# gst: riding the wave; polymers in time-dependent nonequilibrium baths.

<< Directed transport is a characteristic feature of numerous biological systems in response to signals such as nutrient and chemical gradients. These signals often depend on time owing to the high complexity of interactions in these systems. >>

<< In this study, (AA) focus on the steady-state behavior of polymeric systems responding to such time-dependent signals. (They) model them as ideal Rouse polymers submerged in a nonequilibrium bath, which is described by a spatially and temporally varying self-propulsion wave field. Through a coarse-graining analysis, (They) show that these polymers display rich emergent response to the temporal stimuli as a function of their length and topology. >>

<< In particular, long polymers and structures with ring and star topologies ride the wave, displaying a positive drift in the direction of the wave, whereas shorter polymers and fully connected structures drift against the wave signal. (They) confirm these analytical predictions with robust numerical simulations, showing that the response of polymeric systems to temporal stimuli can be controlled by the topology or the length of the polymer. >>

Bhavesh Valecha, Jens-Uwe Sommer, Abhinav Sharma. Riding the wave: Polymers in time-dependent nonequilibrium baths. Phys. Rev. E 114, 015408. Jul 9, 2026.

https://journals.aps.org/pre/abstract/10.1103/9z9n-9p57

arXiv: 2603.02777v1 [cond-mat.soft]. Mar 3, 2026.

https://arxiv.org/abs/2603.02777

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

Keywords: gst, waves, polymers, topology, directed transport, steady-state behavior, self-propulsion wave field. 

# gst: dynamics of coupled stochastic van der Pol oscillators; bifurcations, synchronization and chaos.

<< ️This (AA) work presents a comprehensive analysis of coupled stochastic van der Pol oscillators, a paradigm for understanding synchronization, bifurcations, and chaos in nonlinear systems subject to random fluctuations. The system comprises two or more oscillators with nonlinear damping, linear diffusive coupling, and additive Gaussian white noise. >>

<< ️(AA) develop a unified framework that systematically connects global bifurcations, synchronization phenomena, and chaotic dynamics within a single coherent stochastic model. (They) explore the stochastic dynamics of coupled van der Pol oscillators by seamlessly blending theoretical principles with in-depth numerical simulations. This integrated approach forms a robust framework for analysis, with essential phenomena clearly depicted in the accompanying figures. (AA) then extend this framework to a comprehensive investigation of large networks, focusing on their continuum limit, emergent pattern formation, the role of noise, and the onset of collective chaos. >>

Shenglan Yuan, Xiang Zhou. Dynamics of Coupled Stochastic van der Pol Oscillators: Bifurcations, Synchronization and Chaos.  arXiv: 2606.31445v1 [nlin.CD]. Jun 30, 2026. 

https://arxiv.org/abs/2606.31445v1

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

Keywords: gst, chaos, noise, randomness, disorder, fluctuations, coupled stochastic van der Pol oscillators, synchronization, bifurcations, emergent pattern formation, collective chaos.

# gst: quadruple decomposition of boundary vorticity flux.

<< ️First introduced by Lighthill in 1963 for two-dimensional flows and later generalized by Jie-Zhi Wu to three-dimensional scenarios since 1986, the boundary vorticity flux (BVF) is the cornerstone of boundary vorticity dynamics, which quantifies the vorticity source strength on a solid boundary. Recent advances in vorticity and vortex dynamics have revealed both the rigid-rotation and spin modes of vorticity from multiple perspectives. >>

<< ️In the present study, (AA) propose a novel quadruple decomposition of the BVF on a stationary solid wall, which essentially uncovers the boundary creation rates of the elementary vorticity modes for both the tangential and wall-normal BVF components, respectively. >>

<< The proposed framework is illustrated through skin-friction and surface-pressure measurements for flow over a hill model in a low-speed wind tunnel, revealing a set of intriguing BVF patterns for the first time. These theoretical results are expected to be valuable for global surface flow diagnostics when combined with experiments, as well as for understanding the formation mechanisms of near-wall coherent structures and flow-induced noise. >>

Tao Chen, Tianshu Liu. Quadruple decomposition of boundary vorticity 

flux. arXiv: 2606.28761v1 [physics.flu-dyn]. Jun 27, 2026. 

https://arxiv.org/abs/2606.28761

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

Keywords: gst, vortex, noise, transitions, boundary vorticity dynamics, boundary vorticity flux (BVF), skin-friction, 

surface-pressure, near-wall coherent structures, flow-induced noise. 

# life: continual learning against data poisoning attacks.

<< ️Continual learning (CL), where a model is trained on a sequence of data tasks, is increasingly being adopted across key fields such as large language models and image recognition, yet it remains highly vulnerable to data poisoning that triggers learning divergence or severe excess risk. Despite these threats, a principled theoretical foundation in CL for understanding attack and defense remains lacking. >>

<< ️In this paper, (AA) develop a theoretical framework to analyze strategic attacks and defenses in regularization-based CL, a cornerstone of recent CL theory. By framing the adversary-defender interaction as an online zero-sum game, (They) first establish a fundamental performance limit: no defense succeeds when an adversary poisons a linear proportion of tasks by injecting unbounded noise or pattern shifts in regularization-based CL. >>

<< ️(AA) then analyze two possibly defensible scenarios: infrequent attacks and bounded noise per attack. For the former regime, (They) propose a task-to-task verification mechanism to detect data poisoning and reduce cumulative bias for learning convergence. For the latter regime, (They) derive a robust defense that minimizes the model's sensitivity to poisoned features, provably accelerating the convergence rate. Extensive experiments on realistic tasks further validate our theoretical results. >>

Yiting Hu, Lingjie Duan. Theory of Continual Learning Against Data Poisoning Attacks. Proceedings of the 43rd International Conference on Machine Learning, Seoul, South Korea. PMLR 306, 2026. arXiv: 2606.29841v1 [cs.LG]. Jun 29, 2026.

https://arxiv.org/abs/2606.29841

Also: ai (artificial intell) (bot), nfulaw, noise, in https://www.inkgmr.net/kwrds.html 

Keywords: artificial intelligence (AI), bot, nfulaw, war, life, machine learning (ML), continual learning (CL), large language models (LLM), image recognition, vulnerability, data poisoning, robust defense, adversarial dynamics, adversarial manipulation, adversary-defender interaction, noise, unbounded noise. 

# gst: apropos of avalanche propagations (e.g. large cascades), sandpile models on complex networks.

<< ️(AA) investigate the sandpile model on complex networks by developing a branching-process framework that explicitly incorporates dissipation during avalanche propagation. Unlike classical branching descriptions, which assume conservative transport and locally tree-like independence, the present approach introduces grain-loss effects directly into the offspring distribution, yielding generalized generating functions for dissipative avalanche dynamics. >>

<< ️In the dissipative regime, avalanche-size distributions acquire exponential cutoffs while preserving topology-dependent scaling behavior. Numerical simulations confirm the theoretical predictions on sparse random networks and reveal systematic deviations in highly structured topologies. In particular, by using Holme-Kim clustered scale-free networks, (They) show that increasing clustering continuously lowers the avalanche exponent and enhances the probability of large cascades, demonstrating that short cycles generate strong correlations that invalidate the classical independent-branch approx imation. >>

<< ️Surprisingly, trees also exhibit substantial deviations from power-law because low edge density and the abundance of leaves constrain avalanche propagation. These results show that dissipation, clustering, and sparse connectivity fundamentally reshape avalanche size distribution of the sandpile model on networks and establish quantitative limits for branching-process descriptions of avalanche dynamics. >>

Komlan Fiagbe, Jean-François de Kemmeter, Timoteo Carletti. Sandpile Models on complex networks. arXiv: 2607.02023v1 [cond-mat.stat-mech]. Jul 2, 2026.

https://arxiv.org/abs/2607.02023

Also: network, dissipation, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, network, dissipation, sandpile, branching-process framework, avalanche propagation, grain-loss effects, dissipative avalanche dynamics, sparse random networks, clustering, sparse connectivity.

# gst: sudden expansion stability thresholds modified by lateral flows.

<< ️(AA) study the flow in a symmetric three-dimensional confined sudden expansion with lateral inflow at Reynolds number below 300 and varying lateral-to-central flow rate ratio, using experiments, linear stability analysis, weakly nonlinear theory, and direct numerical simulations. >>

<< ️Three distinct flow regimes are identified. Outside an intermediate band of lateral-to-central flow rate ratio, the flow undergoes a steady symmetry-breaking bifurcation above a critical Reynolds number, deflecting the central jet toward one side wall; weakly nonlinear analysis shows this bifurcation to be supercritical, excepting a very narrow parametric range. Within the intermediate band, no such critical Reynolds number exists and direct numerical simulations confirm that residual velocity asymmetries reflect the imposed geometric imperfections rather than intrinsic amplification. Fluctuations observed experimentally in the intermediate band of lateral-to-central flow rate ratio remain unexplained and warrant further investigation. >>

T. Salamon, R. Debuysschère, A. Chafaï, et al. Sudden expansion stability thresholds modified by lateral flows. arXiv: 2606.30269v1 [physics.flu-dyn]. Jun 29, 2026.

https://arxiv.org/abs/2606.30269

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

Keywords: gst, particles, instability, transitions, fluctuations, criticality, bifurcations, supercritical bifurcations, geometrical defects.

# gst: delay coordinates synchronization and induces abrupt transition in excitable networks.

<< ️Neuronal communication is inherently time-delayed, due to the finite speed of signal propagation. Although often considered challenging or disruptive, such time delays can also endow neural circuits with useful capabilities. Here, (AA) show that delays in excitatory connections between excitable neurons coordinate their synchronization patterns by creating self-sustained oscillations that may be out-of-phase or in-phase. The emergence of these oscillations leads to an abrupt, explosive, transition to in-phase synchronized regimes due to small changes in connection strength or time-delay. >>

<< ️(They) describe the mechanism underlying these phenomena as an interaction between the neuron's excitable dynamics and the delay in signal transmission, explaining many aspects of how the oscillations emerge. (They) show this phenomenon in different network connectivities, neuronal models, with and without excitation, with and without noise, highlighting the generality of the mechanism. >>

Bruno R.R. Boaretto, Kalel L. Rossi, Lyle E. Muller, et al. Delay coordinates synchronization and induces abrupt transition in excitable networks. arXiv: 2606.21703v1 [q-bio.NC]. Jun 19, 2026.

https://arxiv.org/abs/2606.21703

Also: network, brain, pause, noise, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, networks, brain, pause, noise, transitions, neuronal communication, time delay, synchronization patterns, self-sustained oscillations.

# brain: apropos of persistent exploratory predisposition, chaotic pigeons are helping redefine what we know about learning.

<< ️Pigeons seem to defy a century-old psychology law about how rewards and consequences help us learn. >>

<< ️New research suggests the birds themselves avoid stability in their decision-making, instead choosing to live “at the edge of chaos.” As model species for learning and behavior, these birds are helping researchers test a century-old law about how humans and other creatures learn. >>

<< ️When learning something new, people and animals alike tend to repeat behaviors that are rewarded. First proposed by Edward Thorndike in 1898, this principle is so well established in psychology that it's become known as the law of effect. But the law implies that beyond making a behavior more frequent, rewards also make it more consistent: reducing variability in the specific way behaviors are performed over time. >>

<< ️Edward A. Wasserman and his colleagues decided to put it to the test in pigeons—a species that has been integral to the study of learning at the university’s Comparative Cognition Laboratory for more than 50 years. And the study’s results, published in the Journal of Experimental Psychology: Animal Learning and Cognition, suggest these birds experience variability as the spice of life. >>

<< ️You could argue the birds are just utterly resistant to locking into anything stable. >> Edward A. Wasserman.

<< ️this paper leaves open many questions about the [neurological] mechanisms for future scientists to explore. >> Aaron Blaisdell.

K. R. Callaway, Sarah Lewin Frasier. Chaotic pigeons are helping redefine what we know about learning. SciAm. Jun 30, 2026. 

https://www.scientificamerican.com/article/chaotic-pigeons-are-helping-redefine-what-we-know-about-learning

Wasserman E.A., Orr O.R.P., Li S. Variability, stability, and the law of effect. J. of Exp. Psychol: Animal Learning and Cognition, 52(3), 129–138. Jul 2026. 

https://psycnet.apa.org/record/2027-47688-001

Also: brain, neuro, behav, curiosity, game, Nomads, in https://www.inkgmr.net/kwrds.html 

Keywords: brain, behavior, curiosity, games, Nomads.

# aibot: critical percolation as a synthetic data model for interpretability.

<< ️Neural networks learn features that reflect the hierarchical, multi-scale structure of natural data. Synthetic datasets used to evaluate interpretability methods typically lack this structure, limiting their value as realistic toy models. >>

<< ️To close this gap, (AA) introduce a family of synthetic datasets consisting of hierarchical functions defined on critical mean-field percolation clusters embedded in a high-dimensional data space. The percolation data consists of sparse, low-dimensional fractal clusters with a power-law size distribution. Latent variables modeling a taxonomic hierarchy generate each data point's target value. >>

<< The data model is analytically tractable with known critical exponents that fix its properties without requiring hyperparameter tuning. (They) leverage a mapping between percolation clusters, random trees, and additive coalescence to propose an almost linear-time algorithm to jointly sample a random tree and its hierarchical latent decomposition, enabling data generation at arbitrary scale. >>

<< ️Using probing experiments, (AA) find that the model's ground-truth latent variables can be linearly decoded from neural network activations. Together, sparsity, self-similarity, power-law statistics, and analytical tractability make critical percolation a principled testbed for interpretability research. >>

Aryeh Brill, Tom Ingebretsen Carlson. Critical Percolation as a Synthetic Data Model for Interpretability. arXiv: 2606.20347v1 [cs.LG]. Jun 18, 2026.

https://arxiv.org/abs/2606.20347

Also: ai, artificial intell, bot, network, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, ai, artificial intell, bot, networks, neural networks, percolation, criticality, critical percolation, critical mean-field percolation clusters, interpretability research, random trees, fractals, hierarchical latent decomposition, sparsity, self-similarity, power-law statistics.

# gst: localization pattern of a mobile impurity in the disordered Kitaev chain.

<< (AA) study a mobile impurity coupled to a Kitaev chain with chemical-potential disorder and ask whether the impurity behavior distinguishes different regimes of the host system. Exact diagonalization calculations for small periodic chains shows that in the deep topological regime the impurity localizes only partially, with a smooth increase of IPR_d, whereas in the deep trivial regime it undergoes a much sharp transition to nearly single-site localization. >>

<< For open chains at strong interaction, DMRG shows edge-localized impurity density near the Kitaev sweet spot. With increasing chemical potential, the impurity weight spreads into the bulk and eventually becomes almost uniform. (They) explain the edge preference analytically from the Majorana-dimer structure: a bulk impurity rearranges two neighboring dimers, while an edge impurity affects only one. >>

<< Disorder competes with this clean edge bias and can pin the impurity in the bulk. Thus, the impurity is sensitive to the regime of the host system, although (AA) do not find a strict one-to-one correspondence between the impurity localization pattern and the host topology. Instead, the disorder-averaged behavior suggests only an indirect correlation between impurity localization and the underlying phase of the chain. >>

A.V. Sadovnikov, A.N. Rubtsov. 

Localization pattern of a mobile impurity in the disordered Kitaev chain. arXiv: 2606.21499v1 [cond-mat.str-el]. Jun 19, 2026.

https://arxiv.org/abs/2606.21499

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

Keywords: gst, disorder, disorder & fluctuations, mobile impurity, bulk impurity, edge impurity, deep topological regime, deep trivial regime. 

# gst: uncertainty growth in stably stratified turbulence.

<< ️(AA) investigate uncertainty growth and chaotic dynamics in statistically steady, stably stratified three-dimensional turbulence. Using direct numerical simulations of the Boussinesq equations, (They) quantify the divergence of initially infinitesimal perturbations via twin simulations and decorrelator diagnostics. >>

<< ️At short times, perturbations exhibit exponential growth, allowing us to define a (largest) Lyapunov exponent. (AA) systematically examine how this exponent depends on stratification strength, quantified by the Brunt-Väisälä frequency and the Froude number, in a parameter regime relevant to oceanic flows. >>

<< (They) find that increasing stratification leads to a monotonic reduction of the Lyapunov exponent, indicating suppressed chaoticity. Despite this reduction, uncertainty growth retains the universal temporal sequence observed in homogeneous isotropic turbulence—initial decay, exponential growth, and saturation. The growth phase is characterized by self-similar decorrelator spectra, but exhibits strong anisotropy: uncertainty spreads much more slowly along the stratification direction than horizontally, with the disparity increasing with stratification strength. >>

<< ️An analysis of the decorrelator evolution equation reveals that the suppression of chaos arises primarily from strain-mediated alignment dynamics rather than direct buoyancy coupling. (AA) results provide a quantitative characterization of predictability and uncertainty growth in stratified turbulence and highlight the utility of decorrelator-based methods for anisotropic geophysical flows. >>

Mrinal Jyoti Powdel, Samriddhi Sankar Ray. Uncertainty growth in stably stratified turbulence. Phys. Rev. Fluids 11, 064615. Jun 23, 2026. 

https://journals.aps.org/prfluids/abstract/10.1103/xblr-vpl3

arXiv: 2512.05656v1 [physics.flu-dyn].

https://arxiv.org/abs/2512.05656

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

Keywords: gst, chaos, turbulence, transitions, uncertainty growth, three-dimensional turbulence, stratified turbulence, infinitesimal perturbations, stratification strength, anisotropy. 

# gst: oscillating concentrations suppress condensate coarsening.

<< ️Living cells utilize condensates to spatially concentrate molecules in response to dynamic signals. For instance, nuclear condensates respond to oscillations in transcription factor levels in the nucleoplasm, including those involved in repairing multiple DNA breaks. >>

<< ️To understand how oscillating signals affect condensates, (AA) analyze a theoretical model using numerical simulations and analytical theory. While passive dynamics would drive all molecules into a single condensate, (They) find that sufficiently fast oscillations stabilize multiple droplets, allowing control of their sizes. (They) thus reveal a new behavior of chemically active droplets, which could be exploited in synthetic applications. >>

Mathias S. Heltberg, Lukas H. Kristensen, Mogens H. Jensen, David Zwicker. Oscillating concentrations suppress condensate coarsening. arXiv: 2606.16614v1 [physics.bio-ph]. Jun 15, 2026.

https://arxiv.org/abs/2606.16614

Also: drop, droplet, droploid, self-assembly, disorder & fluctuations, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, drop, droplet, droploid, self-assembly, disorder & fluctuations, chemically active droplets, spatially concentration, nuclear condensate. 

# gst: chiral packings in cylinders are ultrasensitive to confinement deformation.

<< ️Sphere packings in circular cylinders have attracted substantial research interest, among which the discovery of chiral helical structures is the most iconic. However, recent experimental results on zebrafish do not match the known packing structures in circular cylinders. >>

<< ️To account for the inherent imperfections of biological tubes, (AA) take elliptic cylinders as the canonical deformation of circular cylinders and investigate the densest packings of hard spheres in them using simulation, theory, and experiments. Starting from the chiral structures in circular cylinders, (They) demonstrate that even a weak cross-sectional deformation can trigger entirely new phases, including ones that either eliminate global chirality or significantly complicate the chiral structures. ️This reveals the significant effect of cylindrical anisotropy. >>

<< ️The new helical phases under anisotropic confinement remain chiral and develop hierarchical periodic structures, which are difficult to obtain by simulations but are predicted by our newly developed theory for helical phases in elliptic cylinders. >> 

<< ️The theory also predicts double oscillated-chain phases without chirality, which perfectly match the simulations. (Their) work offers fresh insights into understanding packings in anisotropic cylinders, which will help researchers to design new materials and to understand many living systems. >>

Xuebin Wang, Jiahao Guo, Yao Li. Chiral Packings in Cylinders are Ultrasensitive to Confinement Deformation. arXiv: 2606.19082v1 [cond-mat.soft]. Jun 17, 2026.

https://arxiv.org/abs/2606.19082

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

Keywords: gst, chirality, transitions, packings, chiral helical structures, elliptic cylinders, cylindrical anisotropy, double oscillated-chain phases. 

# gst: rotation sets and topological entropy for random circle endomorphisms.

<< ️(AA) study the topological dynamics of random circle endomorphisms of degree one over an ergodic measure-preserving dynamical system. Under an integrability assumption, (They) prove that the random rotation set is almost surely the compact interval whose endpoints are the mean random rotation numbers of the associated lower and upper random maps. (They) also show that the natural orbitwise versions of the random rotation set agree almost surely, and on the same full-measure set, every value in this interval is realised as the asymptotic average displacement along an individual orbit. >>

<< ️In addition, every closed subinterval of the random rotation set is realised, on a full-measure set, as the set of accumulation values of the displacement averages along a single orbit. ️Finally, (AA) prove that a positive length of the random rotation set implies a positive random topological entropy, in contrast to random monotone maps, which have zero random topological entropy. (They) illustrate the theory by computing the random rotation set and random topological entropy for a piecewise linear example. >>

Zixu Li, Simon Lloyd, Sergio Romaña. Rotation Sets and Topological Entropy for Random Circle Endomorphisms. arXiv: 2606.16498v1 [math.DS]. Jun 15, 2026.

https://arxiv.org/abs/2606.16498

Keywords: gst, randomness, random rotations, entropy.

# gst: on the geometry of spreading puddles.

<< ️(AA) develop a geometric model for the spreading of shallow, viscous puddles of arbitrary shape, building on the recent 'capillary current' model for axisymmetric droplets. In short, (They) assume that a spreading puddle remains close to instantaneous mechanical equilibrium as it spreads, with hydrostatic pressure balanced by surface curvature. In turn, its contact line advances so as to maximize the rate of energy loss subject to viscous dissipation. >>

<< ️The resulting system yields a natural geometric evolution equation for both the two-dimensional footprint and the three-dimensional depth profile of a spreading puddle. In appropriate limits, it recovers the classical spreading laws for axisymmetric droplets, a local version of the Hoffman-Voinov-Tanner law for small non-axisymmetric puddles, and a nonlocal Hele-Shaw-like description for large, relatively regular puddles. >>

David Darrow. On the Geometry of Spreading Puddles. arXiv: 2606.13893v1 [physics.flu-dyn]. Jun 11, 2026.

https://arxiv.org/abs/2606.13893

Also: drop, droplet, droploid, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, drops, droplets, droploids, spreading puddle, axisymmetric droplets, surface curvature, viscous dissipation.

# gst: dissipation-coherence tradeoff for stochastic oscillations.

<< ️Autonomous noisy oscillations in biochemical and mesoscopic systems require nonequilibrium driving and therefore dissipation. A striking conjecture by Oberreiter, Barato, and Seifert (OBS) proposes a universal lower bound on the entropy produced per oscillation period in terms of the coherence number of the slowest oscillatory mode (L. Oberreiter et al. [Phys. Rev. E 106, 014106 (2022)]). >>

<< ️Here (AA) derive a weaker but rigorous lower bound that preserves the OBS structure while introducing a mode-uniformity factor that quantifies how evenly the oscillatory eigenmode is distributed across states in the steady-state inner product. The result makes explicit that an eigenvalue-only prefactor can fail when the dominant oscillatory mode is localized. >>

<< ️(They) also outline a proof-of-principle route for estimating this factor from low-dimensional data under single-mode dominance and sufficiently informative measurements, and derive an eigenvector-free corollary using only the smallest stationary probability. >>

<< ️Translation-invariant Markov jump processes on a ring provide a symmetry-protected class with 𝜂=1, so the refinement reduces to the OBS form; the drift-diffusion limit on a circle saturates the bound. >>

Jie Gu. Dissipation-coherence tradeoff for stochastic oscillations. Phys. Rev. E 113, 064130.  Jun 15, 2026.

https://journals.aps.org/pre/abstract/10.1103/zxw1-zdb7

arXiv: 2606.05498v1 [cond-mat.stat-mech]. Jun 3, 2026.

https://arxiv.org/abs/2606.05498

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

Keywords: gst, noise, disorder, dissipation, entropy, stochasticity, stochastic processes, autonomous noisy oscillations, stochastic oscillations, disorder-induced localization, time series analysis, transitions.

# life: apropos of singular, bizarre, un.expected convergences, here an asymptotic, extreme, double 'quasistochastic tit-for-tat' exploit (within the same time window).

(A1)

<< “There were no moments of friction or disagreement,” Italian Prime Minister Giorgia Meloni said at a press conference Wednesday. “I found that, overall, there was a desire to work together, and that’s not something to be taken for granted.” >>. 

Myah Ward, Clea Caulcutt, Giorgio Leali. Trump clears low bar for G7 summit in France. Jun 17, 2026.

https://www.politico.com/news/2026/06/17/trump-and-allies-keep-the-peace-at-the-g7-summit-after-months-of-tumult-00966117

(A2)

<< However, Trump has since given a phone interview with Italy's La7 TV channel in which he alleged: "She begged me to take a photo with her; I felt sorry for her." >>. 

Paul Kirby, Europe digital editor, Davide Ghiglione, Rome, James Landale, Diplomatic correspondent. Italy's Meloni says Trump 'made up' story that she 'begged' him for photo at G7. BBC. Jun 19, 2026. 

https://www.bbc.com/news/articles/c20y1ygn707o

(B) 

<< Donald Trump arrived in France yesterday for this morning’s G7

summit and promptly confirmed America’s capitulation to Iran. >>

Tom Nichols. Trump Does Not Understand the War He Lost. The Atlantic Daily. Jun 16, 2026.

https://www.theatlantic.com/newsletters/2026/06/trump-g7-comments-misunderstsand-middle-east/687569/

(A&B)

<< qui i due estremi: era modicamente non cooperatore e ha ricevuto come reazione una "bastonata"; era assolutamente ostile e ha ricevuto la classica "pacca sulla spalla" ... >>

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 

FonT

Ultimately, here too one could hypothesize another case of historic, singular checkmate of 'one against all'. Anzicheforse?

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

Also: here's another checkmate (FonT. Dec 4, 2024)

https://flashontrack.blogspot.com/2024/12/life-apropos-of-saliva-healers-herd.html 

Keywords: Mr. Donald, tit-for-tat, game, dance 

# gst: on maximal delay of stability loss for dynamical bifurcations.

<< ️(AA) consider a dynamical bifurcation caused by a slow passage through a static bifurcation point: in a system depending on a parameter, the parameter changes slowly in time and passes through the critical value corresponding to the loss of stability of an equilibrium via a Poincaré--Andronov--Hopf bifurcation in the frozen system. >>

<< ️If the system is analytic, then the loss of stability is inevitably delayed: phase points attracted to the equilibrium in the stability region remain near the equilibrium for a long time after entering the instability region, so that the parameter changes by an amount of order ~1 independently of how slow the variation of the parameter is. Remarkably, there exists a maximal delay: all phase points attracted to the stable equilibrium before a certain threshold value of the parameter leave a neighbourhood of the unstable equilibrium almost simultaneously near another threshold value of the parameter, known as a buffer point. >>

<< ️A delay of stability loss beyond the buffer point is impossible unless the initial data have a very special form. (AA) assume that, although the equilibrium is non-degenerate for real values of the parameter, one of its eigenvalues vanishes generically for some complex value of the parameter (a complex analogue of a saddle-node bifurcation), and that this complex singularity is, in a suitable sense, the closest one to the real Poincaré--Andronov--Hopf bifurcation point. >>

<< ️(AA) show that the value of maximal delay is determined by this complex singularity: the threshold values defining the maximal delay are the intersection points of the Stokes lines associated with this singularity and the real axis. (They) study these phenomena in the framework of slow--fast dynamical systems. >>

Anatoly Neishtadt. On Maximal Delay of Stability Loss for Dynamical 

Bifurcations. arXiv: 2606.07662v1 [math.DS]. Jun 3, 2026.

https://arxiv.org/abs/2606.07662

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

Keywords: gst, instability, transitions, dynamical bifurcation, bifurcation point, loss of stability, delay, maximal delay, buffer point, saddle-node bifurcation, complex singularity, slow--fast dynamical systems.

# aibot: parasitic masquerade; societal scale human-machine interaction.

<< This (AA) work extends recent developments in studying human--machine interaction by scaling from individual game-theoretic models to a societal-level model. (They) adopt a Graphon Mean-Field Game (GMFG) that models the interaction among four groups of internally-homogeneous but externally-heterogeneous agents in a shared environment. >>

<< (AA) results show that parasitism can masquerade as productive learning, with knowledge distribution and actions appearing healthy while being driven by machine coupling rather than independent investigation. To detect this, (They) measure the direction of information flow and belief entropy of the environment, revealing that human to machine channel dominates across all scenarios, with the asymmetry intensifying under parasitism. >>

<< (They) further demonstrate that the system exhibits coexisting mutualistic and parasitic equilibria, where environmental noise can induce a tipping point that shifts agents past the cognitive cost barrier. These emergent phenomena are not designed into any individual agent but arise from the collective interaction structure, underscoring the need to study the sociology of humans and machines holistically as a complex system. >>

Jiejun Hu-Bolz, James Stovold. Parasitic Masquerade: Societal Scale Human-Machine Interaction. arXiv: 2606.17925v1 [cs.GT]. Jun 16, 2026.

https://arxiv.org/abs/2606.17925

Also: ai, bot, artificial intelligence, analogy, noise, in https://www.inkgmr.net/kwrds.html

Keywords: ai, aibot, artificial intelligence, human--machine interaction, Graphon Mean-Field Game (GMFG), parasitism, masking, masquerade as productive learning, mutualistic and parasitic equilibria, environmental noise, sociology of humans and machines.

# 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.