# gst: collective drift and pinning in active rotator networks with Kuramoto coupling and mixed-sign feedback disorder.

<< ️Active rotator models provide a minimal phase description of excitable and oscillatory systems, and have long been used to study mutual entrainment, synchronization, and collective transitions. >>

<< ️Here, (AA) investigate fully connected active rotator networks with Kuramoto coupling, where a common intrinsic drive competes with local feedback amplitudes drawn from a zero-mean Gaussian distribution. This produces a competition between local pinning and collective phase alignment. >>

<< ️Using mean absolute late-time drift and the fractions of positive and negative drifting oscillators, (They) construct numerical regime maps in the feedback-disorder-coupling plane. At weak coupling, increasing the feedback disorder strength suppresses drift, while stronger coupling can restore positive late-time drift when feedback disorder is not too strong. (They) interpret these regimes using analytical limits for the uncoupled and coherent strong-coupling cases. >>

<< ️(They) also examine finite-size effects and zero-mean distributed intrinsic frequencies. Together, these results show that mixed-sign local feedback alone can reshape the balance between pinning and drifting in coupled active rotator networks, even when the intrinsic drive is homogeneous. >>

Arpan Dey. Collective drift and pinning in active rotator networks with Kuramoto coupling and mixed-sign feedback 

disorder. arXiv: 2606.10032v1 [nlin.AO]. Jun 8, 2026.

https://arxiv.org/abs/2606.10032

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

Keywords: gst, networks, disorder, transitions, active rotator networks, excitable- oscillatory- systems, Kuramoto coupling, local feedbacks, feedback disorder.

# gst: randomised mixed labyrinth fractals.

<< ️In this (AA) paper, the class of randomised mixed labyrinth fractals is introduced. It is a class of finitely ramified Sierpinski carpets that generalize mixed labyrinth fractals. >>

<< ️The structures are generated by randomly selected labyrinth patterns with fixed selection probabilities at each iteration level, offering a flexible framework to study fractal topology, arc dimensions, and shortest path properties. Here, the focus lies on analysing how the randomised mixing of patterns - specifically their shape, symmetry, and path geometry - effects arc dimensions, path lengths, and isotropy restoration. >> 

<< ️The (AA) study reveals that isotropy, previously shown for self-similar fractals, extends to the randomised mixed class. Various scaling behaviours of shortest path dimensions with respect to the mixing probability are identified, including linear and nonlinear monotonic trends, as well as transitions with maxima. The approximated path matrix is proposed as an efficient alternative to extensive iterative simulations, reliably reproducing statistical results. >>

<< ️The findings highlight the relevance of pattern properties in determining fractal structures and dynamics and suggest applications in physical systems such as diffusion, signal processing, and antenna design. >>

Janett Prehl, Ligia Loretta Cirstea, Daniel Dick. Randomised mixed labyrinth 

fractals. arXiv: 2606.07241v1 [cond-mat.dis-nn]. Jun 5, 2026.

https://arxiv.org/abs/2606.07241

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

Keywords: gst, randomness, transitions, fractals, fractal topology, labyrinth fractals, Sierpinski carpets, randomly labyrinth patterns.

# game: apropos of “tit-for-tat” approach, the evolution of lying in a spatially-explicit prisoner's dilemma model.

<< ️(AA) present the results from a spatial model of the prisoner’s dilemma, played on a toroidal lattice. Each individual has a default strategy of either cooperating (C) or defecting (D). Two strategies were tested, including “tit-for-tat” (TFT), in which individuals play their opponent’s last play, or simply playing their default play. Each individual also has a probability of telling the truth (0 ≤ P_(truth) ≤ 1) about their last play. >>

<< ️This parameter, which can evolve over time, allows individuals to be, for instance, a defector but present as a cooperator regarding their last play. >>

<< ️This leads to interesting dynamics where mixed populations of defectors and cooperators with P_(truth) ≥ 0.75 move toward populations of truth-telling cooperators. >>

<< ️Likewise, mixed populations with P_(truth) < 0.7 become populations of lying defectors. >>

<< ️Both such populations are stable because they each have higher average scores than populations with intermediate values of P_(truth). Applications of this model are discussed with regards to both humans and animals. >> 

Gregg Hartvigsen. The Evolution of Lying in a Spatially-Explicit Prisoner's Dilemma Model. arXiv: 2602.02587v1 [physics.soc-ph]. Jan 31, 2026.

https://arxiv.org/abs/2602.02587

Also: tit-for-tat, game, in https://www.inkgmr.net/kwrds.html 

Keywords: game, tit-for-tat, prisoner's dilemma, toroidal lattice, cooperating- defecting- strategies, truth-telling cooperators, lying defectors.

# behav: decomposition of anomalous diffusion in two-state random walks.

<< ️Two-state stochastic models, where motion alternates between distinct dynamical modes, are widely observed in complex systems. Here (AA) study the Two-State Random Walk (TSRW), which switches between a continuous-time random walk (CTRW) rest state and a standard Lévy walk (LW) motion state, each with power-law distributed sojourn times. >>

<< ️Using anomalous diffusion decomposition, (They) show that TSRWs exhibit a generic coexistence of Joseph (correlation), Noah (heavy-tailed increments), and Moses (aging) effects. >>

<< ️Strikingly, although classical Lévy walks alone possess only the Joseph effect, both Noah and Moses effects emerge in TSRWs solely due to stochastic switching with the CTRW phase. >>

<< ️(Their) results demonstrate that coupling between dynamical states can fundamentally reshape the mechanisms driving anomalous diffusion, offering a minimal yet powerful framework for transport in heterogeneous and intermittently switching environments. >>

Abhijit Bera, Kevin. E. Bassler. Decomposition of Anomalous Diffusion in two-state random walks. arXiv: 2606.00149v2 [nlin.AO]. Jun 7, 2026.

https://arxiv.org/abs/2606.00149

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

Keywords: behavior, randomness, walk, walking, two-state stochastic behavior, two-state random walk, stochastic switching, Lévy walk motion, Joseph Noah Moses effects, anomalous diffusion, heterogeneous and intermittently switching environments. 

# gst: localization of active particles on random arrays of parallel filaments.

<< ️Quenched disorder in the environment can fundamentally alter transport dynamics in both active and passive systems. (AA) explore how disordered arrays of filaments govern the distribution of intermittently moving particles which switch between diffusive and processive transport. >>

<<️ Motivated by the mixed-polarity arrangements of parallel microtubules observed in mammalian dendrites, (They) show that such arrays tend to result in localization of particles at regions of convergent filament orientation. In the rapid attachment-detachment limit, the disordered system can be described by a noisy one-dimensional effective energy landscape, whose structure is approximated by a random walk. >>

<< ️The depth and width of wells on this landscape are expressed as a function of the transport kinetics and system geometry. Localization is shown to be strongest at intermediate run-lengths, where biased transport persists long enough to sense the quenched filament polarity but not so long as to facilitate escape from local traps. >>

<< ️These (AA) results demonstrate robust localization of particles moving on random filament networks, highlighting the emergent spatial organization that arises from an interplay of active transport and quenched disorder. >>

Owen Santoso, Elena Koslover. Localization of Active Particles on Random Arrays of Parallel Filaments. arXiv: 2606.00286v1 [cond-mat.dis-nn]. May 29, 2026.

https://arxiv.org/abs/2606.00286

Also: noise, disorder, disorder & fluctuations, random, intermittency, escape, particle, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, noise, disorder, disorder & fluctuations, randomness, intermittency, escape, particles, quenched disorder, transport dynamics, diffusive and processive transport, arrays of filaments, random walk, random filament networks, escape from local traps.

# gst: hierarchical crack patterns; identification of crack generations.

<< ️Hierarchical crack patterns of various origins are ubiquitous in the world around us. (AA) reduce the problem of classifying crack generations in an image of a part of the entire hierarchical crack pattern to the well-known topological sorting of a directed acyclic graph. The classification demonstrates robustness to reasonable shifts in the pattern image boundaries. >>

Yuri Yu. Tarasevich, Andrei S. Burmistrov, Andrei V. Eserkepov. Hierarchical crack patterns: Identification of crack generations. arXiv: 2606.03473v1 [cond-mat.dis-nn]. Jun 2, 2026.

https://arxiv.org/abs/2606.03473

Also: crack, fracture, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, crack, fracture, fragment of hierarchical crack pattern, topological sorting, root cracks, network 

fragment, hierarchical network structure.

# gst: percolation criticality of amorphous-amorphous transitions (in compressed glasses).

<< ️The low-to-high-density transition in compressed silica glass is investigated using percolation theory. Large-scale molecular dynamics simulations of SiO glasses, (..) were carried out (by AA) to investigate the emergence of structural motifs and their growth to system-spanning length scales under compression. >>

<< ️Taken together, these results underline the consistency between the bonded and non-bonded approaches. Native tetrahedral clusters, (..) collapse according to a process close to the random percolation model. >>

<< ️For all other percolation transitions, i.e. involving clusters with higher coordination number and connectivity, the deviation of the exponents instead suggests a different universality class. It can be argued that for these structures, the transition occurs in a medium where the percolating cluster is surrounded by an infinite cluster of lower coordination and connectivity, alongside emerging clusters with higher coordination and connectivity, resulting in topological, and hence elastic, heterogeneities. This behavior recalls topological constraint theory, also known as percolation rigidity, that arises from a flexible to a rigid network as local connectivity changes >>.

Julien Perradin, Simona Ispas, Ricardo V. Paredes, et al. Percolation Criticality of Amorphous-Amorphous Transitions in Compressed Glasses. arXiv: 2606.04748v1 [cond-mat.dis-nn]. Jun 3, 2026.

https://arxiv.org/abs/2606.04748

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

Keywords: gst, randomness, fluctuations, collapse, transitions, percolation theory, random percolation, rigidity percolation, critical percolation, bonded and non-bonded approaches, topological constraint theory, amorphous structures, crystalline polymorphs, origin of plasticity.