 da npoj h eighthvapa bila in izvima to da bi zdravit嘴il na to, izvečjimo, da ima in del, here is my the talk, and I will talk mainly about anomalous diffusiv processes and what is the difference with normal diffusions in systems that show these anomalous diffusiv behaviors, so I will give a short introduction then I will give some different approachesThere are various approaches to this anomalous diffusion. Then I will explain what does it mean Order spare memory and stochastic resetting. And then I will summarize my result. We all know what is normal diffusion. The normal diffusion in terms of the mean squared displacement means that the mean squared displacement here continuously depends on time. in v mnogih sistemih, ta relacija ne bo vzaložila, ali zato ječen, vzaložila, kot zpravilih predstavljanje v tem, da je vzalivosti tudi padega, in tudi, ki se bo na del, bo brzi tudi vzalivosti, bo vzalivosti tudi vzalivosti in tudi je tudi sest, ki se zeloče veči, obroženje karikova, izportsveni svoje zamojne, in v boldu, kot dovrženfti, vsakod hpidari, trafiti vzamoj tudi, potenčne, in in veliko in aktivne, vz fingerprinta. Vizučne vzago prizve, potenčne, kot tudi vzago, potenčne, bi je vzago, in prijevstak sem sredna, da ne bo vsak v vseh ročnje, in ne bo jazimga začeljena začeljena, če se zelo, da se dokonfizije, dokonfizije za poslidnje delov, očenja na srednjih velikim. Kaj je to, kaj je tudi dokonfizije? Kako je bil po vseh zelo, bolje se dovolj, a v to je dovolj vseh. Ne Chingko so vseh zelo, iznačil ležno, in ne vseh zelo, da je vseh dovolj, in tako je dovolj, tako je dovolj, zelo je dovolj. Zelo je dovolj, zelo je dovolj kaj občutno. Kaj je bil dovolj? Kaj je bil dovolj, odnojovat, če pa jaz ovem je generalizovanja izvojila vsehneqov kanal, in punjaj vsehneqov ca. Tkajkaj, zato v srečej režrih so nekaj dobro konstrumenje, kaj ne leži zhljučski del哦om to izvanje me vseče č rodzice, nekaj to je odnami, kje ne pa je je dota nekaj dobro, nekaj ne adiv leži zbično del začinaj, da je to naspojeva, In početim, da se prijelim všeč načo muži, da se početim všeč načo muži, in načo priča, da se početim všeč načo muži, z nekaj početih modelj. Zato sem zelo, da se prijelim všeč načo muži. To je vse nekaj dobro, nekaj dobro izgledaj, zazmavečkosti, če pa vzakajemo. Zato zato, da počakamo zazmavečkosti, ko se je zelo, da je izgledan ga. To je zelo, da je nezakasno, da se izgleda, pa je zelo, da je zelo, da je zelo, da je zelo, da je in vsega vsega vsega vsega vsega vsega vsega vsega, in nekaj nekaj likvit neko je bržem zaaringje, neko je nič nekozvradi tez in res bi je še in echočen v velim č mésfom, in so nami zelo do poličnega svetu, kjer lahko res nekaj da namzlimga zelo do poličnega svetu pri zaaringju klasticub. In nekaj nekaj bolj nekaj vse jel in tu, da nekaj bilo najvej zelo, Career environment. Then, instead of Delta Function, we have some Memory Function, Gamma and in many cases, if this Friction Term is much higher, than the Inertial Term we can simply neglect this inertial Term and easily can solve this Launc凌 equation. So, this was already mentioned, if the correlation of the noise is related tudi nazvo, tudi nazvo je, da這麼 nosimo, da namojo to delovanje vseg vsega teore, ki to se svoje zele in drozna prijezajne, od vsega jer je ne se ne zele. Zelo je se, da to je ta dolžap nene. Nenamjo to do delovanja vsega vsega teore. A vsega, da nazvo u plus začnev tem povolj, da sem izgleda toga in da sem izgleda vsega vsega, da je period, are the means square displacement or the velocity correlation function." If we put gamma of t that is equal to delta function, it's not about white noise where we have a delta correlation, but it's a fractional Gaussian noise. Kako je vsebega zelo, je tudi korelacija vstajnjaja, zelo je to kajige vsebega. Vsebega, ki je poželjno vsebega, poželjno vsebega, zelo je prišeljno, vsebega, kako je začeljno, izgleda se, če je izgleda vsebega. Zelo je bilo vsebega, boj, ko je tudi vsebega, vsebega, da ga se vsebega, konformationalne dinamice v protišnih protišnjih. Tirozine je donor elektroni, Flavina Dino-Kleotiti je akceptor elektroni in vsega vsega elektroni, vsega distančnega vsega vsega vsega vsega. Vsega vsega vsega vsega vsega vsega vsega vsega. zelo je zelo vzela vzela. In druga opročva na anomalousne zvrste je vsega vsega vzela, kaj je vsega vsega vsega vsega vsega, ki je vsega vsega vsega vsega vsega. In nekaj je to vsega vsega? Vsega je, da vsega vsega vsega vsega vsega In vse števne tudi je vse pozicije za vseh tudi. Na vseh tudi, ko je tudi časno vseh tudi vseh tudi, in kako je tudi vseh tudi vseh tudi izgašnji, nekaj nekaj neko je tudi izgleda vseh tudi, nekaj nekaj neko je tudi izgleda na vseh tudi. but if we consider some general form of their waiting time probability distribution function in jump-plants probability distribution function, then we can find the probability distribution function in Forillيد vklas space and we find that this is for standard Brownian motion. But if the instead of exponential waiting time, we have some power law waiting time, which is given by 1 minus s to power of alpha. If we put this power law waiting time in the general form of the equation for the probability distribution function, then we will find that the probability distribution function satisfies such an equation where we have some memory kernel there and we see if gamma is equal to delta function, we have standard diffusion equation. But if we have some power law waiting time or other more general waiting time, then we have some more generalized diffusion equation. And this continuous time random walk can be easily solved. This equation can be easily solved by so-called subordination approach where the random motion is parameterized in terms of some operational time, which is the number of steps of the particle. And if the relation between the physical time t and operational time u is some alpha stable levy noise, then we can find the solution of the generalized Langevin equation by knowing the so-called subordination function. So here is simply Gaussian distribution for the Brownian motion and this is the subordination function. So this is the solution for the standard equation. We know that this is Gaussian, but for the power law waiting time we have some Fox function from where we see that this is a non-Gaussian probability distribution function. But this can be repeated for some general form of waiting time and by using of this subordination approach we can find that the mean square displacement of this equation with memory kernel can be simply obtained by this simple relation and if we put delta function, so this is one, we have normal diffusion, if this is power law, we have some power law dependence on time and such anomalous diffusion can be observed if we consider a diffusion in so-called comp structure, which means that the particle moves in this direction but then can be stuck in the fingers of the comp and when the particle returns back to the backbone it can continue to go in this direction but the particle from here cannot jump here. So because of this geometric constraints in the system then we see that the mean square displacement along the backbone is one-half because the returning probability of Gronian particle to come back to the backbone is T2 minus 3-half and if you consider the returning probabilities of waiting time for the movement of the particle along the backbone, then we put in the equation for the continuous time random walk and we obtain that the mean square displacement has a power law dependence on time and one can derive the diffusion equation so it's a simply two-dimensional diffusion equation but the diffusion along the x-direction contains this delta function which means that if y is different than zero this term is equal to zero so the movement along the backbone is only at y equal to zero. This can be generalized, for example, for three-dimensional comp so we have a backbone, fingers of the backbone and then fingers of the fingers and then because of this additional axis then the mean square displacement along the backbone is one T2 power one-fourth in y is T2 one-half and in z we have simple Brownian motion. So the tempered memory, what does it mean tempered memory? This means that if we consider one-showing equation and in the memory kernel after some characteristic crossover time we have exponential cutoff of the memory kernel and if we put this tempered memory kernel in the equation we will find that the mean square displacement can be represented by this three-parameter metakrefter function but if we analyze the asymptotic behaviors we will see that the system from sub-diffusion in the long time limit goes to normal diffusion because we cut this exponentially we have exponential cutoff of the memory and that's why we have, in the long time limit we have normal diffusion. We can calculate the velocity correlation function and it was shown that such model can be used to describe the diffusion of lipid bilayers membrane and these lipid structures if we immersed in water and room temperature they form these bilayers and according to the simulation it is shown that these bilayers move together but they don't perform jump processes they satisfy this equation and if we try to fit the experimental results with the theoretical results we see that we have a perfect agreement and we see that crossover from sub-diffusion to normal diffusion appears at 10 nanoseconds which is observed by the simulations and this process of tempered memory can be generalized to different continuous time random work processes where instead of this memory kernel gamma which appears due to the waiting time in the system if we have exponential cutoff in the waiting time then we have this additional term in the diffusion equation and if we solve this equation we will see that in the short time limits the mean square displacement is like there is no tempering but if we observe normal diffusion because of the exponential cutoff of the memory kernel and this was shown that it can be applied to describe the transient diffusion of telomers in the nucleus of mammalian cells so I will now go in details but in such systems this crossover from anomalous diffusion to normal diffusion has been observed because of this exponential cutoff of the waiting time of the particle and at the end I would like to talk about stochastic resetting how many minutes I have 10 minutes so this is another process where we also have some transition in the system for example from anomalous diffusion to some non-equilibrium steady state because of if we introduce a stochastic reset of the particle to the initial position so why this stochastic resetting is important because there are it has applications in various fields starting from foraging dynamics or animal search for food maybe some computer algorithms and web searches but also it applies in economy and finance for example if we have some sudden market crushes where this income dynamics is reset to some previous state but there are also many works nowadays on quantum dynamics with resetting and this is still very topic that is worth to be considered in the future and what is stochastic resetting, this means that after some time the particle starting from some initial position is reset to this initial position and between two resetting events the particles perform free diffusion and this is the paper by Evans and Majunda which is published ten years ago and this year or last year there was a special issue about ten years of this seminal paper by Evans and Majunda and this process of stochastic resetting can be described by this renewal equation where we have the resetting part where there is no resetting up to time t and if we multiply this equation by x square integrate we will see that the mean square displacement also satisfies this renewal equation and if we want to solve this equation we will see that in case of no resetting we have some Gaussian distribution but if we introduce resetting in the long time limit we obtain some non-equilibrium steady state and it has Laplace shape of the distribution where this alpha zero is the inverse time scale and the mean square displacement from normal diffusion goes to some saturation which depends on the resetting parameter and this approach we can introduce for example in this generalized large event equation which describes continuous time random walk long tail waiting time and if we start from the renewal equation and then we try to solve this renewal equation we can arrive again to another generalized diffusion equation but this memory kernel here satisfies also renewal equation of the first diffusion equation so to solve this we obtain that there appears stationary distribution and it's again Laplace distribution like for a simple Brownian motion with resetting this means that a normal diffusion with stochastic resetting in the long time limit approaches also this Laplace distribution and then we can easily calculate the mean square displacement if we analyze in the short and long time limit we see that in the short time limit it behaves like without resetting in the long time limit it saturates so we have this transition dynamics this is for the standard diffusion equation how from this gamma if we use delta function we arrive to this known equation for the stochastic resetting in the long time limit we obtain some non-equilibrium stationary state but now this inverse time depends on alpha and we can apply this mechanism to come structure where the particles is reset to initial position or it is reset to the backbone or it is reset to the fingers terms are given here for different resetting mechanisms and if we do the numerical simulation and then perform the calculations we will see that in the first case if the particles is reset to the initial position all the marginal distributions in all three directions approaches stationary state and we have transition most diffusion to some saturation but in case of resetting to the backbone this means that in the equation we have something like exponential cutoff of the memory due to resetting because when the particles is stuck in the fingers you reset to the backbone then you cut off the memory and because this term is e to minus r t then we have this characteristic cross over time appears at 1 over r so we see that in this case along the backbone there is no non-equilibrium stationary state because we have observed the diffusion but in the other directions we have this transition to the non-equilibrium stationary state from the additional fingers to the main fingers that the situation is a bit more complicated and again we can find the solution of the problem by this generalized diffusion equation but here the memory kernel can be a convolution of memory and resetting and because of this we have transition from anomalous diffusion behavior to another or transition from anomalous diffusion to normal diffusion and along that direction we have a simple Brownian motion with resetting which means that we have transition to the stationary state so with this presentation I try to give two examples of processes where we have exponential troncation of the memory in one case we have transition from anomalous diffusion to normal diffusion in another case from anomalous diffusion we have stationary state so there are many works also related with heterogeneous diffusion with stochastic resetting or geometric Brownian motion with stochastic resetting where this approach can be applied and these are some works by our group and I would like to thank to all my collaborators we will have three posters there and also we just started to do some resetting in quantum systems on Friday Vladimir will give a talk about this problem that we are working on and at the end I would like to thank the organizers for the invitation and these funding gauges things Thank you very much