# gst: from chimera states to spike avalanches and quasicriticality; the role of superdiffusive coupling.

<< ️The partial synchronization states of collective activity, as well as the spike avalanches realization in systems of interacting neurons, are extremely important distinguishing features of the neocortical circuits that have multiple empirical validations. However, at this stage, there is a limited number of studies highlighting their potential interrelationship at the level of nonlinear mathematical models. >>

<< ️In this study, (AA) investigate the development of chimera states and the emergence of spike avalanches in superdiffusive neural networks, as well as analyze the system's approach to quasicriticality. >>

<< ️The analysis of the available ideas suggests that partial synchronization states, spike avalanches, and quasicritical neuronal dynamics are all directly implicated in core cognitive functions such as information processing, attention, and memory. Given this fundamental role, the results presented in this (AA) work could have significant implications for both theoretical neuroscience and applied machine learning, particularly in the development of reservoir computing systems. >>

I. Fateev, A. Polezhaev. From chimera states to spike avalanches and quasicriticality: The role of superdiffusive coupling. Phys. Rev. E 113, 014215. Jan 20, 2026.

https://journals.aps.org/pre/abstract/10.1103/rmx5-8fys

Also: network, brain, neuro, behav, chimera, random, walk, walking, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, networks, neuronal network models, chimera, random, walk, walking, avalanches, neuronal avalanches, collective behaviors, criticality.

# gst: apropos of Parrondo paradox, controlling quantum chaos via Parrondo strategies on noisy intermediate-scale quantum hardware

<< ️Advancements in noisy intermediate-scale quantum (NISQ) computing are steadily pushing these systems toward outperforming classical supercomputers on specific well-defined computational tasks. In this work (AA) explore and control quantum chaos in NISQ systems using discrete-time quantum walks (DTQWs) on cyclic graphs. To efficiently implement quantum walks on NISQ hardware, (They) employ the quantum Fourier transform to diagonalize the conditional shift operator, optimizing circuit depth and fidelity. >>

<< ️(AA) experimentally realize the transition from quantum chaos to order via DTQW dynamics on both odd and even cyclic graphs, specifically 3- and 4-cycle graphs, using the counterintuitive Parrondo paradox strategy across three different NISQ devices. >>

<< ️While the 4-cycle graphs exhibit high-fidelity quantum evolution, the 3-cycle implementation shows significant fidelity improvement when augmented with dynamical decoupling pulses. (Their) results demonstrate a practical approach to probing and harnessing controlled chaotic dynamics on real quantum hardware, laying the groundwork for future quantum algorithms and cryptographic protocols based on quantum walks. >>

Aditi Rath, Dinesh Kumar Panda, Colin Benjamin. Controlling quantum chaos via Parrondo strategies on noisy intermediate-scale quantum hardware. Phys. Rev. E 112, 054219. Nov 18, 2025.

https://journals.aps.org/pre/abstract/10.1103/m89r-2dy5

arXiv: 2506.11225v2 [quant-ph]. Nov 4, 2025.

https://arxiv.org/abs/2506.11225

Also: parrondo, noise, walk, walking, order, chaos, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, parrondo, noise, walk, walking, quantum walk, order, chaos, quantum chaos, transition, dynamical decoupling pulses, cryptography.

# gst: universal criterion for selective outcomes under stochastic resetting

<< ️Resetting plays a pivotal role in optimizing the completion time of complex first-passage processes with single or multiple outcomes and exit possibilities. While it is well established that the coefficient of variation—a statistical dispersion defined as a ratio of the fluctuations over the mean of the first-passage time—must be larger than unity for resetting to be beneficial for any outcome averaged over all the possibilities, the same cannot be said while conditioned on a particular outcome.  >>

<< ️The purpose of (AA) article is to derive a universal condition that reveals that two statistical metrics—the mean and coefficient of variation of the conditional times—come together to determine when resetting can expedite the completion of a selective outcome, and furthermore can govern the biasing between preferential and nonpreferential outcomes. The universality of this result is demonstrated for a one-dimensional diffusion process subjected to resetting with two absorbing boundaries. >>

<< ️Processes with multiple outcomes are abundant in nature starting from gated chemical reactions, enzymatic reactions, channel facilitated transport, directed intermittent search in cellular biology such as cytoneme based morphogenesis, motor driven intracellular transport and in artificial systems such as queues, algorithms and games. Many such systems have resetting integrated to their dynamics either intrinsically or externally (..).  >>

Suvam Pal, Leonardo Dagdug, et al. Universal criterion for selective outcomes under stochastic resetting. Phys. Rev. E 112, 034116. Sep 5, 2025.

https://journals.aps.org/pre/abstract/10.1103/p3yc-kmt1

arXiv: 2502.09127v1 [cond-mat.stat-mech]. Feb 13, 2025.

https://arxiv.org/abs/2502.09127

Also: 'stochastic resetting', in https://flashontrack.blogspot.com/search?q=stochastic+resetting

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

Keywords: gst, walk, walking, random, resetting strategy,  stochastic resetting.

# gst: dynamics and frictional dissipation for treading slowly in a puddle.

<< ️The process of producing a liquid column is common in daily life and industrial applications, such as walking through a puddle and roller printing. While governed by the Navier-Stokes equation, its dynamics are often studied by numerical means, which hinders a full understanding of the rich mixture of physics behind, for instance, the competition of surface and potential energies, and how the pinch off is affected by the kinetic energy and water jet when a large cylinder is used. For pedestrians rushing out of the rain, the water column inevitably involves turbulence and defies simple theoretical analyses.  >>

<< ️As a result, this (AA) work will focus only on cases with a low Reynolds number to enable laminar flow and the existence of reversible and quasistatic stages. Combined with simple models, (They) elucidate the mechanism that drives the change of morphology and derive analytic expressions for the critical height and upper radius for the liquid column when transiting between three stages. >>

<< ️Stage I is characterized by a static and reversible profile for the column whose upper radius 𝑟𝑡 equals that of the cylinder. The column becomes irreversible and 𝑟𝑡 starts shrinking upon entering stage II. It is not until 𝑟𝑡 stops shrinking that the column neck accelerates its contraction and descends toward the pool, the quantitative behavior of which is among the successful predictions of our theory. Pinch off dominates the second half of stage III without its usual signature of self-similarity. This is discussed and explained with an interesting incident involving a water jet similar to that made by a dropping stone. >>

Chung-Hao Chen, Zong-Rou Jiang, Tzay-Ming Hong. Dynamics and frictional dissipation for treading slowly in a puddle. Phys. Rev. E 112, 025105. Aug 25, 2025.

https://journals.aps.org/pre/abstract/10.1103/7t1g-f3fz

arXiv: 2310.09737v2 [physics.flu-dyn]. May 18, 2024.

https://arxiv.org/abs/2310.09737

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

Keywords: walk, walking.

# behav: souvenir collector's walk; the distribution of the number of steps of a continuous-time random walk ending at a given position.

AA << consider a random walker performing a continuous-time random walk (CTRW) with a symmetric step lengths' distribution possessing a finite second moment and with a power-law waiting time distribution with finite or diverging first moment. The problem (They) pose concerns the distribution of the number of steps of the corresponding CTRW conditioned on the final position of the walker at some long time 𝑡. >>

<< ️For positions within the scaling domain of the probability density function (PDF) of final displacements, the distributions of the number of steps show a considerable amount of universality, and are different in the cases when the corresponding CTRW corresponds to subdiffusion and to normal diffusion. >>

They << ️moreover note that the mean value of the number of steps can be obtained independently and follows from the solution of the Poisson equation whose right-hand side depends on the PDF of displacements only. >>

<< ️This approach works not only in the scaling domain but also in the large deviation domain of the corresponding PDF, where the behavior of the mean number of steps is very sensitive to the details of the waiting time distribution beyond its power-law asymptotics. >>

Igor M. Sokolov. Souvenir collector's walk: The distribution of the number of steps of a continuous-time random walk ending at a given position. Phys. Rev. E 112, 024101. Aug 1, 2025

https://journals.aps.org/pre/abstract/10.1103/6j5n-bqcf

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

Keywords: behavior, walk, walking, random walks, randomness.

# gst: interactive anisotropic walks in 2D generated from a 3-state opinion dynamics model.

<< A system of interacting walkers is considered in a two-dimensional hypothetical space, where the dynamics of each walker are governed by the opinion states of the agents of a fully connected three-state opinion dynamics model. Such walks, studied in different models of statistical physics, are usually considered in one-dimensional virtual spaces. >>

In this article AA has performed the mapping << in such a way that the walk is directed along the 𝑌 axis while it can move either way along the 𝑋 axis. The walk shows that there are three distinct regions as the noise parameter, responsible for driving a continuous phase transition in the model, is varied. In absence of any noise, the scaling properties and the form of the distribution along either axis do not follow any conventional form. >>

<< For any finite noise below the critical point the bivariate distribution of the displacements is found to be a modified biased Gaussian function while above it, only the marginal distribution along one direction is Gaussian. The marginal probability distributions can be extracted and the scaling forms of different quantities, showing power-law behavior, are obtained. The directed nature of the walk is reflected in the marginal distributions as well as in the exponents. >>

Surajit Saha, Parongama Sen. Interactive anisotropic walks in two dimensions generated from a three-state opinion dynamics model. Phys. Rev. E 111, 064123. Jun 18, 2025.

https://journals.aps.org/pre/abstract/10.1103/5c2y-yj1z

arXiv: 2409.10413v3 [cond-mat.stat-mech]. Apr 28, 2025. 

https://arxiv.org/abs/2409.10413

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

Keywords: gst, walk, walking, random walk, randomness, noise, transitions, noise-induced transitions, criticality.

# gst: apropos of absorbing targets, persistence exponents of self-interacting random walks

<< The persistence exponent, which characterizes the long-time decay of the survival probability of stochastic processes in the presence of an absorbing target, plays a key role in quantifying the dynamics of fluctuating systems. Determining this exponent for non-Markovian processes is known to be a difficult task, and exact results remain scarce despite sustained efforts. >> 

In their Letter, AA << consider the fundamental class of self-interacting random walks (SIRWs), which display long-range memory effects that result from the interaction of the random walker at time 𝑡 with the territory already visited at earlier times 𝑡′ <𝑡. (AA)  compute exactly the persistence exponent for all physically relevant SIRWs. As a byproduct, (They) also determine the splitting probability of these processes. >>

<< Besides their intrinsic theoretical interest, these results provide a quantitative characterization of the exploration process of SIRWs, which are involved in fields as diverse as foraging theory, cell biology, and nonreversible Monte Carlo methods. >>

J. Brémont, L. Régnier, et al. Persistence Exponents of Self-Interacting Random Walks. Phys. Rev. Lett. 134, 197103. May 16, 2025.

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.134.197103

arXiv:2410.18699v1 [cond-mat.stat-mech]. 

https://arxiv.org/abs/2410.18699

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

Keywords: gst, walk, walking, self-interacting random walk, walker self-repulsion, walker self-attraction, stochasticity, absorbing targets.

# gst: influence of disorder on the spreading and entanglement properties of coined quantum walks.

AA << investigate the influence of disorder on the spreading and entanglement properties of coined quantum walks. Specifically, (AA) consider quantum walks on the line and explore the effects of quenched disorder in the coin operations. (They) find that coin disorder alters the usual ballistic transport properties of coined quantum walks considerably and yields an extremely slow dynamics with strong evidence for localization behavior. (They) investigate this slow dynamics by comparing different properties of the walker occupation probability with the standard Hadamard walk. (They) find that the walker distribution, and a number of properties associated with it, are significantly altered by the coin disorder. Special focus is given to the influence of coin disorder on entanglement properties. (AA) observe that generically, coin disorder decreases the coin-walker entanglement. The behavior of the entanglement properties further supports the premise that coin disorder induces localization in coined quantum walks. >>

Louie Hong Yao, Sascha Wald. Coined Quantum Walks on the Line: Disorder, Entanglement and Localization. arXiv: 2303.15978v1 [quant-ph]. doi: 10.48550/ arXiv.2303.15978. 28 Mar 28, 2023.

https://arxiv.org/abs/2303.15978

Also

Voli a casaccio. Notes. Oct 01, 2006. 

(quasi-stochastic poetry)

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

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

keyword 'walk' | 'walking' in FonT

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

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

keyword 'passo lieve' | 'walk' | 'walking' in Notes

(quasi-stochastic poetry)

https://inkpi.blogspot.com/search?q=passo+lieve

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

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

Keywords: gst, disorder, quantum physics, walk, walking, coined quantum walks

# behav: learning walks related to home burrow navigation (among desert grassland scorpions Paruroctonus utahensis)

<< The Navigation by Chemotextural Familiarity Hypothesis (NCFH) suggests that scorpions use their midventral pectines to gather chemical and textural information near their burrows and use this information as they subsequently return home. For NCFH to be viable, animals must somehow acquire home-directed “tastes” of the substrate, such as through path integration (PI) and/or learning walks. >>️

AA << found that once animals established their home burrows, they immediately made one to several short, looping excursions away from and back to their burrows before walking greater distances. We also observed similar excursions when animals made burrows in level sand in the middle of the arena (i.e., no mound provided). These putative learning walks, together with recently reported PI in scorpions, may provide the crucial home-directed information requisite for NCFH. >>️

Douglas D. Gaffin, Maria G. Munoz, Marielle Hoefnagels. Evidence of learning walks related to scorpion home burrow navigation. bioRxiv 2021.12.28.474378; Dec 30, 2021. 

https://www.biorxiv.org/content/10.1101/2021.12.28.474378v1

Also

keyword 'walk' | 'walking' in FonT

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

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

keyword 'passo lieve' | 'walk' | 'walking' in Notes (quasi-stochastic poetry)

https://inkpi.blogspot.com/search?q=passo+lieve

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

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

Keywords: behav, walk, walking, learning walk, NCFH

# gst: assembling colloidal spheres into rods of several lengths to walk above a pattern.

<< Detailed control over the motion of colloidal particles is relevant in many applications in colloidal science such as lab-on-a-chip devices. Here, (AA) use an external magnetic field to assemble paramagnetic colloidal spheres into colloidal rods of several lengths. The rods reside above a square magnetic pattern and are transported via modulation of the direction of the external magnetic field. >>

<< The rods behave like bipeds walking above the pattern. Depending on their length, the bipeds perform topologically distinct classes of protected walks. >>

<< Using such loops, (they) induce the collision of reactant bipeds, their polymerization addition reaction to larger bipeds, the separation of product bipeds from the educts, the sorting of different product bipeds, and also the parallel writing of a word consisting of several letters. >>

Mahla Mirzaee-Kakhki, Adrian Ernst, et al. Simultaneous polydirectional transport of colloidal bipeds. Nat Commun 11, 4670. doi: 10.1038/ s41467-020-18467-9. Sep 16, 2020.

https://www.nature.com/articles/s41467-020-18467-9

Controlled dynamics of colloidal rods. 

Bayreuth University. Sep 16, 2020. 

https://phys.org/news/2020-09-dynamics-colloidal-rods.html