Stefanos 5. lekču. Mateo, možete me vzlušati, da imače vzlušanje. V 2022 sem nekaj, da se vzluša, da se vzluša, da se vzluša, da se vzluša, da se vzluša. In tudi nekako bo vzelo, da nekako vzelo, da je nekako nezavršen. Meni nekako nezavršen, da je za prv vič nekako in na prv vičen na vzelo from Bangalore, and Tata Institute is a fantastic scientist, and also ... a very nice person. I know him well. By the way I could mention of him that ...  A druga vse je John Hopfield. Sveš je zelo jazem povedo, oj Matheo, ne? Se se da bila v zelo v 80-iljah, ne? Maybe you can say what about him, because you know better, but okay, essentially it's neural networks, and as you know, neural networks and I mean artificial neural networks have a long history, they started in the 50s with perceptrons and then there were the contributions of megalogue and pits, but I think John Hopfield was the first one to really formulate attractor neural networks, so the concept that the dynamics of artificial neural networks could lead to an attractor, so to something that could look like a memory, so then open the field to how you could store different attractor so that would correspond different memory patterns, so I think that's the contribution of John was, I don't know, maybe Mateo knows better than me the field so he can add some words. Okay, so unfortunately the medals will not be given this year because the conference, the start of this conference has been moved to next year because of the COVID pandemics, so they will be delivered only next year, and I would like to add that there is also a young scientist prize of the Commission of Statmec, and I know that they are working on the candidates now, and the young scientist prize will be announced later during the year, so okay, so I think, I don't know if you want to ask something about John Hopfield, but I think it's enough, I think it's... It's also worked on kinetic proofreading, so proofreading, I mean, why is it that when DNA replicates in ourselves that is, I mean, the error is much, much smaller than what you would expect just from random errors. Very good, so, last year, as you know, we had the second Nobel Prize in Statmec, we could say, so the first one was to Wilson in 80, something around 80, and the second Nobel Prize was to Giorgio Parisi, so the field has been honoured by two Nobel Prizes, now one fortunately died. I was a member of the Commission of Statmec, and of the C3 Commission for a few years, and I was always sending messages to Kenneth Vincent, he never replied the messages, so it was a very peculiar person, so the two Nobel Prize winners are very peculiar persons, so okay, so before starting the talk, I would like to give you an exercise, so okay, so I hope that you will devote some time during the weekend to solve some of these, so you have seen in several of my examples, there was a line, there was a line of second order phase sensations, and there was what is called the canonical trichritical point appearing here, and this is the line of second order phase sensation, and usually the line extended to farther in micro canonical phase transition, and the canonical phase, or maybe this was the canonical trichritical point, canonical trichritical point, and the micro canonical trichritical point, which is the endpoint of a second order line, and it was usually going farther, so the line ended in the canonical trichritical point in the canonical ensemble, then if you go to the micro canonical extended farther, and this is exactly the region where you can find negative specific trichritical point, so this is exactly the region, this can be proven formally in a Landau expansion, so what I propose is an exercise, I propose take the mass potential as a function of beta in m, or beta in x, and the entropy, as a function of epsilon in m, and then show these, show that there is a gap between the two, and that the canonical, the micro canonical, micro canonical, micro canonical, second order line extends beyond CTP, so as a hint, as a hint try to expand beta, and then s, this is a hint, beta as you know in the micro canonical ensemble is a function of epsilon, so it can be proven formally that this is true in a Landau expansion, so it's not only a property of the specific models that we have looked at, but it is a generic property of the massier potential, so this in some sense proves the genericity of the negative specific heat in this context, because if you have this extension of the line of second order, it is exactly in this region that you hope to find, the negative specific heat region, so now let's go to this lecture, there so first part of the lecture is, if you want a continuation of what we have learned, but most of the lecture will be devoted to dynamics, let me try, I have a pointer now, thanks to our assistant, technical assistant today I have a pointer, very clever assistant, so first of all, oh it doesn't change, I have a pointer but not, I cannot change, ah yes it works, okay, so all the lecture will be devoted to an extremely simplified version of all the models that you have seen, it's a model that I introduced long ago, it was in the 90s and there were studies of such a model, such a model by Kuni Kaneko from Japan and also in the Astro community, Shogo Inagaki, so as one used to say for any problem, there is always someone who did it before and in this case there were these two persons and okay, so the model can be seen as a model of several different physical systems, but okay, you can think of as an xy model, but you can also think of the model as a system of particles moving on the circle, okay, so the position of the particles is the angle and the particles interact with an attractive potential, cosine potential, so if the particles attract, the potential energy will have the tendency to bring the particles to the minimum of the potential, but there is a kinetic energy that's moved the particle around, so there is a competition among the kinetic energy which tends to spread the particles in the circle and the potential energy which tends to attract the particle in the minimum of the potential and what happens is that at some point they will sort of balance and that's the phase transition point is the point at which the particle from being clustered go to a phase where the particles are sort of moving around on the circle and so we are in the gas phase, so I arrived at this Hamiltonian in a very funny way, at that time I was visiting a plasma physics group and the head of the group put me in front a Hamiltonian with horrible Hamiltonian with many, many different terms and then he asked me what is a phase transition and I said, okay, phase transition is a singularity of the free energy and then he looked at me and said, don't tell me this bullshit, I don't understand anything about singularities, you should tell me what is a phase transition, so I started to cancel all several terms in this Hamiltonian and I arrived at this Hamiltonian that was not too different, so I went to his office and said phase transition is a point at which kinetic energy competes with potential energy and then he understood, that's interesting that you could reply to my question what is a phase transition, okay, and it happens, of course, also for finite systems and so on, okay, what is the order parameter, the order parameter is the is the magnetization M, I have to learn how to use it, okay, is a Ferrari in the hands of an inexpert driver, so which is the limit as N goes to infinity of the average of the cosine and the average of the sine, so you see that these are sample average, okay, so it's interesting, no, you could solve this model using large deviations, but I will not do it today, I will solve it in a different way, okay, so it's a model with a second order phase sensation and the solution of the model is pretty simple, but you will see that the dynamics is extremely interesting, okay, so let's look at the solution in the canonical ensemble, I would be slightly more sloppy today because I can do it on a very simple example, so the configurational partition sum, you have to do an integral over all the angles of the exponential of minus beta N, the sum of the cosines and the sum of the sines, then you have two squares here and you can introduce two auxiliary fields in the Habas-Tartonovich transformation, x1 and x2, and then you can integrate because the square linearizes and you get the logarithm here of the modified best function of zero order as a function of the auxiliary fields, and then you exploit the fact that there is a rotational invariance in the model, so you can rotate freely the angles and which is another property that you can see through the modified best function, so that you can write the best function in terms of two variables cosines and sines in terms of a single variable with the modules z of the two fields, so this is just to be slightly more sloppy in what we have done quite quickly in other models, so you can see how it works, and then go into polar coordinates, this was z before, sorry, what is x here is z before, there is a mismatch, in the thermodynamic limit I look for the minimum of this, sorry for the maximum in x of this, or the minimum, so okay, the minimum in the large n here because there is a minus here, and so I get the free energy, and this is the expression of the free image, I have to take an infimum of this quantity here, and if I derive with respect to x, I get this consistency equation in terms of the ratio of the modified best function of first order to the best function of zero order that I have to solve, then, I don't know if I have, I don't think I have put the graph, oh yes, yes, okay, so this ratio, this ratio is something very similar to the touch, is something like that, with two asymptotes, so I'm only plotting the right part, and you see that either you have a solution, which corresponds to the broken phase, sorry, a non-zero solution, or you have only the zero solution, and so if you vary the temperature, you have a usual mean field type of phase transition of second order, so, goes in the wrong, ah, yes, sorry, I have to learn how to use it. Okay, so this is a plot of the temperature versus the energy, you have seen this type of plots, and in the inset there is the plot of the magnetization versus the energy, versus the average energy, and you see that the simulations agree quite well with the lines, the lines are obtained in the canonical ensemble, and they agree almost everywhere, apart from here. You see that there is a region here where they don't agree, and this was the sign that something went wrong for this model, and it was the beginning of a story of the quasi-stationary states and ergodicity breaking in this model, so, and moreover, you see that these points, they correspond to the largest system, so you would expect, if it would be a finite size effect, if you go to larger sizes, you would get points closer to the lines, but in fact you don't, and moreover, this is a remark, that you see that some of these points, they lie on the continuation of the high energy line, and in fact, if you go there and check, instead of being ferromagnetic, the state is paramagnetic, so these are paramagnetic states that resist a lot to converge to the ferromagnetic state, and if you increase the size of the system, if you want to the collapse phase, if you increase the size of the system, they don't want to go to equilibrium, so they resist to go to equilibrium, and as you increase the size of the system, okay, I will tell you the end of the story, these are states that whose lifetime increases with system size, so, which usually you don't find in such type of models, unless you have dissolved, there are other features that induce this type of behavior, but for completeness, let us look also at the canonical, at the micro canonical solution to convince ourselves that the ensembles give the same prediction, let's use the mean max method that we have learned how to use, so I have to invert the infimum in x with the, I'm always confused about sup and inf in x, but don't worry, it's working, so the reason is that sometimes is the, the legend is defined in a way or another, so at some point I will decide to fix this point in my slides, because it's okay, so the, you will check, okay, so the stationary points are the same in the two ensembles, so you can derive the massier potential as a function of beta in x, and this, at the level of the first derivative, it will give the same result, this is the derivative with respect to beta and respect to x, and this system of equations can be solved in beta to give a consistency equation in x, which is slightly different form than what we get in the canonical ensemble, b here is the inverse of this function, so you have to rotate your head and see the inverse, and there is a unique solution for x equals zero of this consistency equation, you can check for energies above 3 over 4, and otherwise there is a non-zero solution, and the non-zero solution as you can see, since it must come from the intersection of this curve with a line, so it must be between minus 1 and 1, although x extends from minus infinity to plus infinity, the equilibrium solution are those that are confined in the interval minus 1, 1, and you get the entropy that has this expression, once you have solved this consistency equation, you replace it here, and you get the entropy, and if you derive the free energy from this entropy by the plus, by the general transfer transform, you get the free energy of the canonical ensemble, so the entropy is concave, you can check it is concave, and there is a second-order phase transition, so there is a point where the two concavities don't have the same curvature, because there is a point of second-order phase transition, but this is not enough to create an ensemble in equivalence, the function is singularity, but it is not enough to create an ensemble in equivalence, so when I started to work in this field for me, I knew that this solution was the same in the two ensembles, but it took time before we got all the techniques that could allow us to solve this model in the micro canonical ensemble and be sure that they were the same. In the end, it's very simple, but as you know, once they are done, they look simple, but before, it's not like that. The model has a very interesting dynamics, I would like to point this out to you, the equations of motion of the model, they are the equations of a perturbed pendulum, and for a long time, we tried to understand the dynamics using this analogy, so you see that I can write the equation in this form for the single particle, there is an external field m, which is like gravity, but both m and phi, the phase of this pendulum, are time dependent, and in fact, if you have a look at the motion of the particles in this phase space, you will see that they move like in a pendulum, so and for a long time, we wanted to use the analogy, in fact, in the original paper on this, we used this analogy even to compute more or less where to locate the phase transition of this model. Okay, but what is the clue? For the analysis, come with this idea of the water bag, so what is a water bag? The water bag is a distribution that is non-zero and constant in a given domain, and it's clearly non-equilibrium, because you will see the equilibrium in a while, and by this, we can define a set of initial states with given delta theta and delta p that are directly related with energy and magnetization. So what you know from Statmec, you know that if the trajectories move on the surface at constant energy, the average should depend only on the energy. So if I fix delta theta and delta p and I let the system go, there should be no dependence on m0. m0 is the initial magnetization. So what counts is the energy, and the motion should evolve on top of the surface at constant energy, and the detail on what is m0 should not be important. So this term was used in plasma physics, so I took it from there. So water bag means, okay, there is, and also in gravitational systems, so you will see a slide by later. So this is a sort of very far from equilibrium initial state, okay, and you expect that the dynamics drives it to equilibrium after some time, okay, and how you check equilibrium that the final result should not depend on m0, should depend only on u, on the initial energy, and you will see very interesting results that in fact show that this is not true, and in fact it depends on m0 also. So, okay, so this is the equilibrium in the phase space of, in the so-called Boltzmann mu space, so these are 10,000 particles, and I'm in a region where the water bag relaxes to equilibrium, so the initial water bag was a rectangle here, was a rectangle here, in the middle of the spot, and this was drawn by a Japanese collaborator, so for him white is a lot of mass, dark is less mass, so I wouldn't plot the inverse, but it's interesting how light is more density, and dark is less density, okay, which is, by the way, reasonable. Okay, so essentially what is this distribution? This distribution is nothing but if you have q and p, this is nothing like e to the minus beta h of q and p, okay, so you see that there is more mass near the, so I've shown you that the dynamics of this system is the one of a pendulum, and here you see the phase space of the pendulum, okay, because h is nothing but the single particle h is nothing but p squared over 2 minus epsilon cosine, cosine q, cosine theta, so you see that the system should reach this equilibrium, and when it reaches this equilibrium, the beta, beta depends only on the energy, and okay, so you are gonna feel it, what happens when it does not go to equilibrium? This is, for instance, a simulation where you see that this is the value of m of the magnetization, and I'm in a region where I should go to the Boltzmann Gibbs equilibrium, which is here, is here, is this level here, which is quite high, is around 0.3. On the contrary, I do simulations with increasing values of n from 10 to the 2 to 2, 10 to the 4, and you see that there is an initial phase where the system looks that it moves away from m equals 0, but then it flattens down, and then you see that it converges to equilibrium, converges to equilibrium, but the time it takes to converge equilibrium is longer and longer as you increase the number of particles, and you can see that in fact there is a constant shift to the right of the pointed twitch, the system starts to go to equilibrium, which converted into a low tells you that this is a power low, because in logarithm there is, this is log t, in logarithm there is a constant shift to the right, which means that there is a power low behind this relaxation to equilibrium. In this case, the water bag initially has delta t equal pi, so it's a homogeneous water bag, so you distribute the particles homogeneously on the circle, and so initially m0 is 0, and the final equilibrium, the one that does not depend on the initial m0, should have m, should have m non-zero, the magnetization should be non-zero, but the system wants to stay close to the initial state and doesn't want to go to equilibrium, and as you increase the system's sides, the effect is even more drastic, and the system stays for very, very long time, 10 to the 4, 10 to the 5, 10 to the 6, out of equilibrium. So we have learned a lot about equilibrium in this lecture, in these four lectures, and then we discovered that equilibrium might not be relevant for system with long-range interactions. It's not always true, of course, because you have seen that in the plot of the relation, temperature, energy, there were regions in which everything was okay, so those regions I can trust equilibrium statistical mechanics, but there are other regions where I cannot trust, because if I start the system in some region of the phase space, it doesn't go where I am expected that it goes. So we denoted this state as quasi-stationary states, and they appear almost everywhere, so we discovered plenty of, so I maybe I will put on the Slack physics report paper by Jan Levine, which is a sort of good review, because I will not, this will be the only lecture devoted to quasi-stationary states, is I would have to introduce you a little bit more of kinetic theory, so it's a course in itself, but just to give you a feeling that there is a problem with dynamics of long-range systems, and I will derive a few simple results. If I have time, okay, I have a code of this model with comments in yellow, I prepared it for you, so I will put it in the Slack, maybe if I have time I can show you the code, and it's a Fortran code, because I'm old enough to continue to use Fortran, so if you want to transform it into a Python code, it's okay, but it's a 100 lines code, and you can play with this code, it's very simple and okay, it's an alternative to learn kinetic theory, so playing with a code and see what happens, okay, you can even reproduce these results there, nowadays these are simulations of 94, 95, so now you can run these on a cell phone, at the time it was harder. Okay, so what is the power law? Our estimate at the time was 1.7, you see we were limited to 10 to the 4, 10 to the 5 part, but then there was CUDA, CUDA is a software that allows to run very, very large systems, and this is a group from Brazil, and you see that the feet is 1.7 is okay, so in the region that we explored it was okay, 1.7, but then if you enlarge the region you see that it goes to 2, so 1.99, so these are systems with millions of particles, so instead of 10,000 particles, so it means that asymptotically it goes to n square, so it takes a time of order n square to relax, to relax to equilibrium, and to understand these n square relaxation, it took a very long time, I will tell you only some parts of the story, one has to write kinetic equations for these systems that are in the class of the Lenar-Balesko equation, which is finite and corrections to the Vlasov equation, and I will show you the Vlasov equation, and then you had to compute corrections of the Lenar-Balesko equation to very high order, and only recently Pianari Shavanesev from Toulouse to the force using Maple Mathematica and computing hundreds of diagrams were able to show that the correction is n square, so but this is analytic now, so it takes a time of order n square to reach equilibrium, so if you look at the system on a short time scale you will not realize that it is in equilibrium, it will stay very far from equilibrium for a very long time, I think this is an interesting result and could explain why also in many long range systems, so here is the scaling in the second part of the, is the same group, is another paper, and they show that it's in a region of where the system is homogeneous, the time to relax to Boltzmann, this is Boltzmann value, is n square because if you do the collapse of the different curves they will go on top of each other with n square, so this is now well assessed that even analytically and numerically that there is this very long time scale in the system, it's not exponential n, but it's power of n, but it's nevertheless a relaxation that is extremely slow to the equilibrium value. Okay, so there is a paradigm emerging in this area of research that is the following, you have systems where you have, you start the systems somewhere in phase space, so you have an initial condition, and there is a phenomenon that is called via relaxation by in astrophysics, I will give you some information about that, in which if you, you have a relaxation to a new type of equilibrium that we call Vlasov equilibrium, I will try to say a few words about this Vlasov equilibrium, and then you have collision relaxation on a much longer time scale, which is Boltzmann equilibrium. So the initial relaxation is the one that you have seen, and maybe at the end of the lecture so I will also show you some movies, I have movies that show how the relaxation goes on, and okay, so this is essentially the scheme, you have an initial phase, which is well described by the Vlasov equation, and finite n corrections are not important, so everything happens on a time scale of order one, order of the parameters of the Hamiltonian, and then there is a much slower relaxation to equilibrium, and you remember even yesterday when I showed the relaxation of the intensity of the laser, there was this initial level of relaxation, and then on a much longer time scale convergence to Boltzmann equilibrium, that was exactly the same phenomenon, that the laser was relaxing to a Vlasov equilibrium, and then very, very slowly it was going to the Boltzmann equilibrium. Okay, so what is the Vlasov equation? I don't know if this is the time to enter in this, but okay, maybe I just show some pictures that for the end of the lecture are good, so you see, for instance, this is the initial water bag, it is smoothed on the boundaries, okay, so I put back, because if it's not smoothed, then there are singularities in the simulation, you get problems in the boundaries, so you can see the smoothing by the orange boundary here, and then you run it in time, so with the Hamiltonian dynamics, so just solving the system of the particles, and you see that it forms a sort of two vortex here, and then the vortices split, and they become two vortices in a center of the band, and if you go on with time, you will see these two vortices moving, the one vortex here is a positive momentum, the other one is a negative momentum, so I joking with my good friend Freddie Boucher from Lyon, I told him this is like the Jupiter red spot, but then he took it seriously, and he did the Jupiter red spot with similar concepts, so there is an analogy between the Vlasov equation and the Euler equation in topology, and you can in fact prove that this quasi-stationary state arrives also in these systems, in geofizical systems, and this is right thinner, so it was after the diet, the quasi-stationary state, the water back is now narrow, and you see a more turbulent behavior, there are more vortices, but still you are very far from equilibrium, so the system relaxes to some states that are very, very far from equilibrium, and then you, so, and this is an old picture by Lynden Bell, it's a paper in the 60s, there were no computers at the time, and the system is totally different, it's a self-gabithetin system, and this was drawing this sort of a picture of what should happen in that case, so, and that's the water bag, okay, the distribution is constant in a, is constant in a, in a, in a region, and so the dynamics deforms the water bags, there are boundaries to the, to the phase space, so, so you can cut, you can cut the distribution and the distribution is, but what is important is that the area of this initial water bag is conserved, and, and, and the distribution is cut, and it goes on finer and finer, finer and finer scales, until you reach, you reach this sort of band, it's amazing how similar it is, no, so there is no relation among the two, but the picture is very, is very similar, okay, so, and this is drawn by hand, and this is done on the computer, so, I think he had a good imagination, this guy, so, to understand what, what was going on without knowing that the thing was going like that, so, so, is there an increase of entropy in this system or not? So, if you compute the Gibbs entropy on this, on these states, you find that it does not grow, that it is constant, but you have to define a sort of fine grained entropy, so, so, for instance, if I cover this space with boxes, and then I look at the density in such small boxes, then here, for sure, is more homogeneous in the box than here, okay, because here you find boxes that are empty, and below you find boxes that are more empty, that are filled, so, there is an evolution of a fine grained entropy, and in the next hour, I will give you the theory by Lindembell, how you can define an entropy that grows during the evolution of this system, and so, then you can define maximum entropy states of this entropy, solve variational problem using this entropy for this model, and find the quasi-stationary states or plus of equilibrium states in these systems. Okay, this subject gets me closer to other courses, this is the first time I mentioned this relaxation to equilibrium, dynamical entropy, and so on. So, I need a little bit of theory, so, take the Hamiltonian H with kinetic and potential energy U of a system of particles, and then define a discrete one particle time-dependent density function, so, you are summing all trajectories up to time t, and you are, this is the empirical measure, so, you are counting how many, what is the density around theta, and what is the density around p, so, is a sum over all trajectories, and the distribution is normalized to n, so, called the Clemontovic distribution, and then you can prove that using a property of the delta function x delta x minus y is y delta x minus y, one can get the Clemontovic equation. Clemontovic equation looks like the Vlasov equation, it's very much like the Vlasov equation, so, there is the evolution of the density plus a transport term, so, the evolution in the direction of theta times the momentum times the evolution, which is due to the force, which is the potential, the potential evolution V, and the potential is given by an integral over the, over the phase space in theta and p, so, you get this closed equation. It looks like the Vlasov equation, but it's essentially a rewriting of the Hamiltonian motion, so, I'm, so, all the information about the trajectories is contained in this, in this equation. So, what I have to do, and is to smooth this distribution, because it's extremely singular distribution, and distribution is concentrated on the orbits, and so, you have to average the distribution, say, over the initial condition, so, it's sort of hard to do that, so, I'm just giving you the rough idea, so, in my review and in my book, you will find the derivation, and then you realize that the average equation has a, has an average potential here, and there is a correction to the right, and this correction, one can show that it's, it's one over n, so, you see that there are fluctuations here, this product of fluctuations, you can prove that it is one over n, this correction, so, if n is large, you get the Vlasov equation, where V is the average potential, so, the evolution of the one body distribution function f is transport, this part, plus the effect of the average potential, and as the system gets larger and larger, this term gets smaller and smaller, and the, then, okay, to finish this part of the lecture, I will remove, I hope I can do it, I'm still on screen, no? Yes, I hope it works, is a movie, these are evolutions of the, of the model at various energy, this was energy 0.55, now I go closer to the, to the phase transition, and even closer to the phase transition, so, you see the filaments of these evolution, okay, the formation of these clusters, and the relaxation to equilibrium is driven by the granularity of the system, so, if the system is finite, it will realize its granular, and after some time, and this time is order n square, and when it realizes its granular, it's made of particles, then it will remember, oh, there is Boltzmann around, and will converge to equilibrium, okay, so, it's the granularity plays the role of collisions, so, in fact, in the kinetic equation that I've given to you, the right part, sometimes it's called collisional part, but it's not through collisions, because the particles do not see each other, and it's granularity of the system that brings the system to equilibrium, in fact, one can prove an h theorem for the equation, the full equation, including the right part, one can prove that entropy increases, that Boltzmann entropy increases with time, once you include the effect of the, of the second, the right hand side of the equation that I've written, so, okay, so, this is the end of the first part of the lecture, and five minutes of rest. Very good, so, take five minutes of break. These are full simple. No, it's green. Okay, maybe it was not working. Okay, so, this is the code that I will briefly describe, because otherwise you will be lost, so, it's Fortran Coda, so, where it uses an algorithm that is voted here, it's a McClack-Lanatela algorithm, it's a symplektic algorithm of Fortorder, and you see here there is a number of particles, position and momenta, x and xv, and then, okay, there is, in order to start the code, you have to initialize a random number generator, there is a transient, so, this is, for instance, this is the seed to the to the random number generator, and you can either start, okay, so, let's go on, so, these are numbers that are important for the routine that evolve the Hamiltonian, it's a number that I took from the paper of McClack-Lanatela, this is a water bag initial condition, or an alternative is to have a Gaussian of Maxwell Boltzmann Maxwell initial condition, then you enter the code you compute, the magnetization, the two component of the magnetization, there is a transient, and then this is a central loop, you see that all the program is here, from the instruction 100 and the instruction 100 here, all the code is here, but it calls the leapfrog here, this is the routine that is here below, and, okay, it's a routine that I wrote myself to integrate the motion, and this is a code that produces these pictures that I've shown, so, so, if you run it for, say, 100,000 particles instead of 1000 particles, then you can plot the positions of the particles, and then with the density plot you get the evolution, so, it's really simple, so, I wanted to show it because it's nothing complicated, it's a really simple code, and I will put it in the in the slack, if you want to try, how many no fortress, no one, one, and how do you code usually with C? Python, Python, Python, Python, so, all the Python code will be 10 lines, this is 100 lines, but I think the Python code will be 10 lines, because you will do vectors and everything like that, and also the graphics will not be so much shorter in Python, but maybe you understand the logic, and it's easy to translate it in Python. By the way, are there artificial intelligence network that translates, fortunately, into Python? Perhaps, yes, it should be easy, I think. Okay, so, the first, the last part of the lecture of the week, so, is the last, I don't understand, when it starts doing like this, I got crazy. Okay, so, that is the velocity equation for the, for the HMF model, it's a very simple partial differential equation, so, just to resume, okay, you see the distribution function is a function of theta and p and p, okay, then you have to solve this partial differential equation, but with a caveat that V is a function itself of the distribution, so, it's a nonlinear partial differential equation, okay, so, here is linear, okay, and this term, because V is a function of F, makes this equation nonlinear, so, it's highly nontrivial partial differential, nonlinear partial differential equation, but you know what is V, V is the average, so, you see mx and y are the two components of the magnetization, so, mx is the integral of F cosine theta, and then y is the integral of F sine theta, you can prove, so, I think this could be an exercise also, so, given this set of, given this equation, given this definition, prove that the specific energy, which is a functional now, okay, is conserved, and also that momentum is conserved, so, okay, so, the derivative of e and the derivative of p are constant, so, so, this is the equation for the one body distribution function, so, each particle of my simulation will obey on average, this equation, and will move by itself, because there is a momentum, so, there is transport, so, you are seeing, for instance, and the vortices that are transported to in the positive momentum part, it's because of this transport terma, to the right with momentum p, if p is positive, to the left with negative momentum, if the momentum is negative, and then there is a part, which is due to the interaction, for instance, the formation of vortices is due to the interaction, okay, but this is a closed set of equation, it's very interesting, it's a closed set of equation, and, okay, there's been a lot of mathematical studies on this, and if you go to the literature, you will find that the mathematicians call it the Vlas of HMF, because it's, in the past, that they had studied more complicated equations, but for this set of equations, it's much easier to prove some theorems in kinetic theory, so it's, okay, but it's an interesting set, so, you could take a solver for this equation, okay, and which is different from the particle solver, so, the solver that I gave you is a solver that solved the Hamilton equation that are behind these partial differential equations, so, by integrating the trajectories of all particles, this is a connection with Krimontovic, Krimontovic is set of particles, no, and then the average gives you the Vlas of, but you can also start from the continuum equation and integrate this continuum equation with a solver, so, the, the, okay, okay, so, what is, otherwise, I don't have time, what is the Lindemberg, it's a very interesting statistical theory, I like it, so, I like to teach this theory, it's due to a British astronomer, Lindemberg, Donald Lindemberg, is famous for other things, that has to do with astrophysics, but he has also a very nice theory, and the idea has to do with the, of constructing the Lindemberg entropy, has to do with this picture, so, you see that the area, the area of the, one can prove that given a, given a shape in the single particle distribution function, and you fill the shape with constant distribution, any shape will conserve the area, this is a theorem, it's a volume conservation for the Vlas of equation, okay, so, how can a drop that you put into a, a glass of water mix if the area is, should be conserved, it will be deformed, and then it will create filaments, and then it, the steering that of this drop will never reach mixing, but the steering can be so fine, so fine, that is close to mixing, so, any, any square of little square that you put on these, the, if here it was lemon and this vodka, okay, and here it's all lemon, and here it's all vodka, okay, in the end, if I take a small square here, the size of my drop, the size of my pointer, for instance, there will be more or less a certain percentage of lemon and certain percentage of vodka, so, it's not mixed, but it's almost mixed, okay, so, how do you describe this mixing? So, and that's the idea of Lindenbell, so he says, okay, I have vodka, he's a red vodka, and what I can do with my vodka is to move out the vodka from here and put it there, okay, but I cannot take vodka from here and move it here, because otherwise it will be blue, so, blue vodka, it's not the same vodka as I had before, okay, so, it's a sort of, this is how I see it, at the time Lindenbell didn't have the idea, this is like Monte Carlo, no, if you want, but it's a different interpretation, you can do this move, yes, you can do this move, but you cannot do this move, because you reduce the area, no, because you put mass on top of other mass, so, you can see this as a sort of exclusion principle, so, in each part of your phase space, you can have, you can have either zero vodka or one vodka, but you cannot have two vodkas, so, vodka is like fermions, okay, you cannot put, and you will see that the statistics will look very much like fermi statistics, although it's a classical system, it will look very much like fermi statistics, okay, so, how do you cook out this, cook up this idea, this is not exactly as Lindenbell did, so, this is my own reconstruction, and you find it in the book, you will find a better derivation with all the details, so, you take a system and you define microcells and macrocells, okay, then, there are new microcells of volume omega in a macrocell, and a macroscopic configuration has an i microcell occupied with level f0 in the i macrocells, and they remain occupied with level 0, so, this is my vodka, okay, in each of the macrocells, I put a certain number of microcells that are occupied and a certain number that are not occupied, and the distribution is coarse grained on a macrocell, so, you will see that the f bar distribution will have a growing entropy, not the f distribution, the f distribution, the fine grained distribution has an entropy which does not increase, while the coarse grained distribution, the distribution that I average on a macrocell, will have an increasing entropy, okay, the total number of occupied microcells is big n, such that the conserved total mass is nothing but the integral of the distribution over d theta and dp, and this n, the number of microcells times omega, the volume of a microcell, of a microcell times f0, which is the level of the vodka, okay, f0 is how much vodka I put, okay, it's sort of complicated, I've tried to put it all in a slide, so, this is generic, so, you can do it for k levels, so, in that case was a level 0 and level f0, and you can do it for k levels, there is no problem, you define the mass of the levels, and there is a result, which is a very important result for the values of equation, that is the fact that there is an infinite set of conserved quantities, so, all functions of f are conserved in time, and the Gibbs entropy, of course, is a particular casimir, so, because it's f log f, okay, the Gibbs entropy is a particular casimir, so, it does not increase its constant, but you can define a coarse grain distribution for any set of levels here, it was restricted in the previous slide to two levels, but I could increase the number of levels, so, what happens is the following, so, you can prove a mapping, it's very interesting, from the casimir to the levels, so, you can prove if I have a distribution with many levels, each level will be conserved, and the infinite number of level conservation, of mass of level conservation corresponds to the conservation of the infinite functions of f, of the infinite functionals of f, so, this is a complicated theorem, but, essentially, it means the following, if you have a zero vodka or one vodka, the one vodka and the zero vodka will be conserved, if you have a zero vodka, one vodka, and two vodkas, the zero vodka, the one vodka and the two vodka will be conserved, and this is conservation of the casimir, okay, you would like to know this distribution, but how can you get this distribution? You have to integrate the equations of motion, and you cannot, so, the idea is to introduce a statistical mechanics, so, to do accounting, so, there is a given set of microstates, okay, and you would like to count how many they are in terms of microstates, and, okay, so, you have, and you have an i, so, you remember what is n, so, maybe you have lost big n, big n is the total number of occupied microcells, okay, microcells, so, there are microcells, and there are microcells, and all these small dots, black dots here, you count all of them, and there is, and they are big n, okay, they are big n, all the number of small dots is, so, that's Boltzmann counting, no, Boltzmann counting is nothing but n factorial divided by product of n i factorial, as if you have a gas of small dots, you have many boxes, the macrocells, and you distribute the macrocells in the boxes, okay, but then, then you have to, you have an exclusion principle, because you cannot put so, this count, this is this term, okay, so, this is like Fermi counting, if you go to the book of Wang that I attacked very, very strongly in my lecture, but, okay, go back to the book of Wang and go to the chapter on Fermi statistics, it will have exactly this term, because if I have a certain number of drops, and I have to put them in the macrocells, I have to first put one, but then I cannot put one on top of the other, so you have Fermi counting, so, this is Fermi, and this is Boltzmann, it's a very strange distribution, you don't find it in Boltzmann, in the one book, it has two counting terms, one is a Boltzmann counting, and the other one is Fermi counting, and now you do stealing, so, this is why I like this theory, because it brings me back to the other part of my lectures, and if I use stealing, and I compute log of omega, I get this distribution, which, if I rewrite in terms of the course-grain distribution function, is nothing but a Fermi entropy, f log f, one minus f, log one minus f, so, Lindelbell entropy is nothing but Fermi entropy with an extra ingredient, which is Boltzmann counting of the states of the macrocells, so, now what I do, I maximize this entropy at fixed energy, so, I've told you that the energy and momentum are conserved, so, now I maximize this entropy at fixed energy, and this is a very complicated variational problem, you can see that these are the consistency equations for the HMF model, and this is the course-grain distribution that I get for the HMF model, these are Fermi functions, f0, f2 are Fermi functions, I have to solve this variational problem, but it's a one-to-one solution, so, given the initial condition, I don't have three parameters, I have to solve these set of equations, and I get the distribution, and then I compare the distribution with data, and this is the comparison, no three parameters, so, you see there are details that are not reproduced, here there were two peaks, the peaks usually corresponds to vortices, and this distribution is not perfect, but you see that it's amazing that you are able, by this very simple theory, to reproduce, and what does the theory says? It says that the distribution depends on m0, so, you see that in these formulas, somewhere it takes into account that the distribution depends on m0, so, it does not depend only on energy, it does depend also on m0 on the property of the initial state, so, I will be brief because I don't want to be, okay, this picture is recent, and there is a lot of computation in this picture, so, this is m0, then I will go back to previous slides, and this is energy, so, I've told you that this model, what statistical mechanics tells me is that there is a line here at 3 over 4, so, 0.75, and all states below this line are clustered, so, the particles are clustered, so, magnetization is, or, ferromagnetic, and all states above are gas, so, they are, particles are distributed, but I was finding the, in simulation, that this is not true. Now, this black line is the Lindembell line, so, is the line that I obtained by solving this very complicated variational problem, and according to the theory, it divides states that are clustered, or, that are here, small energy, from states that are gas, okay, in the initial convergence, so, in the glass of equilibrium, okay, so, in the glass of equilibrium, the states that are here are ferromagnetic, and the states that are here are paramagnetic, and you see that, okay, there are points where it fades miserably, okay, here, no, it gives a blue below, what is above the black line should be all blue, and what is below the black line should be all red, but, on average, it's not so bad, so, in each of these squares, with a student from Brussels, we divided this big square into 100 small squares, even more, I think, you can see the sides of the, of each, maybe, it's one over 20, there are 20 by 20, something like that, and, and then, we averaged the magnetization in the initial relaxation, so, before it goes to the Boltzmann equilibrium, and so, so this is the glass of equilibrium, and there is a line of phase transitions, which differs from the Boltzmann line, the Boltzmann line would be a straight line at point 75 irrespective of the value of m0, there is a transition at energy 3 over 4, while the Lindenbell theory gives me a phase transition, a non-equilibrium phase transition, on a line that reaches point 75 only when m0 is 1, otherwise, it's below, below, I can compute analytically this line, and this line, moreover, we can prove that this line of phase transition of non-equilibrium phase transition, it's a very interesting variational problem that you can solve, and you discover that there is a tri-critical point here, and the line is a line of a second of the phase transition that ends into a line of first-order phase transition, and this is some point that we can compute exactly, 7 over 12, so, and also something has been done also on other points more carefully. So, apart from the tour de force that you can imagine is behind all this theory, what is interesting and I would like to transmit here before I close this lecture, is that there is a theory for the Vlasov equilibrium, it's maybe not a rigorous theory, but it's a theory that I like, so it's very simple, and by this theory, you can introduce a variational problem, you can solve a variational problem, so instead of solving that, it's a theory that is exactly in the spirit of Boltzmann, so you don't solve the partial differential equation, which would be very hard, and for any initial state, you would have to solve a different equation, but you solve a variational problem, which gives a prediction on the coarse-grained state, it's not the detailed state of the dynamics, it's a coarse-grained state, it's the same that you do with a gas, when you want to understand more or less the pressure, the volume, and so on, it's more detailed because it gives the distribution function, not only the macroscopic variables, then from the distribution function, I can derive the magnetization, the energy, the momentum, so the macroscopic variables, it's a very detailed information, and it can be used for different models, we have done it for the free electron laser, and it gives the result of the convergence to the first level for the free electron laser quite well, it has been used also for systems like plasmas in the papers by Jan Levine, and I put the report of Jan Levine, and this is very nice, I think it's very nice exercise, I don't know if this concept of coarse-grained entropy is used in other fields, but it's a very useful concept, it can be used for situations in which you don't have mixing, but you have steering of the distribution, so you have a conservation law that avoids to suppose that the system is mixing, conservation law that avoids can be different conservation laws, and then if you take into account these different conservation laws, you would define your proper coarse-grained entropy, and this coarse-grained entropy will reach a maximum somewhere, and this serves as a tool to solve the dynamics. So, I think we'll leave time for a few questions, a discussion, if you want, about that, five minutes, three, four questions and discussions. My question? Yes? Yeah, this stable state is due to maximization of this coarse-grained entropy. You can view it as this, it's a theory, so it's not the theorem. It's a difference between a theory and the theorem, it's not the theorem, it's a theory. Yeah, so my question is like in this theory interpretation will be like for a long range interaction system, sometimes it's like a competition, first the entropy is the quantity that is more important, and after some long time energy start being relevant, that's the idea. Yes, yes, on the very long time the only entropy is the Boltzmann entropy, and the system will recognize by granularity that the right function to maximizes Boltzmann entropy, so as the trajectory invades all the phase space, you will reach the state of maximum Boltzmann entropy, but on a much shorter time scale, which is not too short, is n square, so if you have a system of thousand particles, it will be a million proper times. You see that there is a convergence to some value, and you don't know anything about this value. What's going on? What's going on is that is this steering of the distribution, so the distribution is not mixed, it's stirred, and this lindenbel entropy takes into account the steering of the distribution by introducing a sort of coarse grain scale over which this Fermi-like entropy reaches a maximum, and if I use this optimization problem using this entropy, I get the line, I get the black line that I've shown. It's not perfect, so you see that there are blue parts below the line, but it separates two regions of initial states. One region of initial states where you converge to the Boltzmann equilibrium quite well, other in which the convergence is much slower, and these are exactly those points in my simulation that had troubles to reach the temperature energy relation that I get from solving the equilibrium model. In the end, you will be Boltzmann, but on short time, you will be Vlasov. This is more or less the message, and collision will bring you to this final state at some point. Have you think about this in a cosmological level? Šua, šua. In the review, so I'm not an expert in this field, but for instance, Pierre Henry Chavanisse is working a lot in this direction in Toulouse. So for instance, this could explain why you observe many galaxies of many different forms, or I mean solar systems that are very different one from the other. So it could be that the reason why the sky is so different is that it's not a gas, and the long range interaction brings the universe into a mixture of interesting states for us also, although we are a bit stupid and we do worse, so at some point we will disappear. So, but also in plasmas, for instance, this idea has been used. So in plasmas, you really observe in plasmas system that are really big problems to relax the equilibrium, and you see that the plasma is confined into some states. Jan Levine thinks that the Lindembell theory is not perfect, and it does not like like me. So he likes, I like very much the Lindembell theory, it does not like. He has alternative theories based on resonances, and okay, my point about the Lindembell entropy is that it is very simple, so even a baby can understand it, and it's general. So there is a principle behind, and there is a symmetry behind. So I like it so much that I tend to over stretch it and to say that it works even when it doesn't work. So this is my failure, because I like it. It's a beautiful theory, and it's an example where I mix two different statistics, the Boltzmann one and the Fermi one. So it's a very nice theory to teach, and it's simple, you define, you change the model, the entropy is the same, so you don't have to change the entropy to change the model, so it's sort of universal. So maybe when it was formulated, it was not clear the power of the theory, so it was a sort of, so the Lindembell formulate it as a new entropy, but in fact it's not a new entropy, you find it in books. You just have to do things properly and define these micro and macro cells, and by the way the same theory was developed independently for the Euler equation. It's very similar to the Lindembell theory, it was formulated for the Euler equation. Even there there is a conservation law in two dimensions for the Euler equation, and you apply it to the climate, to understand why you see cyclones, anti cyclones, heat waves, so why you see all this complexity in the climate. Freddie Boucher, for instance, he was my postdoc for three years and we developed together a big part of this approach, he is now working on heat waves, he has specific programs to understand heat waves, heat and because these are sort of equilibria that appear regularly in climate and you don't know where they come from because climate is chaotic, should be mixing, but we know that climate is not mixing, because we see from time to time the same patterns, so the idea is that these theories could serve as a frame, not as a specific and predictive tool, but they can serve as a frame for understanding the complexity of climate, for instance. This is another system for which there are long range interactions, fluids in 2D are long range. Correlation function in fluids in 2D does not decay sufficiently fast, decay sufficiently fast in 3D, but in 2D no. So the Euler equation is a good example of long range system. And then you put the topography and you get the equations that everybody uses for large scale climate. So I did it at the level of master. These are very simple models, but they hide a lot of complexity that is very interesting to project onto the complexity of the universe, of the climate, but I don't want to be too exaggerated because I tend to be modest. So for instance similar things have been done for the Euler equation. For instance, you can study a very interesting problem, a slightly more difficult is a shear in Euler. So you take a 2D fluid and you shear. And the vortex formation at the center of the fluid, which grows by the instability as a name. So there is an opening of an eye in the center of the flow. It's an instability, a Rayleigh instability. And that's exactly the same as the HMF. You've seen in my picture the fact that it shears and then at some point it opens an eye in the center. You can formulate that problem exactly as a Rayleigh instability. But in the Euler is likely more difficult and still there are problems in the Euler, so technical problems. But this shear instability you can see it in this model. It's very simple model and shear because you have a part of positive momentum and a part of negative momentum. So particles are going in this direction because they have positive momentum and in this direction because they have negative momentum. So there is shear and in the middle below a certain kinetic energy you get the opening of this eye in the center of the phase space. So this phenomena are sort of, you find them here and there. For instance, I have a movie. I mentioned to you the confined plasma. So maybe I'm doing too much, I don't know. But I have a movie that I took from Japan, from my visit to Japan. I think this is this one. Yes. This is not my model. This is what happens for, now I know that it's put here. So I told you that you can confine electrons onto magnetic lines, the swirl of magnetic lines, and then you confine the electrons like this. And then you can make a cut here somewhere and you can observe the charge density here. This is exactly that. So the charge density initially is on a ring and as time evolves it forms these swirls, these vortices. And there is a theory for this charge density evolution that is exactly the same theory as the Lindenbell theory for. So this charge density is described by maximum entropy. Again, it's not perfect, but it can be done. This is a lab. It sounds quite general. Sorry? Sounds a lot like it could be really general. Yeah. Maybe it's general but wrong. So this is what my suspicion is. If a theory is too general it can be wrong, but it's beautiful, so I like to teach it. Ok, very good. What about the coughing? So thank you very much Stefano. We recommend in 15 minutes or so.


는  는  는                                                                                Now, for us now, we're going to burn four pesticides. All pesticides containing malefie and liban. All pesticides containing diazenol. All pesticides containing carbaryl. And all pesticides containing clopirephus and clopirephicinifile in liban is pesticides. In terms of the dilistin of pesticides, we have 310 pesticides in the list of the two pesticides. We think we pesticides that are no longer being manufactured, pesticides whereby the formulations have changed, and pesticides that persons have not imported for the past 10 years, we're going to waste those pesticides. And if in case somebody want and people permit for those 310 pesticides, we're going to ask them for information, latest information and those pesticides. And then we're going to re-register those pesticides. So they can be re-registered? Yes, once you come with the latest information because we have pesticides that we registered in the early 1980s. So in 2023, a lot has happened in terms of the chemistry of those pesticides. It is very important for the board to review the two pesticides and take this very important decision to make sure that the products that persons are using now, the methods, farmers and structural pest control, those pesticides are safe for human health environment and plant health. I really mentioned malathion and I'm coming to Mrs. Leo because at one time I think in your, before giving you all these other malathion, are you still using that? Yes, so we're still using this malathion as one of the pesticides that, you know, for adults I didn't kill in the adult mosquitoes. We don't recognize, like all other pesticides, that there are negative effects of using the pesticide. And of course, at Ministry of Health, the health and safety of our solution public is our number one concern. Hence the reason we're looking at alternative pesticides that we can use to ensure that it is effective at getting rid of the mosquitoes at the adult stages. And it poses as a little harm to the human population. So this is definitely something that we are currently working on. The things malathion is on the listing, it's bound to be on the listing. We're going to ban malathion. So how does that effect to use you as your department? Okay, so like I said, we're going to be looking at alternatives. But we have seen, which is the sad thing, we have seen resistance to some of the other alternatives that are actually out there on the market. So we've had resistance testing done with the Caribbean Public Health Agency. And they saw that resistance, which is one of the reasons that we went back into using malathion. Right? Yes. So we are looking at, because it's been a couple of years since we've used some of these other pesticides. We're looking at if we still have resistance to it. Because if we continue using just malafion, we may develop some resistance to it. So where does that leave us? But malathion has been used for a long, long time. Yes. But I think it's been a couple of years, for a good couple of years, we did not use it at the ministry. We were using other pyre for its other chemicals. It was only in 2015 that we started using malafion again. And we're trying our best to promote not just the alternative pesticides, but we're looking at improving the education, the sensitization that we're doing with our general public. Because if we focus on just the use of chemicals and we don't address the situation at the root, the problem is just going to persist. So in many instances people call us and they ask us to come to do the fogging. But when we go and we do the fogging, it only kills the mosquitoes at the adult stage. It won't get rid of that mosquito that you have in your drama and your containers, your tires and so forth. So we're really trying to encourage persons before we even get to the point where we need to use malafion or we need to go in to spray any chemical in any neighborhood that they're doing what it is that they're supposed to do at their home. So just ten minutes walk around your home and show that you have no mosquito breeding sites, any active or potential mosquito breeding sites. Check your containers, your roof gutter in, get rid of all appliances like your washing machines and your fridges and so forth, tires that can actually collect water and breed mosquitoes. So we're really trying to take home that message before we get to the point of having to use chemicals and pesticides in our environment. It is the last resort. It is the last resort. So we really want to push that proactiveness. You've been involved in that for many years now. I've been involved in it for almost twenty years. I've pesticides as a whole for over thirty-five years. Hearing the delisting, how does that affect you? The delisting of malafion would not affect any area-wide mosquito management program. In my view, simply because of what Charlotte has said, it's just one part of an area-wide mosquito management program. So if one were to look at mosquito management around their homes, it's about understanding the behavior of the mosquito and we go back to simple biology. It's life cycle, complete metamorphosis. So if we get rid of the immature stages we only have to, we would have less adults to worry about. And fogging would only be something that would happen maybe after a week or something after a rain event where you would not have been able to get rid of all mosquito breeding sites or water sources. That's one. You have modular killer films, products you could put on the surface of water that's not being used to prevent the mosquitoes from surviving if they were to lay their eggs in there. Or you have bacteria that can be used, put into the water, the larvae eat it and it kills them. You also have growth regulators that can be used in water sources to actually prevent the larvae from becoming a mosquito. So there are several options out there. But I agree for a challenge. I said the most important thing is to understand those breeding sources and try to reduce them as much as possible. Other than most people come through and your company do other... Yes, we do the wide range of pests. We stress integrated pest management. The average person calls and says, I have a rat, I have cockroaches and they will come and spray. And we educate people that it's not about spraying. It's spraying just like the use of marathons and aerial weapons because management is only one aspect of integrated pest management. So you need to know why you have a problem. If you look at bed bugs, for example, which is something that's around. People talk a lot about it. A bed bug cannot walk into your house. It's a hitchhiker, you carry it into your house.  If you come back home, your clothes where you put it, you need to pay attention to those things. Then the breeding will be placed in your home if you don't take care of them. But we do a wide range of pests. And we stress to every person. You must first inspect and understand what caused the pest problem. So we refer to us for conducive conditions. Food, shelter, water, temperature to a lesser extent. These are what encourage pests to be in the environment. So if I can reduce one of these conducive conditions, like in the case of mosquitoes, if I remove the water source, I reduce the incidence of the pest feeding environment. Do you use inorganic chemicals? We use inorganic chemicals, but we limit the use and we use them in a targeted way. So for example, you can do a crap and crevice treatment, for example, where you put the pesticide directly in where the pest is. So let's say a human cockroach or a bed bug, they are fig motartic, they like to stay in tight spaces. So you can put the pesticide in there. We use a lot of baiting systems. Even in the case of mosquitoes, we use our mosquito trap. We use a baiting system for pest like termites where because of the way they feed and communicate, they transfer information mouth to mouth. And you can have them transfer the pesticide to where you don't know when they are. So that's the modern way of looking at pest management. I'm not just spraying large volumes of pesticide because if I see a termite mound, for example, and I spray it, it doesn't mean I killed off the queen, which means you're weighing. So I rather get the pesticide transferred to her. So if you look at pesticide from an agricultural point of view back in the bad days, you would apply permissive to the soil. And these pesticides would absorb stick to the soil and the pest would get impacted. So if I were to do that in the case of less than two mites, I am basically limiting my application to there and hope that these termites carry the pesticide on the way back. But I have rain and I have other factors that can impact it. So if I use bait, I know for sure I can always come and monitor and look at what's happening and keep on feeding them and eventually take out the population. So right now, your highest percentage of chemicals are organic. Not all of them. We still have inorganic products and we have sleeping minerals like borax that we use. But we use the synthetic products strategically. Not wide scale. If you look at agriculture and you have a crop, you spray the entire crop. But if I have a pest problem because we have to understand the biology, we know where they would be. So we target them in that space. So if you look at the American cockroach, for example, people say they fly into my home. You have two of them that look almost as the same. There's the Australian cockroach, which is a vegetarian. And the American cockroach, which is not. But you'll get it more like in your septic tank area, wet places, right, on their kitchen sink where you might have a leak. So if you say to us, you have that problem, we would come to inspect to figure out exactly where it is and treat accordingly. Okay. So the de-listing chemicals, and those you ban, okay? I remember some years ago, there were lots of chemicals here. I'm sure they part of the de-listing. FAA was involved in trying to get them out. One of the problems is to get chemicals out of your island. After the de-listing, what happens? You're not going to issue important points for these pesticides. Okay.  So what is going to happen? We're going to phase it out. Since we're not going to issue new important things, it means whenever that what is available on island presently is exhausted, it means that we will be able to manage the stock. Yes, we had a project with the FAO where we collected obsolete stocks from a number of countries in the United Arabian. But what we have to understand is that these things do not... It's not sustainable. It only happens once in a while. So we have not had this program for about five years. And presently, we have a lot of pesticides that are accumulating in a container. We have that. Because when you bring in, as I said, the board is responsible for the regulation of pesticides. So for example, if you bring in on-registered pesticides, those pesticides are confiscated and stored in a container at Union. So definitely we need to have a system in place, not only a system for regularly listing of pesticides, but also disposal is very important for us as well. So there's no mechanism in place for... Presently the Solid Waste Management Authority is not responsible for pesticide disposal. That's a loophole in the legislation. We'll talk about that before our break. You're watching Agriculture to Move. Stay tuned. We'll be back very soon. The Ministry of Agriculture, Fisheries, Food Security and Rural Development is placing heavy emphasis on the concept of food security. It's our prosperity, our future. The farmer incentives program of the Ministry of Agriculture, Fisheries, Food Security and Rural Development is aimed at reducing the cost of production and promoting food security and accessibility. All farmers, fishers and agro processors who've registered and own a farmer's registration card qualify. These incentives include the percentage reduction of excise tax and import duties for agricultural and fisheries production inputs which are imported. These include approved agricultural products for an approved agricultural project. For example, vehicles, fishing vessels, animals, animal feed, planting materials and other farm inputs. Farmers can apply by completing the application form and submitting with all relevant documents attached. For further information, contact the deputy director of agricultural services at 468-4125. Welcome back to the program agriculture on the mode of course if you are tuning in lately we are talking about pesticides, use of pesticides delisting of pesticides and of course I have people in here who are well apt enough to discuss this activity here. You mentioned FAO and the list of chemicals that are not in use but they are studied union. You mentioned also that solid waste is not responsible How are you going to get those chemicals out of there? Normally you have projects collecting, when you have special projects in the region they collect those pesticides and we are hoping that very soon some project will come up and they will take the seeds out of those pesticides. You hope it's a motor motor. I said originally and locally we do not have the facilities to deal with those pesticides.  That is why we have the facilities to incinerate them to one. So if nothing comes around those chemicals are going to be in a continued union Yes until such project. So in terms of the key of the holding material The pesticides are stored in special containers these places that we are acting in they are stored in special containers so it will take some time before that happens. Okay because I know people are complaining about that the chemical torturing and people are around the area Yes we had a particular pesticide that was very volatile that was stored in the container but so far we have dealt with the issue Nothing happened So you are still waiting for the potential to come around Yes Miss Leon Apart from the control of the musty tool Are there any pace that you are responsible to household pace that you are responsible for control? Okay we also do control of rodents as well So we have a rodent control aspect of our program So the sad thing is that due to limited human resources we are not able to do this type of rodent control in all communities but we focus pretty much on the towns and the cities on the island So in castries we would normally have officers in the city of castries doing rodent control they would be doing the assessments looking at areas where you see higher populations of rats and mice they would be doing the same thing in view for sofray would also be responding to the complaints if we get any complaints in various communities that they have issues with rodents and so forth So we would do that we would also attend to issues with fly infestation rodents we would give the home owner or community members advice on what should be done but we do not have the chemicals for the treatment then we would indicate to them that they may need to use a private pest control company or something So in other words is more educational for the people in the community? Educational yes but we do do treatment we do treatment as well So we would go in like I said we would do the assessments look at where we see in higher populations we look at the signs of infestation we look for the rub marks the tracks we look for evidence of annoying in a particular area and so forth we look at the other factors which would contribute to the proliferation of rats and mice So take for instance rats and mice they need free things to survive food, water and shelter in many instances in our communities in our cities and towns we provide all of those things for the rats So we would go out and we would do the education but we also cannot run away from the level of treatment and beating that we would have to do in these communities and the cities How did you turn a rat? Because I remember at one time there was this chemical beat you wanted to bring in for that called biorats I heard it was called tuber What was the situation? It was not allowed because it was said that one of the active ingredients was someone else Yes and based on that the God took a decision not to bring it in as to where it is right now I don't know So that's what it is right now As he said one of the active ingredients yes it was biopesticide one of the active ingredients in this particular pesticide was salmonella and when he researched salmonella that was in this particular period there was a great possibility that it mutated so what had no choice but to have the huge registration of that particular period and not all the Caribbean countries as well did not register biorats because of that particular reason So what bit do you all use? So what we would use we tend to rotate our bit so we would look at the various active ingredients in the bit because you have fast killing bit you have slow killing bit fast killing bit is not something that you can use for a very long period of time because of course when the rodents are very smart when they see that they are dying because they are eating that particular rodenticide so you have to have a rotation so we may be using contract we may use clear rat we will look at other bits so we may use fast if we see a very high infestation we would use a brand of bit where you have a quicker kill so it's fast killing and then phase it out into a more slow kill bit so we would have that rotation happening at our department maybe some devil applicator I remember when I was a rat when you heard that just run in the same but I noticed the applicators are well armed well clad right and what happened to the public okay so the reason the applicators are well clad is because they are exposed to the chemical at a higher concentration and for a longer period of time so they are more at risk because when we fog people tend to say oh the smell, the smell, the smell what we smell more of is the solvent that we use is the diesel that we smell more of versus the malefion so in that solution you have a much higher volume of diesel in it versus the malefion the other thing is that the fog dissipates very very quickly and again in our our geography the wind always carries it around so it never it never stays in that area confined area for a very long period of time very quickly dissipates and it goes off and again the concentration that the public is exposed to it is so low and it breaks down so quickly that it doesn't pose a risk but of course because of just the nature of malefion we are trying our best to avoid any issues to mitigate any potential risk so this is one of the reasons that we do look for alternatives although we know that we are using it the right way and we are not causing too much harm to our people malefion affect the insects which are very important I remember as a child we used to run chase butterflies in the savannah if you keep on spraying malefion you are not going to have butterflies to chase so it's going to kill the butterflies it's going to kill your dragonflies it's killing your bees and pretty soon if we keep on spraying and spraying and spraying we are not going to be able to eat they they are essentially responsible for that exactly so because of that we are trying our best to only spray for mosquitoes in response to dengue outbreaks on our island what are the issues any problems you face is it to be involved in this pest management business the biggest problem to me is people come to you most times and the problem is out of hand or maybe they have tried certain options and it hasn't worked and they want you to solve it one time and based on my background I seek to, I need to understand the problem because if I just apply a pesticide charlatan made the point about the rodenticides you have what's called acute poisons which is a poison that the rat must it has set in the mouth to die if it doesn't eat it it can get sick but it will remember what it ate and it will not eat that far so it is not up to stream mice which is a much higher and prevent the rodents from eating it anticoagulants and the cold cassifera which will they wouldn't know it's a poison so these can vary based on the generation of pesticide and you can kill us in the last 24 hours for more so you need to know that so if somebody says I have a rodent problem it's not just coming to put bait to get rid of it because if you put the bait in the current situation the rat has a menu it doesn't mean it's going to take so sanitation becomes very important exclusion becomes very important and educating people that we have three rodents in civilization there's the roof rat what you see on trees is different from what you see on the ground and you have the house mouse so you need to know which one you're dealing with and how to bait for them and what you need to do to prevent them from getting into your space so the control is different the control can vary because the rodents are neophobic and also neophobic so you don't trust anything new you feel it means the alpha rats will force the other rats to do stuff for them or they will be aggressively going after them so you need to understand that behavior and know how to deal with it so people need to understand that it's not just about applying a pesticide it's understanding the environment that the pesticide and reacting accordingly by removing food, shelter and water or one of these then applying pesticides well ladies and gentlemen you have come to the end of the program I was about to ask for a final point submission but I was thinking that these two years have one minute less than one minute left so I really want to thank you all for being here Mr. Registrar I hope all the chemicals will be out of solution very soon but we will not let you hold to that and Ms. Leo, thank you for being here of course face cancer game and I wish you all success thank you you've been watching our report on the move thank you for being in the program remember our report on our business keep fresh which is the best thank you again I'm Philip Sidney saying goodbye


Hello, hello! I wanted to do a quick video for you guys today about disconnecting your situation in life from your emotional well-being. Now, let me ask you a quick question.  Do you find yourself, for example, running your business and getting super stressed when things don't happen or when things stack up that should happen? Or maybe in your relationship there's a problem with your friends or your partner and you find yourself in a really, really bad mood. I know I've definitely experienced this for years, with my business especially, where if I had a lot of stuff to do, I would just get really, really stressed and I would just wake up with stress, I would do the day with stress, I would go to sleep with stress, because I would always have more to do. And even today I have a lot of stuff to get done. I need to focus on a lot of things and there's a lot of things to get done. But I did this separation a while ago that really changed the game for me.  I would just feel really, really bad all day long. I would work reluctantly. I would not like to upload videos because I was in a bad mood. I would always think like, oh my God, what about this client and what about this thing that I need to deliver and it would just be bad. So a big epiphany that I had was that I can actually completely separate my life situation from my emotions.  And then I was thinking, wait, why am I feeling like this? Why am I feeling so stressed and anxious?  I've got to get stuff handled and why do I got to get it handled? Well, I want to feel good. I want to feel happy and I won't feel happy till I get it handled. And I just asked myself a question. I just asked myself, what happens if I just choose to be happy now? Regardless of the chaos, the situation, being late, the clients are late, my projects are late. What if I just choose to feel good? And again, that doesn't mean to not pay attention to stuff, to be okay with being late, to not have responsibility. We still do all that.  But what if you just choose to feel good? Again, not as an exercise, just as a choice. I want to feel good. I want to be happy, I want to smile, I want to feel good. I don't care that the things are late. I don't care that I'm late to the meeting. I don't care that there's a lot of stress and pressure. I'm just going to feel good. And what happened when I made that decision was I started feeling really good. And the unexpected thing was that my productivity actually went up. So suddenly I started taking more action. I was more fluent, more fluid. I was taking kind of more spontaneous action. I was creating opportunities, making more content. Actually, you know, coming up with creative solutions, doing things that I would usually be reluctant to do, or would avoid because of the bad mood. So I just started feeling better. And the situations would still be the same. I would still be late to some appointments. I would still be late on some deliveries. Some things would not be really good. There would be arguments once in a while, but I would just do them with a smile. Like, okay, I'm just going to feel good.  I don't care. I don't want to be changed my life because I still have the same pressures that I did before, but now I feel good during the day. I don't feel stressed anymore. And that's actually very productive for me because it makes me take more actions and become more charismatic. And being a coach and a lecturer and a marketer, I'm very, very dependent on being charismatic and persuasive. So I hope this tip helps you. I haven't really worked with clients on this area. Not very much. So this is just my experience with it. Let me know if you have any questions. Thank you for watching. Feel free to subscribe and download my free 70-plus page guide to making $2,000 sales on a weekly basis on my website at robifrank.com. So thank you again for watching. Please subscribe and I'll see you in the next video. Bye-bye.


Hi everyone, Joe for jaspyscasebrakes.com. Happy Tuesday coming at you with jaspys five box top shelf hockey mixer and team break number two. Includes a box cup hockey. We got four boxes of 2021 product, black diamond, SPX, Trilogy and Synergy. And then we have box of 2019, 2020, the cup hockey in here as well. Pretty solid break. Big thanks to everybody here and we've got another five box break up so we can run this back too. Big thanks everybody here for getting in on the action. I appreciate it. Thanks to the people who bought their spot, most people buying their spot straight up and congrats again to the winners of the filler. There was only one filler, so we put a little rooftop next to your name that means you won that spot and that allure pack break. And there's all 31 teams right here. Let's roll it and randomize it. Three and a five, eight times for names and teams. One, two, three, four, five. Six, seven and once more, eighth and final time. After eight, we got Steven down to Mike. Three and a five, eight times for the teams. One, two, three, four, five, six, seven and eighth and final time. Blues down to the Calgary Flames. Now we will pause the video just for a second or two. We'll do more in like a minute or two, not a second or two, but we're gonna pause the video now for a little bit of trading if you want to. So trade window is open. Steven, with the Blues, David with the Devils, Nick with the Jets, Sean M with the Blackhawks, Kevin with the Kings, Panthers and Bruins. Sean with the Ottawa Senators, Daniel with the Preds, Sean with the Ducks, Daniel with the Golden Knights, Sean with the Islanders, Kevin with the Lightning, Matthew with the Oilers, Mike with the Wild, Sean M with the Sabres and Coyotes, Steven with the Maple Leafs, Eric with the Caps, Jonathan with the Stars, Kevin with the Rangers, Sean O with the Flyers, Brian with the Red Wings, Sean M with the Penguins, Daniel with the Sharks, Kevin with the Blue Jackets, Sean M with the Canucks, Mike with the Hurricanes, Daniel with the Avs, Jack with the Canadians, and Mike Tower with the Calgary Flames. All right, let's sort by column B and we're gonna pause the video when we come back. We're gonna see if there's any trades and then the break, be right back. All right, welcome back folks. No deals were done. So here's the list, hot off the presses. Thanks everyone for hanging with me on a Tuesday night. Appreciate it. Good luck everybody. We're gonna start with the Synergy Box and Trilogy, SPX, Black Diamond, and of course we'll close with the cup. Chad, did your Mariners win? Is there a chance for the M's? The Dodgers beat the Padres 2-1, but they need help from the Diamondbacks here. I'm not sure if they're gonna get it, but they're only down a couple runs, so let's see if the Dodgers can gain a game on the NL West. We half came back with four to go. Could be exciting times for Seattle. All right, there's John Carlson, Nick Robertson to 749, Sebastian Ajo gave Velarde to 749, Alexander Barthkov to 749, Roman Yossi, a lot of numbered cards here. I think sometimes you can find some hits in these boxes. There's Tyler Benson, Riley, 349, Johnny Goudreau. Oh, there's an autograph, there we go. Steven Lorenz, 27 out of 35. That's a rookie auto, 27 out of 35 for Carolina. That's gonna be for Mike Tower and the Carolina Hurricanes. Rock you like a hurricane. All right, a bunch of numbered cards in here too for everybody. Oliver is saying that the San Diego Padres are 12 and 30 in their last 42 games. Yeah, they must have really lost that mojo when they didn't get Scherzer. Yeah, they lost a little bit of focus. I think they're starting pitching really didn't help them either just in general. All right, Trilogy. I don't know, Padres are gonna be a dangerous team though. I think the Padres, would you argue that the Padres may be like one the off season? I feel like they made so many moves. Everyone thought they had won the off season, but that won't do it. But if they kind of, you know, that seems to happen in sports a lot. The team that wins the off season doesn't necessarily, sometimes they fall a little flat during the regular season, but they're gonna be dangerous. So let's see what we got here. We got rookie Premier Jason Robertson to 9.99 and we've got a Brady Kachuk for the Senators. That's gonna be for Sean M and Ottawa. And the Kale McCarrey, I don't think that's rookie Kale McCarrey right now, it's not. And we got a, ooh, this is a cool hit right here. Crystallized autograph, Kasperi Kapanan. You can see it's almost like a plexiglass material there. It's awesome. That is for Toronto. That's for Stephen, last spot Mojo. Got the last spot straight up and gets his cool looking autograph. Nice. What is that? Oh, that's a little bit of top loader dust in here. Is that on the inside? There you go. Nice and clean. There's Belzeal and there's Rookie Superstage, Alexi LaFrenier for the Rangers, Kevin. There's a McDavid here. That's to 9.99. Anthony Angelo, Rookie Superstage, Red, Quinn Hughes, Lucas Carlson and Roman Yossi. All right, SPX. Yeah, Chad saying we need one more win. Mariners need one more win out of the Orioles. Two wins out of the Jays. And then it'll be Insanity for the last few days of the season. I said Giants win 6-4. Giants still two game, Diamondbacks did not help the Dodgers. Giants still two games ahead of the Dodgers. One fewer game left. There's Calvin Thurkhoff, 13 out of 375. Rookie, Jersey and Autograph for Columbus. That's gonna go to Kevin Kelly in the Blue Jacket. He won that spot in our filler pack. We've got Obsidian Jersey, Elias Pedersen. 156 out of 249. And that's for Vancouver. That's gonna go to Sean M. and the Canucks. Got Josh Norris, Finite Rookies, Senators. Sean Maddock with Ottawa. Little five box hockey mixer, top shelf hockey mixer. And we got, I love these old King's jerseys right here. Arthur Kalyev, 003 out of 399. I think King's had a preseason game today, right? Here's the next one. 2020, 2021, Black Diamond hockey. And then the cup, I think it's just a relic on the bottom here to use that playing card to hide the hits a little bit. There's Nate McKinnon, Nathan McKinnon to 349 for the abs. Sparkling Scripps Autograph, Phil Esposito. Old school hockey player, 11 out of 25. Boston Bruins, Kevin Kelly.  Carter Hart, run for the cup. Flyers, Sean O'Leary. Going to a 180 top bar, it's pretty thick here. We got a Kerry Price, 16 out of 50, premium relics. Nice. Montreal, Canadians, that'll be for Jack. We got Diamond, Black Diamond, Dimonation. I get it, 47 out of 99. Nico's Lidstrom for the Red Wings. Good cool diamond pattern. In there, it's pretty cool. That'll be for Detroit, Brian Heyman with the Red Wings. And last but not least is Bowen Byron, Exquisite Performers, 155 out of 199 for Colorado. Daniel Katz with the abs. Now the big one, 2019, 2020, upper deck, the Cup Hockey. We got 115 out of 249. Larry Robinson, all-time alum, card for the Canadians. It's gonna go to Jack. Emile Benstrom, rookie patch and autograph, 149 out of 249. Columbus, Kevin Kelly with the blue jackets, won that spot in the filler. Exquisite Collection Endorsement Relics. Rook, no, just a patch auto. Jake Goonsell, 17 out of 50. For the Penguins, that'll be for Sean M, Pittsburgh. Ooh, that looks cool right there. Color-coded, 22 out of 33. Dante Fabro, yellow ink, autograph. That's pretty sweet. Matches the color of the team. That's pretty sharp too. That's Daniel Katz with Nashville. It's pretty sharp. Couple more here. Ooh, Buffalo! Inked insignia, that is, Victor Olofsson. You got the Buffalo Sabres logo. And his on-card autograph, 28 out of 75. Sean M with the Buffalo Sabres, won that spot in the filler. And the last one is, Patrick Kane, nice. Emblems of Endor, even I know this guy. Five out of 15, dual relic and autograph. Looks like the piece of the Blackhawks logo in there. On-card auto. Chicago, Sean M, Chicago Blackhawks. Nice. You can kind of see like the relic is kind of almost bulging out of the cars. Too much relic there. That's awesome. Thanks everybody for watching and breaking with us. That was Jaspie's five box top shelf hockey mixer, Random Team Two. We've got another five box break up on the site right now. Just FYI, the cup is from a, we've been pulling these from a fresh case and the black diamond is also from a fresh case as well. So there's a chance that we can find those diamonds in that black diamond box. That could be the next one. Keep an eye out for it. Jaspie'scasebrakes.com. I'm Joe and I'll hockey with you some more next time. Bye-bye.


We've got the third annual duck float. It's in conjunction with the city of Pival and the University of Pival It's a great event for not only the students, but visitors to our area It usually lasts the river part lasts about two and a half three hours according to how the flow is on the river But it's a great way for students to come in that are new here get oriented with Pival relax a little bit because Not only have they went through orientation, but they've also went through their first Week or two of school and they probably need to relax a little bit. It's stressful The duck float not only stops here that takes us roadhouse boat dock the scenery here is unbelievable When they're floating down the river, they can see the 8th one of the world as we call it the cut-through project All the way up and down the river. It's just beautiful today beautiful weather and we're glad to have everybody here Students only get to enjoy this event Through the university which the university does a great job and providing stuff for the kids to do They have bingo nights movie nights Great ways for the students to relax and enjoy their time here It's a great feeling know that I work for an organization that really cares about its students no matter if they're high school or the university and We really want them to know that they're appreciated and we welcome them here with open arms