# gst: apropos of interweavings, linking dispersion and stirring in randomly braiding flows.

     Fig. 5 (a)

<< Many random flows, including 2D unsteady and stagnation-free 3D steady flows, exhibit non-trivial braiding of pathlines as they evolve in time or space. (AA) show that these random flows belong to a pathline braiding 'universality class' that quantitatively links dispersion and chaotic stirring, meaning that the Lyapunov exponent can be estimated from the purely advective transverse dispersivity. (AA) verify this quantitative link for both unsteady 2D and steady 3D random flows. This result uncovers a deep connection between transport and mixing over a broad class of random flows. >>️

Daniel R. Lester, Michael G. Trefry, Guy Metcalfe. Linking Dispersion and Stirring in Randomly Braiding Flows. arXiv: 2412.05407v1 [physics.flu-dyn]. Dec 6, 2024.

https://arxiv.org/abs/2412.05407

Also: random, chaos, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, random, random flows, randomly braiding flows, chaos

# gst: apropos of random walks, intermittent random walks under stochastic resetting

AA << analyze a one-dimensional intermittent random walk on an unbounded domain in the presence of stochastic resetting. In this process, the walker alternates between local intensive search, diffusion, and rapid ballistic relocations in which it does not react to the target. >>

AA << demonstrate that Poissonian resetting leads to the existence of a non-equilibrium steady state. (They) calculate the distribution of the first arrival time to a target along with its mean and show the existence of an optimal reset rate. In particular, (..) the initial condition of the walker, i.e., either starting diffusely or relocating, can significantly affect the long-time properties of the search process. >>

<< the presence of distinct parameter regimes for the global optimization of the mean first arrival time when ballistic and diffusive movements are in direct competition. >>️

Rosa Flaquer-Galmes, Daniel Campos,  Vicenc Mendez. Intermittent random walks under stochastic resetting. Phys. Rev. E 109, 034103. March 4, 2024. 

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.109.034103  

Also: walk, walking, random, in https://www.inkgmr.net/kwrds.html

Keywords: gst, walk, intermittent random walk, stochasticity, stochastic resetting

# evol: the hypothesis of quasi-stochastic 'jazzy' metamechanics of biological evolution (in Arabidopsis thaliana)

<< Mutations occur when DNA is damaged and left unrepaired, creating a new variation. The scientists wanted to know if mutation was purely random or something deeper. What they found was unexpected. >>️

<< We always thought of mutation as basically random across the genome, (..) It turns out that mutation is very non-random and it's non-random in a way that benefits the plant. It's a totally new way of thinking about mutation. >> Grey Monroe. ️

Study challenges evolutionary theory that DNA mutations are random. UC Davis. Jan 12, 2022.

https://phys.org/news/2022-01-evolutionary-theory-dna-mutations-random.html

Monroe JG, Srikant T, et al. Mutation bias reflects natural selection in Arabidopsis thaliana. Nature. doi: 10.1038/ s41586-021-04269-6. Jan 12, 2022.

https://www.nature.com/articles/s41586-021-04269-6

FonT 

for a long time I have developed the suspicion that the small plant cared for by grandmother on the windowsill could be a not trivial image of (r)evolution ... 

The three ways of the plastoquinone inside the photosystem II complex. May 23, 2017.

https://flashontrack.blogspot.com/2017/05/s-phyto-three-ways-of-plastoquinone.html

Also

keyword 'evolution'  in FonT

https://flashontrack.blogspot.com/search?q=evolution

keyword 'evolution' | 'evoluzione'  in Notes (quasi-stochastic poetry)

https://inkpi.blogspot.com/search?q=evolution

https://inkpi.blogspot.com/search?q=evoluzione

keyword 'jazz' in FonT

https://flashontrack.blogspot.com/search?q=jazz

keyword 'jazz' in Notes (quasi-stochastic poetry):

https://inkpi.blogspot.com/search?q=jazz

keywords: evol, dna, mutations, randomness, quasi-stochasticity, jazz

# gst: random walk model for dual cascades in wave turbulence.

<< Dual cascades in turbulent systems with two conserved quadratic quantities famously arise in both two-dimensional hydrodynamic turbulence and also in wave turbulence based on four-wave interactions. >>

<< in wave turbulence the systematic spectral fluxes observed in a dual cascade do not require an irreversible dynamical mechanism, rather, they arise as the inevitable outcome of blind chance. >>️️

Oliver Bühler. Random walk model for dual cascades in wave turbulence. Phys. Rev. E 109, 055102. May 1, 2024. 

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.109.055102

Also: waves, turbulence, random, weak, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, waves, turbulence, weak turbulence, random, random walks

# gst: apropos of weakly coupled oscillators, a new approach to depict about their spontaneous stochastic activities

<<  Many systems in physics, chemistry and biology exhibit oscillations with a pronounced random component. Such stochastic oscillations can emerge via different mechanisms, for example linear dynamics of a stable focus with fluctuations, limit-cycle systems perturbed by noise, or excitable systems in which random inputs lead to a train of pulses. Despite their diverse origins, the phenomenology of random oscillations can be strikingly similar. >>

<< Here (AA) introduce a nonlinear transformation of stochastic oscillators to a new complex-valued function Q∗1(x) that greatly simplifies and unifies the mathematical description of the oscillator's spontaneous activity, its response to an external time-dependent perturbation, and the correlation statistics of different oscillators that are weakly coupled. >>

AA << approach makes qualitatively different stochastic oscillators comparable, provides simple characteristics for the coherence of the random oscillation, and gives a framework for the description of weakly coupled oscillators. >>️

Alberto Pérez-Cervera, Boris Gutkin, et al. A Universal Description of Stochastic Oscillators. arXiv: 2303.03198v1 [nlin.AO]. Feb 27, 2023. 

https://arxiv.org/abs/2303.03198

Also

'oscillations' in FonT

https://flashontrack.blogspot.com/search?q=oscillations

Keywords: gst, oscillations, random oscillations, weakly coupled oscillators

# gst: discontinuous transition to chaos in a canonical random neural network

AA << study a paradigmatic random recurrent neural network introduced by Sompolinsky, Crisanti, and Sommers (SCS). In the infinite size limit, this system exhibits a direct transition from a homogeneous rest state to chaotic behavior, with the Lyapunov exponent gradually increasing from zero. (AA)  generalize the SCS model considering odd saturating nonlinear transfer functions, beyond the usual choice 𝜙⁡(𝑥)=tanh⁡𝑥. A discontinuous transition to chaos occurs whenever the slope of 𝜙 at 0 is a local minimum [i.e., for 𝜙′′′⁢(0)>0]. Chaos appears out of the blue, by an attractor-repeller fold. Accordingly, the Lyapunov exponent stays away from zero at the birth of chaos. >>

In the figure 7 << the pink square is located at the doubly degenerate point (𝑔,𝜀)=(1,1/3). >>️️

Diego Pazó. Discontinuous transition to chaos in a canonical random neural network. Phys. Rev. E 110, 014201. July 1, 2024.

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.110.014201

Also: chaos, random, network, transition, neuro, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, chaos, random, network, transition, neuro

# gst: apropos of transitions, randomness can stabilize edge states in short- lifetime regions of disordered periodically-driven systems

<< lifetimes of the edge states exhibit universal behavior when random potentials exist since the edge- and bulk- dominant eigenstates are mixed, leading to that lifetimes are prolonged by random potentials in the region II (short- lifetime region) and shortened in the region I (long- lifetime region). >>

<<  it is an intriguing phenomenon that random potentials tend to stabilize edge states in the region II (short- lifetime regions). >>

Ken Mochizuki, Kaoru Mizuta, Norio Kawakami. Fate of Topological Edge States in Disordered Periodically-driven Nonlinear Systems. arXiv: 2108.00649 (nlin). Aug 2, 2021.

https://arxiv.org/abs/2108.00649

Also

keyword 'random' in FonT

https://flashontrack.blogspot.com/search?q=random

keyword 'disorder' in FonT

https://flashontrack.blogspot.com/search?q=disorder

keyword 'disordine' in Notes (quasi-stochastic poetry)

https://inkpi.blogspot.com/search?q=disordine

# gst: random walk to describe a interplay between the inter-chain hopping and the intra-chain hopping in amorphous Polyimide nanofibers

AA << report the observation of a crossover of heat conduction behavior from three dimensions (3D) to quasi-one dimension (1D) in Polyimide(PI) nanofibers at a given temperature. A theoretical model based on the random walk theory has been proposed to quantitatively describe the interplay between the inter-chain hopping and the intra-chain hopping in nanofibers. This model explains well the diameter dependence of thermal conductivity and also speculates the upper limit of thermal conductivity of amorphous polymers in the quasi-1D limit. >>

Lan Dong, Qing Xi, et al. Dimensional crossover of heat conduction in amorphous Polyimide nanofibers. National Science Review. nwy004.  doi: 10.1093/nsr/nwy004. Jan 09,  2018.

https://academic.oup.com/nsr/advance-article/doi/10.1093/nsr/nwy004/4794956

<< The intrinsic structure of amorphous polymers is highly disordered with long, entangled molecular chains >>

Science China Press. "Random walk" of heat carriers in amorphous polymers. Mar 01, 2018.

https://m.phys.org/news/2018-03-random-carriers-amorphous-polymers.html

gst: actually and counterintuitively a coherent jump could generate disorder.

AA << consider a quantized version of a model for “random walk in random environment.” (..) For a ring geometry (a chain with periodic boundary condition) it features a delocalization-transition as the bias in increased beyond a critical value, indicating that the relaxation becomes underdamped. Counterintuitively, the effective disorder is enhanced due to coherent hopping. >>

Ben Avnit, Doron Cohen. Quantum walk in stochastic environment. Phys. Rev. E 108, 054111. Nov 7, 2023. 

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.108.054111

Also:  Voli a casaccio. Notes (quasi-stochastic poetry). Oct 01, 2006.

https://inkpi.blogspot.com/2006/10/2066-voli-casaccio.html

Also: 'random', 'transition', 'disorder', 'chaos', in https://www.inkgmr.net/kwrds.html

Keywords: gst, walk, random walk, quantum walk, qu-walk, jump, transition, disorder, chaos

# gst: apropos of transitions, scrambling trajectories in a radiative random unitary circuit.

AA << study quantum information scrambling in a random unitary circuit that exchanges qubits with an environment (..). As a result, initially localized quantum information  not only spreads within the system, but also spills into the environment. >>

<< The transition is also easily extended to higher dimensions, where higher-dimensional DP (directed percolation) universality classes will control the critical behavior. >>

<<  The transition in operator spreading  coincides with an information-theoretic 3 transition, which can be framed by  viewing (AA) circuit as a toy model for an evaporating black hole (..). >>️

<< Depending on the initial state of the swapped-in qubits, (AA) observe a corresponding entanglement transition in the coherent information into the environment. >>

️

Zack Weinstein, Shane P. Kelly, Jamir Marino, Ehud Altman. Scrambling Transition in a Radiative Random Unitary Circuit. arXiv:2210.14242v1 [quant-ph]. Oct 25, 2022.

https://arxiv.org/abs/2210.14242

Also: 'transition', 'random', in https://www.inkgmr.net/kwrds.html

Keywords: transition, quantum information, entanglement transition, scrambling, directed percolation

# gst: Parrondo paradox revisited, a chaotic switching approach

<< Parrondo's paradox is a phenomenon where the switching of two losing games results in a winning outcome. >>

<< Suppose I present to you the outcome of the quantum walker at the end of 100 coin tosses, knowing the initial position, can you tell me the sequence of tosses that lead to this final outcome?" (..) In the case of random switching, it is almost impossible to determine the sequence of tosses that lead to the end result. However, for periodic tossing, we could get the sequence of tosses rather easily, because a periodic sequence has structure and is deterministic. >> Joel Lai.

<< This led to the idea of incorporating chaotic sequences as a means to perform the switching. The authors discovered that using chaotic switching through a pre-generated chaotic sequence significantly enhances the work. For an observer who does not know parts of the information required to generate the chaotic sequence, deciphering the sequence of tosses is analogous to determining a random sequence. However, for an agent with information on how to generate the chaotic sequence, this is analogous to a periodic sequence. According to the authors, this information on generating the chaotic sequence is likened to the keys in encryption. >>

Using quantum Parrondo's random walks for encryption. Singapore University of Technology and Design. Oct15, 2021.

https://phys.org/news/2021-10-quantum-parrondo-random-encryption.html

Joel Weijia Lai, Kang Hao Cheong. Chaotic switching for quantum coin Parrondo's games with application to encryption. Phys. Rev. Research 3, L022019. June 2, 2021. 

https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.3.L022019

Also

<< usando l'output di una logistica (per certi valori dei parms) un ipotetico Donald potrebbe avere il vezzo di ottenere stessi risultati con serialita' numerica generata meccanicamente anziche' in modalita' casuale; >>️

#POTUS race: Donald, what he can do (with less than four lines ...). FonT. May 23, 2016. 

https://flashontrack.blogspot.com/2016/05/p-usa-potus-race-donald-what-he-can-do.html

Also

keyword 'parrondo' in FonT

https://flashontrack.blogspot.com/search?q=parrondo

keyword 'parrondo' in Notes  (quasi-stochastic poetry)

https://inkpi.blogspot.com/search?q=parrondo

Also

keyword 'chaos' | 'chaotic' in Font

https://flashontrack.blogspot.com/search?q=chaos

https://flashontrack.blogspot.com/search?q=chaotic

keyword 'caos' | 'caotico' in Notes (quasi-stochastic poetry)

https://inkpi.blogspot.com/search?q=caos

https://inkpi.blogspot.com/search?q=caotico

keywords: gst, games, life, chaos, Parrondo, Parrondo chaotic switching approach

# gst: apropos of transitions: effects of random waves interacting with a coherent structure

<< Solitary waves interacting with random (..) waves (..) are studied. Two opposing types of dynamics are identified: First, the random thermal waves can erode the solitary wave; second, this structure can grow as a result of this interaction. These two types of behavior depend on a dynamical property of the solitary wave (its angular frequency), and on a statistical property of the thermal waves (the chemical potential). >>

<< Either process leads to an increase of the wave entropy. >>

Yuanting Chen, Benno Rumpf. Growth or decay of a coherent structure interacting with random waves. Phys. Rev. E 104, 034213. Sep 15, 2021.

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.104.034213

Also

keyword 'waves' in FonT

https://flashontrack.blogspot.com/search?q=waves

keyword 'onda' in Notes (quasi-stochastic poetry)

https://inkpi.blogspot.com/search?q=onda

# gst: synchronization and chaos in complex systems with delayed interactions.

<< Explaining the wide range of dynamics observed in ecological communities is challenging due to the large number of species involved, the complex network of interactions among them, and the influence of multiple environmental variables. >>

AA << consider a general framework to model the dynamics of species-rich communities under the effects of external environmental factors, showing that it naturally leads to delayed interactions between species, and analyze the impact of such memory effects on population dynamics. >>

<< Employing the generalized Lotka-Volterra equations with time delays and random interactions, (AA) characterize the resulting dynamical phases in terms of the statistical properties of community interactions. (Their) findings reveal that memory effects can generate persistent and synchronized oscillations in species abundances in sufficiently competitive communities. This provides an additional explanation for synchronization in large communities, complementing known mechanisms such as predator-prey cycles and environmental periodic variability. >>

<< Furthermore, (AA) show that when reciprocal interactions are negatively correlated, time delays alone can induce chaotic behavior. This suggests that ecological complexity is not a prerequisite for unpredictable population dynamics, as intrinsic memory effects are sufficient to generate long-term fluctuations in species abundances. >>

Francesco Ferraro, Christian Grilletta, et al. Synchronization and chaos in complex ecological communities with delayed interactions. arXiv: 2503.21551v1 [q-bio.PE]. Mar 27, 2025.

https://arxiv.org/abs/2503.21551

Also: pause, silence, random, chaos, network, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, pause, silence, random, chaos, chaotic behavior, network, delay, time delay, delayed interactions, random interactions, memory effect 

# gst: route from avalanches with random fields to stochastic branching events

<< Many complex systems with discrete symmetry breaking exhibit avalanche dynamics. Under quasistatically slow external driving, the temporal evolution v(t) of physical observables appears to be split between long periods of quiescence and well-delimited fast transformation events, the so-called avalanches. >>

<< Due to their fast nature, such avalanches can be regarded as instantaneous and labeled as point events k in time with a branching parameter. (..) Many physical systems exhibit criticality in the form of scale-free avalanches rendering power-law distributions of sizes and durations. >>️

<< Avalanches in mean-field models can be mapped to memoryless branching processes defining a universality class. (AA) present a reduced expression mapping a broad family of critical and subcriticial avalanches in mean-field models at the thermodynamic limit to rooted trees in a memoryless Poisson branching processes with random occurrence times. (They) derive the exact mapping for the athermal random field Ising model and the democratic fiber bundle model, where avalanche statistics progress towards criticality, and as an approximation for the self-organized criticality in slip mean-field theory. Avalanche dynamics and statistics in the three models differ only on the evolution of the field density, interaction strength, and the product of both terms determining the branching number. >>

️

Jordi Baró, Álvaro Corral. A universal route from avalanches in mean-field models with random fields to stochastic Poisson branching events. arXiv: 2502.08526v3 [cond-mat.dis-nn]. Feb 15, 2025. 

https://arxiv.org/abs/2502.08526

Also: waves, instability, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, waves, instability, transition

# behav: the benefit of ignorance for traffic through a random congestible network.

<< When traffic is routed through a network that is susceptible to congestion, the self-interested decisions made by individual users do not, in general, produce the optimal flow. This discrepancy is quantified by the so-called "price of anarchy." >>

AA << consider whether the traffic produced by self-interested users is made better or worse when users have uncertain knowledge about the cost functions of the links in the network, and define a parallel concept that (They) call the "price of ignorance."  >>

AA << introduce a simple model in which fast, congestible links and slow, incongestible links are mixed randomly in a large network and users plan their routes with finite uncertainty about which of the two cost functions describes each link. >>

<< One of (Their) key findings is that a small level of user ignorance universally improves traffic, regardless of the network composition. Further, there is an optimal level of ignorance which, in (the) model, causes the self-interested user behavior to coincide with the optimum. Many features of (AA) model can be understood analytically, including the optimal level of user ignorance and the existence of critical scaling near the percolation threshold for fast links, where the potential benefit of user ignorance is greatest. >>️

Alican Saray, Calvin Pozderac, et al. The benefit of ignorance for traffic through a random congestible network. arXiv: 2503.09684v1 [cond-mat.dis-nn]. Mar 12, 2025.

https://arxiv.org/abs/2503.09684

Also:  network, behav, random, uncertainty, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, networks, behavior,  randomness, uncertainty, price of anarchy, price of ignorance

# gst: irregular sampling design to address behaviours

<< Animal movement studies have become ubiquitous in animal ecology for the estimation of space use and the analysis of movement behavior. In these studies, animal movement data are primarily collected at regular time intervals. (AA) propose an irregular sampling design that could lead to greater efficiency and information gain in animal movement studies. (The) novel sampling design, called lattice and random intermediate point (LARI), combines samples at regular and random time intervals. >>

<<  in each of the data and simulation examples explored in this paper, LARI sampling results in more accurate and precise parameter estimation and, thus, better prediction of missing data as well.  >>

Elizabeth Eisenhauer,  Ephraim Hanks. A lattice and random intermediate point sampling design for animal movement. Environmetrics. doi: 10.1002/env.2618. Jan 3, 2020.

https://onlinelibrary.wiley.com/doi/abs/10.1002/env.2618

Gail McCormick. Including irregular time intervals improves animal movement studies. Pennsylvania State University. Jan 15, 2020.

https://m.phys.org/news/2020-01-irregular-intervals-animal-movement.html

Also

keyword "pause" in Notes

https://inkpi.blogspot.com/search?q=pause

keyword "pause" in FonT

https://flashontrack.blogspot.com/search?q=pause

# gst: when a phase transition could be controlled by a fixed point of infinite disorder

AA << apply a real-space block renormalization group approach to study the critical properties of the random transverse-field Ising spin chain with multispin interactions. First (They) recover the known properties of the traditional model with two-spin interactions by applying the renormalization approach for arbitrary size of the block. For the model with three-spin couplings (They) calculate the critical point and demonstrate that the phase transition is controlled by an infinite disorder fixed point. (AA) have determined the typical correlation-length critical exponent, which seems to be different from that of the random transverse Ising chain with nearest-neighbor couplings. Thus this model represents a new infinite disorder universality class. >>️

Ferenc Iglói, Yu-Cheng Lin. Random quantum Ising model with three-spin couplings. arXiv:2503.18690v1 [cond-mat.dis-nn]. Mar 24, 2025.

https://arxiv.org/abs/2503.18690

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

Keywords: gst, disorder, order, transition

# gst: apropos of "Anomalous Diffusion"

<< Consider a chaotic dynamical system generating diffusionlike Brownian motion. Consider a second, nonchaotic system in which all particles localize. Let a particle experience a random combination of both systems by sampling between them in time. What type of diffusion is exhibited by this random dynamical system?  >>

Yuzuru Sato and Rainer Klages. Anomalous Diffusion in Random Dynamical Systems. Phys. Rev. Lett. 122, 174101 doi: 10.1103/PhysRevLett.122.174101 Apr 29, 2019.

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.122.174101  

# gst: the generation of waves by random point sets

<< amorphous Chern insulators can be readily constructed from arbitrary underlying structures, including hyperuniform, jammed, quasi-crystalline and uniformly random point sets >>

Noah P. Mitchell, Lisa M. Nash, et al.  Amorphous topological insulators constructed from random point sets.
Nature Physics (2018)
doi: 10.1038/s41567-017-0024-5.
Jan 15, 2018

https://www.nature.com/articles/s41567-017-0024-5

<< You don't have to be perfectly organized to pull off a wave >>

Gyroscopes lead scientists to unusual state of matter in a disorganized structure. Jan 15, 2018.

https://m.phys.org/news/2018-01-gyroscopes-scientists-unusual-state-disorganized.html  

# gst: small-scale random perturbations, Arnold's cat spontaneously stochastic

<< Multi-scale systems (..) may possess a fascinating property of spontaneous stochasticity: a small-scale initial uncertainty develops into a randomly chosen largescale state in a finite time, and this behavior is not sensitive to the nature and magnitude of uncertainty (..). >>

A << intriguing form is the Eulerian spontaneous stochasticity (ESS) of the velocity field itself: an infinitesimal small-scale noise triggers stochastic evolution of velocity field at finite scales and times. >>

AA << prove that a formally deterministic system with scaling symmetry yields a stochastic process with Markovian properties if it is regularized with a vanishing small-scale random perturbation. Besides its significance for understanding turbulence, (their) model extends the phenomenon of ESS beyond the scope of fluid dynamics: (AA) discuss a prototype of a feasible experiment for observing ESS in optics or electronics, as well as potential applications in other physical systems.>>

Alexei A. Mailybaev, Artem Raibekas. Spontaneously stochastic Arnold's cat. arXiv:2111.03666v1 [nlin.CD]. Nov 5,  2021.

https://arxiv.org/abs/2111.03666

keywords: gst, Arnold's cat, randomness, stochasticity, spontaneous stochasticity, small-scale random perturbations, noise, turbulence, chaos