# gst: when generalized diffusion could result from stochastic processes.

<< Despite the success of fractional Brownian motion (fBm) in modeling systems that exhibit anomalous diffusion due to temporal correlations, recent experimental and theoretical studies highlight the necessity for a more comprehensive approach of a generalization that incorporates heterogeneities in either the tracers or the environment. >>

AA present << a modification of Lévy's representation of fBm for the case in which the generalized diffusion coefficient is a stochastic process. (They) derive analytical expressions for the autocovariance function and both ensemble- and time-averaged mean squared displacements. Further, (AA)  validate the efficacy of the developed framework in two-state systems, comparing analytical asymptotic expressions with numerical simulations. >>️

Adrian Pacheco-Pozo, Diego Krapf. Fractional Brownian motion with fluctuating diffusivities. Phys. Rev. E 110, 014105. Jul 1, 2024.

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.110.014105

Also: disorder, fluctuations, network, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, fractional Brownian motion, fBm, Lévy, disorder, fluctuations, anomalous, network, transition

# gst: Lévy flights and Lévy walks under stochastic resetting.

<< Stochastic resetting is a protocol of starting anew, which can be used to facilitate the escape kinetics. (AA)  demonstrate that restarting can accelerate the escape kinetics from a finite interval restricted by two absorbing boundaries also in the presence of heavy-tailed, Lévy-type, α

-stable noise. However, the width of the domain where resetting is beneficial depends on the value of the stability index α determining the power-law decay of the jump length distribution. For heavier (smaller α) distributions, the domain becomes narrower in comparison to lighter tails. >>

<< Additionally, (AA) explore connections between Lévy flights (LFs) and Lévy walks (LWs) in the presence of stochastic resetting. First of all, (They) show that for Lévy walks, the stochastic resetting can also be beneficial in the domain where the coefficient of variation is smaller than 1. Moreover, (They) demonstrate that in the domain where LWs are characterized by a finite mean jump duration (length), with the increasing width of the interval, the LWs start to share similarities with LFs under stochastic resetting. >>️

Bartosz Żbik, Bartłomiej Dybiec. Lévy flights and Lévy walks under stochastic resetting. Phys. Rev. E 109, 044147. April 22, 2024.

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.109.044147

Also: keyword Lévy in FonT

https://flashontrack.blogspot.com/search?q=Lévy&m=1

Also: escape, noise, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, escape, noise, stochastic resetting, Lévy

# gst: near a critical point, switching between exploitation and exploration, to approach life with Lévy's (chaotic) walk

<< Lévy walks are common biological movements. However, the functional advantages of Lévy walks emerging near a critical point are poorly understood. >>

AA << showed that there could be functional advantages associated with Lévy walks emerging near a critical point, including a large dynamic range to stimuli and highly flexible switching between exploitation and exploration. >>

Masato S. Abe. Functional advantages of Lévy walks emerging near a critical point. PNAS.  doi: 10.1073/ pnas.2001548117.  Sep 14, 2020.

https://www.pnas.org/content/early/2020/09/11/2001548117

Chaotic 'Lévy walks' are a good strategy for animals. Riken. Sep 17, 2020.

https://phys.org/news/2020-09-chaotic-lvy-good-strategy-animals.html   

Also

Lévy flight hypothesis, not only for predation ...  Nov 22, 2015.

https://flashontrack.blogspot.com/2015/11/s-gst-levy-flight-hypothesis-not-only.html

keyword 'Lévy' in FonT

https://flashontrack.blogspot.com/search?q=L%C3%A9vy&m=1