like a fountain when it falls down it simply makes turbulent irregularities on the top of the fountain of the plasma fountain just because of the interplay electric, magnetic and gravitational now what happens is that typically in your simulations you assume that there are some seedings so to speak at the beginning so you say the ionosphere has some irregularities here and there let's see how the nonlinear evolution develops those irregularities here the idea is very different you consider that actually the equations of motion of fluctuations that is represented here this big object I am not going into details however it is a little bit bigger with these quantities r and psi here that are basically related to gradients in their space or time gradients of local quantities and they are understood as widely fluctuating so they are noises if they are noises the system will develop in probabilistic way in order to calculate so you can define a probability to go between the time initial time and final time initial ionospheric configuration into the final given ionospheric configuration this depends on how the deterministic dynamics couples with noise between the initial and final time and you can calculate this kind of path integral that is very complicated and I didn't there to put the calculations until the end but basically what I want to know is that as in quantum mechanics you once you accept the presence of probability in the turbulence as in quantum mechanics you throw your reactance into the accelerator and you say ok this is the initial condition I give the final let's say products I want to see and I calculate it through a path integral to go from here to there from this configuration to this final other configuration in this time the same thing can be done for a turbulent field for in a regular field I start from a given condition initial condition I want to see whether for instance two polarity of magnetic field will reconnect or not and such thing and I can calculate it in principle via a path integral which is one of the most complicated thing I know in the mathematical physics in turbulence this has already been told by Giuseppe so I will be very fast on this multi fractals and fractals appear basically what we discovered that domains of physical interest may be not space filling that is not having a dimension like 3 or 2 that is an integer dimension but rather domains which are self-similar and have a real that is non-integer household dimension for instance in the multi fractal formalism you collect the let's say demography of the degree of casps that you find in your turbulence sigma saying that a given property of the casps like going like this for instance is present in the locus of the points that has for instance dimension household dimension 0.4 while another non-casp in this case regular behavior 0.4 which dimension is 0.6 so it is a collection of singularities and the population of singularities different singularities have non-integer dimension and are non-space filling domains what you discover is that fractals are not all beautiful, bizarre and nice but may be useful to try understanding the phenomena like space plasma like faster connection that is the dependence of the magnetic connection rate which is faster with respect to the number than what is predicted by the traditional mechanism so if you assume that the locus magnetic connection takes place is not space filling but rather a fractal dust of let's say dimension D the dependence on the fast of the magnetic connection rate on this Reynolds number is faster than what happens if you assume that the space in which the connection takes place is space filling so you observe actually something like this in nature you can't explain it without assuming that it is difficult to explain it one attempt could be assuming that the place where this connection takes place is a dust of suitable dimension okay the second how many minutes do I have 10 more okay so I will be I will be very fast on this point because I wanted to speak about a little bit on trophic webs okay so this is simply another way of describing this dissipative systems that are systems with dissipation breaking the beautiful Hamiltonian formalism that has the great with property of algebraizing the basically the dynamics okay I'll just come to the to the conclusion here there exists a multiplexed formalism which is a formalism extending the pure Hamiltonian part of the motion via a part in which you have the combination between a symmetric symmetric matrix G and the gradient of the entropy of those microscopic degrees of freedom through which dissipation transfers energy and this is equivalent to creating let's say a non-unitary motion in quantum theory. The basic thing is that this algebraic scheme allows you to study systems like thermodynamic systems in which the energy is conserved while entropy grows okay these are the systems to which the multiplex system has been applied okay let's go to discuss a little bit about a traffic web is the evolution, the cultural evolution of a traffic chain of a food chain when we were children we were told that there is the grass that is eaten by the herbivore that is eaten by the small carnivore that is eaten by the large carnivore in a chain now we have understood of course that ecological systems work much more like networks of relationships instead of chains so traffic webs are networks that represent the interaction among the different species in having a given environment and having ecological relationships like prevention competition, cooperation and so on the beautiful thing, the nice thing of the traffic webs is that they describe the environment not taking care only about the evolution of the single species but focusing on the interactions among them so that the dynamical variable of the describing network or a traffic web describes the whole state of the system so I will tell you about two traffic webs on which I have been working that is the competition between two algae different algae species so to speak that are grazed by sea urchins and that are grazed in different things in different ways I'm sorry between the two different species of algae and the phenomenon of kleptoparasitism of wild boar on woods now what does this have to do with all the plasma physics that we have been speaking about actually these are manifestations of complexity because as we are going to see the phenomena that we have been taking care of in order to write the equations of these traffic webs are basically due to the interaction not only between the species but also between among the different individuals of a given species in a food chain you have a wolf that kills a rodeer and that's it meets a wild boar if he is fit enough it's a wild boar and that's it so interactions like the Maxwell particle in a traffic web with this phenomenon described as I'm going to show you if I have time basically the interactions on the number of individuals the nature itself of the interaction depends on the number of individuals of the two different species in a sense enhancing the fact stressing the fact that how to say force may be made by union so if the ratio between one species competing to the other is of a certain nature then a certain behavior appears so okay this is the competition between the chistoseira which is an arborescent alga and turf which is a meta-community of invasive smaller macroalgae that may take profit of the disappearance of chistoseira and both these algae are eaten by sea urchins like and they compete among each other so both algae have the same grades but they interfere with each other so these are the things that one has to take into account to write the equations I'm going to show you so first of all as recruitment you have an alga that propagates its seeds so to speak in the, it uses its seeds in the environment now what happens is that in the case of chistoseira if the propagule pulls this object here, if the seed pulls outside the canopy then it survives while it pulls inside the canopy the shadowing of algae may kill it so what happens is that the recruitment of the population does not depend on the nature on the behavior of the single individual but by the presence of the whole group the same thing happens to the propagules of the turf with the difference that the propagules of the turf may be brought by the current of the seed so they can come from the far not only the propagules of chistoseira survive inside a turf while turf may survive as epiphyte or as let's say undergrowth like here in the canopy of chistoseira last but least there is a big difference between the grazing of sea urchins on the turf algae that are small like a carpet and may be grazed all over the place while chistoseira are like big trees for their sea urchins and they rarely there to enter rarely manage to enter the canopy but simply eat the border of the canopy this and the one on the top mean that actually there are relationships like the predation so to speak of sea urchins of chistoseira and the reproduction of chistoseira itself that only take place on precisely to precise topological topologically precise places that is the border of the place where this algae and this will affect deeply the form of the equations these are the formula of the equations those who among you have a little bit of familiarity with the trophic webs and interactions among species may recognize that for instance chistoseira basically has a free term that is like the logistic equation so this tends to saturate at a certain maximum carrying capacity that is sustainable by the environment but it behaves like not only the population see but only the square root of it just to mimic the fact that only the border individuals due to this complex behavior of interference among individuals of the same species survive I will not touch very much the other terms not to be boring but however basically for instance here the presence of this square root here instead of the first power like here mean that the sea urchins may only the border of the group of the sea urchin may interact with the border of the group of chistoseira while here all the sea urchins and all the individuals of turf may interact with each other precisely because here we are speaking about the border interaction and here we are speaking about just a mass interaction okay I don't I will skip the last part because I don't think I have time but however such a complex system here may be studied in terms of bifurcation for instance varying this parameter that is the mortality of sea urchins and you may see that there is a situation if you increase these sea urchins of the sea urchin mortality of chistoseira and turf and sea urchin themselves what happens is that there are scenarios where these get extinct they survive scenarios in which there are oscillations and scenarios in which there are other fixed points here with respect to the small delta u regime this means not only that the system may be fit to represent different ecological scenarios but also that very okay so this is a very rich dynamical system but that maybe can be used to make some kind of management adaptive management of the environment okay I will skip the last example of and thank you very much for having been able to run after me or see if you follow me or look at me at least all over the seminar thank you very much I'm sorry so we have questions or online can you check online okay please go ahead I don't know if you could take a few minutes just to summarize the work we are doing said okay okay I don't have the presentation on this computer but however there will be a repetition however since 2019 I have had a great pleasure to interact with professor and the about a crazy but beautiful project a don't you shop like project a project of research I'm not thinking about management okay to answer these basic questions that is how predictable the ionosphere the local ionosphere is so the idea basically because this is a very important question both on the applicable point of view and the basic idea that we had and has made me push for instance the ICTP group and Giuseppe Rosolini's group to meet and to start working together is that we can we have to understand the dynamics of the ionosphere from another perspective probably with respect to what mission is done importing in the dynamics of the ionosphere the tools and ideas of complexity in particular we have started to practice sorry to say we had to wait for the end of the pandemic because it was not easy to work and we all had other other pains and problems but however what has come to as a very beautiful gift that we made ourselves is the starting to study a proxy very commonly used proxy of the local ionosphere state that is the vertical total content time series of this quantity analyzed as the same proxy of the dynamical system of which one wants to reconstruct both let's say the dynamics at least from a geometrical point of view so first of all to reconstruct the number of dynamical variables necessary to describe the system the evolution of which this rise this proxy via the embedding procedure going from the one-dimensional series of the vertical total electron content to in the case we have three-dimensional phase space or motion space let's say in through which a representative system let's say encoding the local ionosphere dynamics should move in order to produce the key cvc and not only this space is reconstructed but also the household dimension of the possibly strange attractor along which the system moves and the degree of self ignorance let's say translation of information that the complex system produces instant by instant that is more properly said by Kolmogorov and Shapiro and it's inverse that is basically the time horizon of things so or else I think that this is a very beautiful course I like otherwise I wouldn't participate nearly but this is on the propaganda what I can say is that this is a very important attempt to import this kind of mathematical physical culture into the ionosphere and the space not that we were the first ones to do it definitely not that we are possibly the best ones to do it but however we are trying to it is my pleasure and honour to say that one of the most important that say reference for ionosphere community ICTP Schellers group is interested in this adventure we have an interesting question in the chat I will read it to you the question is from Fabio Guedes he says for your presentation you mentioned the eclosive reach as an example of complex structure of the equatorial plasma is there any sense to use the dotted web approach to manage a typical phenomena like the formation of plasma or is this useful only for biological scenarios so thank you very much Fabio where should I look at Fabio over there possibly I think that actually trophic webs are a graphical way to represent a kind of interacting not really interacting variables so if you have I don't know sorry I cannot if you have some vector like this so you have a vector and dynamics each that's like I don't know xk that is a function xk itself xn you have many variables interacting among each other each defending from the other this may be represented as a trophic web in a sense or as an example so may these variables be species of animals plants or whatever you want or physical dynamic or variables for instance fields and pressures or whatever basically they work in the same way for instance there is a beautiful model of all magnetostatic currents that is the wind mean I don't know how updated and how modern these dates back many years ago in the 90s they were correctly come wrong like a complicated circuit electric circuit not particularly complicated actually with resistors and to other kinds of influences on currents now the beautiful thing is that these circuit written like a set of ordinary differential equation coupled together it rise to chaos it rise to different regimes like the main mean my scenario was speaking about so these simple representation without fields, without statistics without anything dangerous is already able to state ok the magnetosphere is not a trivial object standing there with no dynamics so yes of course we have other questions from from the lab great presentation here thank you the presenter what have you made to understand the dynamics of the various processes in the magnetosphere nonlinear tools how possible can we advance the direction the charge of drawing the stone the IA with nonlinear approach well I would like to say this answer mine is the following we have many tools like I feel like ok possibly I am drunk but I feel like at the beginning of quantum revolution that is how could we advance in understanding why electrons don't behave like balls of a billard try this model try Eisenberg's matrices try function this try that and then human culture composes full picture we have different components we have different tools we are trying to put them together and do what is probably necessary I would like to add something if the problem is this one first of all it's a matter of time scales the first point is at which time scale we would like to predict the response of the dynamics of such a thing the second point is ok you if we accept the second time scale we can use some methods to provide forecasting of the global evolution of these things but if you would like to move to a shorter and shorter time scale when we have no control of the past dynamics as I've shown before the problem is that ok probably we have to use an approach which is different from the standard one which is much more similar to the meteorological approach where you can you can use a probabilistic approach ok we have let me say an ensemble dynamics so you can perturbate the dynamics starting from your equations and then also non-linear equations if we are capable of writing a simple non-linear equation you can try to perturbate the initial condition to try to extrapolate the dynamics after a certain time so you can just make a probabilistic description in terms of mean and confidence limit of this so this is something that we can do because we have no control and not enough capabilities to follow the variables that we have in this system so the approach could be this one in terms of the probabilistic one as you can find in meteorological forecasting as they say tomorrow it will with 550% of mobility this is the only thing that I can see right now so I don't believe that we will be able to have a deterministic prediction but only a probabilistic one so this is a way how we can change our mind also because we have too many variables sometimes as I showed you we are in a critical state so we don't know exactly what is the evolution because as more details can influence all the systems and so this is my Thank you to finish the seminar I thank you again for everything to forget to my STI colleagues that we don't have specific title to those that are online and also to Nicoleta who is online thank you of course on remote thank you very much for your experience