# life: apropos of trick-shot artists, one shot, twenty-one balls; existence and rarity of a total clearance in a single stroke of snooker.

<< ️Snooker folklore holds that no single stroke can pocket all twenty-one object balls. (AA) examine the claim in an idealized but fully specified model of billiard dynamics. Within the model (They) exhibit an admissible configuration of the twenty-two balls and a stroke of the cue ball that pockets all twenty-one object balls, and (They) show that the set of such strokes has positive Lebesgue measure in the natural shot space: total clearances are not flukes of measure zero but open events. >>

<< ️For the regulation opening configuration (AA) conjecture the same and explain both why a simulation cannot settle the conjecture by brute force and what kind of computation could settle it in principle. Monte Carlo experiments in the same model estimate the probability P(k) that a uniformly random stroke pockets exactly k balls; the observed decay of P(k), extrapolated conditionally on the conjecture, places the probability of a total clearance from the break far beyond anything observable. The folk claim is thus right in practice and wrong in principle, and the gap between the two is exactly the distance between measure zero and unobservably small. >>

Avner Kantor. One Shot, Twenty-One Balls: Existence and Rarity of a Total Clearance in a Single Stroke of Snooker.  arXiv: 2607.12995v1 [cs.CG]. Jul 14. 2026.

https://arxiv.org/abs/2607.12995

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

Keywords: life, billiard, snooker, single stroke, games. 

# gst: stability of vortex lattices in rotating flows.

<< Vortex lattices—highly ordered arrays of vortices—are known to arise in quantum systems such as type II superconductors and Bose-Einstein condensates. More recently, similar arrangements have been reported in classical rotating fluids. However, the mechanisms governing their formation, stability, and eventual breakdown remain poorly understood. >>

<< (AA) explore the dynamical stability of vortex lattices in three-dimensional rotating flows. To that end (They) construct controlled initial conditions consisting of vortex lattices superimposed on turbulent backgrounds. (They) then characterize their evolution across different Rossby numbers and domain geometries. >>

<< By introducing an Ekman drag (AA)  are able to reach a steady state where vortex lattices persist with near constant amplitude up until spontaneous breakup of the lattice, or an equivalent of “melting,” occurs. (They) examine an ensemble of runs in order to determine the mean lifetime of the lattice as a function of the system parameters. >>

<< (AA) results reveal that the stability of the lattices is a memory-less random process whose mean lifetime depends sensitively on the system parameters that if finely tuned can lead to very long-lived lattice states. These metastable states exhibit statistical properties reminiscent of critical systems and can offer insight into long-lived vortex patterns observed in planetary atmospheres. >>

Julián Amette Estrada, Alexandros Alexakis, Marc E. Brachet, et al. Stability of vortex lattices in rotating flows. Phys. Rev. Fluids 11, 074401. Jul 10, 2026. 

https://journals.aps.org/prfluids/abstract/10.1103/k8zw-s6kj

arXiv: 2510.06374v1 [physics.flu-dyn]. Oct 7, 2025.

https://arxiv.org/abs/2510.06374

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

Keywords: gst, vortex, turbulence, randomness, vortex lattices, rotating flows, mean lifetime, spontaneous breakups, memory-less random process, metastable states, criticality.

# life: epistemic horizon minority games: when abundance reduces strategic value.

<< ️In ordinary language, abundance suggests value. In strategic systems this intuition often fails. >> 

<< ️Strategic value can fall when an option becomes visible. A route, signal, bet, or opportunity may be attractive because few agents see it; public attention can erase the advantage it reveals. >>

<< ️(AA) formalize this mechanism as an epistemic-horizon minority game (EHMG), where agents have bounded observation horizons, action-specific awareness, desire-biased utilities, and payoffs that decline with crowding, and where the object is not a fixed congestion game with omitted actions but an awareness-transition game on a finite lattice. (They) prove fixed-awareness potential-game reduction, finite monotone awareness convergence, logit mean-field uniqueness under an explicit norm condition, non-reducibility from static count-based congestion games, and sensitivity bounds for nonlinear revelation. >>

<< ️(AA) separate the target price of information from aggregate welfare loss, showing that they can coincide, diverge, or recommend opposite disclosure policies, while modeling private revelation, public common revelation, and correlated group disclosure as distinct signal structures with different equilibrium effects. Experiments regenerate awareness sweeps, public visibility shocks, horizon-desire grids, information-constrained Braess examples, disclosure optimization, minimum harmful revelation, and counterfactual baselines isolating the epistemic mechanism from ordinary full-awareness congestion. >>

<< ️Strategic trace encodings are evaluated as a controlled regime-recognition benchmark using raw trajectories, Fourier summaries, recurrence and Gramian images, image bundles, local-filter features, leakage probes, phase-scrambled controls, resolution and recurrence-threshold sweeps, spectral carriers, and IAAFT-matched null parameter-shift controls to test whether trace encodings recover strategic structure under robust nulls. >>

Faruk Alpay, Levent Sarioglu. Epistemic Horizon Minority Games: When Abundance Reduces Strategic Value. arXiv: 2607.02765v1 [cs.GT]. Jul 2, 2026.

https://arxiv.org/abs/2607.02765

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

Keywords: game, life, strategic values, epistemic-horizon minority game (EHMG), awareness-transition game, awareness sweeps, disclosure optimization, aggregate welfare loss, minimum harmful revelation, leakage probes, full-awareness congestion, recurrence-threshold sweeps, robust nulls. 

# gst: spatially heterogeneous noise restructures flocking into geometry-locked and vortex states.

<< ️Spatially heterogeneous environments continually challenge the ability of active matter to sustain coherent collective motion. Understanding how collective motion remains robust under changing environments is central to both the functioning of biological systems and the design of smart active matter. >>

<< ️Here, (AA) extend the Vicsek model to include a circular non-noisy region surrounded by a noisy environment - a configuration in which the noise difference sets up a contrast in local directional order between the two regions. (They) find that, as the surrounding noise is increased, the system passes through three distinct dynamical regimes: (i) conventional global flocking at low noise; (ii) geometry-locked motion, aligned with simulation boundaries, at intermediate noise; and (iii) vortical motion within the non-noisy region at high noise. >>

<< Extending the environment to multiple non-noisy regions, (AA) find that the geometry-locked regime can develop a directional coupling, while the vortex mode leads to antiferromagnetic order between the regions. Taken together, (Their) results demonstrate that the spatial modulation of order and disorder offers a powerful and generic strategy for steering active matter, aligning with recent experimental observations of active particles in patterned landscapes. >>

Ankush Semwal, Mahak Poonia, Pintu Patra. Spatially heterogeneous noise restructures flocking into geometry-locked and vortex states. arXiv: 2607.05870v1 [cond-mat.soft]. Jul 7, 2026.

https://arxiv.org/abs/2607.05870

Also: particle, noise, vortex, order, disorder, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, particle, noise, vortex, order, disorder, active matter, steering active matter, coherent collective motion, noisy environment, vortical motion, geometry-locked regime. 

# life: apropos of bifurcations from stable consensus to periodic multiconsensus, consensus-breaking global Hopf bifurcation in memory-based Multi-Agent Systems.

<< ️This (AA) dissertation provides the first systematic study of symmetric consensus-breaking bifurcation to periodic multiconsensus in multi-agent systems. It analyzes this for three classes of multi-agent systems based on three different types of memory, whose closed-loop dynamics equations form delay differential equations of retarded type, neutral type, and pseudoneutral type - a subclassification of retarded type equations introduced in this dissertation which bridges retarded and neutral type delay equations. >>

<< ️Equivariant twisted degree is used to analyze the symmetric global Hopf bifurcation problem in these systems, i.e. bifurcation from a stable consensus to periodic multiconsensus. This shows how the effects of memory allow self-organizing agents to move beyond mere stationary consensus. Theoretical results for the global Hopf bifurcation and symmetric classification of periodic multiconsensus solutions across all three systems are provided, and numerical results are conducted to both validate and enhance the theoretical predictions by providing stability information on the branches which is not obtainable by the degree alone. >>

<< These principles are demonstrated in three real-world applications: one involving the control of formations of UAVs (Unmanned Aerial Vehicles), allowing them to maintain their overall spatial relationships while dancing in complex selectable oscillations; and two more in networked asset markets featuring different traders with different memory-based strategies, showing how similar mechanisms can be responsible for economic cycles of bubbles and crashes. >>

<< Finally, (AA) also numerically investigate resonant double Hopf bifurcations in the neutral delay system, showing strong evidence of a breakdown to chaos via the Ruelle-Takens-Newhouse scenario and the existence of riddled basins. >>

Casey Maikalani Crane. Consensus-Breaking Global Hopf Bifurcation in Memory-Based Multi-Agent Systems. Dissertation. The University of Texas at Dallas. Aug 2026. Supervising Professor: Wieslaw Krawcewicz, Chair.  arXiv: 2607.02388v1 [math.DS]. Jul 2, 2026.

https://arxiv.org/abs/2607.02388

Also: network, swarm, bubble, crack, chaos, transition, dance, in https://www.inkgmr.net/kwrds.html 

Keywords: life, gst, networks, swarm, bubbles, crack, chaos, transitions, dance, multi-agent systems, symmetric consensus-breaking bifurcation, stable consensus, periodic multiconsensus, symmetric global Hopf bifurcation, self-organizing agents, economic cycles of bubbles and crashes, riddled basins. 

# gst: hyperuniform systems are maximally irreversible.

<< ️Hyperuniform systems, defined by the anomalous suppression of large-scale density fluctuations, are a paradigm of non-equilibrium self-assembly. While mechanisms underlying the self-assembly of hyperuniform states have been widely studied, the energetics of this process remain unexplored. This raises a fundamental question: what is the energetic cost of self-assembling a hyperuniform system? >>

<< ️Here, (AA) address this question across several noisy particle systems drawn from soft matter and machine learning, in which hyperuniformity can be induced by tuning noise correlations. Despite their distinct microscopic dynamics, (They) uncover a universal behavior across all systems: hyperuniform states are maximally irreversible, as quantified by the entropy production rate. >>

<< ️Further, (AA) develop a path integral formulation of the entropy production rate directly from the microscopic dynamics, which explains (Their) observations. (AA) work establishes a direct link between emergent long-range structure and time irreversibility and opens a new avenue of probing the energetic cost of hyperuniform self-assembly, ubiquitous across physics, biology, and materials science. >>

Mathias Casiulis, Satyam Anand, Stefano Martiniani. Hyperuniform systems are maximally irreversible.  arXiv: 2607.07411v1 [cond-mat.soft]. Jul 8, 2026.

https://arxiv.org/abs/2607.07411

Also: particle, disorder & fluctuations, self-assembly, noise, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, particles, fluctuations, self-assembly, noise, transitions, tuning noise correlations, entropy production rate, long-range structure.

# life: apropos of anomalous (meta)mechanical responses, from active to odd to smart matter.

<< ️The study of active matter has reshaped our understanding of collective states of matter far from equilibrium by proving that energy pumped into the microscopic scale leads to order on the macroscopic scale, collective motion, and anomalous mechanical responses. >>

<< More recently, the discovery of odd elasticity and nonreciprocal mechanical couplings has extended these ideas to solid-like active systems, revealing materials with nonconservative elastic response. >>

<< ️Simultaneously, innovative developments in swarm robotics, programmable metamaterials, and learning algorithms have led to the emergence of a new frontier in which collective behavior and mechanical response are no longer fixed by design, but adapted, optimized, and learned toward functional goals. >>

<< ️This perspective proposes a unifying trajectory, from active to odd to smart matter, organized along two intertwined axes: the traditional gas-liquid-solid progression of condensed matter, and the more recent paradigm shift from spontaneous collective dynamics to task-driven functionality. >> 

<< ️(AA) try to highlight emerging principles, conceptual shifts, and open challenges that come along this trajectory, and argue that learning may play the role of a specific form of emergence, which could advantageously replace the more traditional view of control, at least in the realm of physics. >>

Olivier Dauchot. From active to odd to smart matter. Phys. Rev. E 114, 011001. Jul 8, 2026.

https://journals.aps.org/pre/abstract/10.1103/tzyr-t47w

arXiv: 2607.06051v1 [cond-mat.soft]. Jul 7, 2026.

https://arxiv.org/abs/2607.06051

Also: 'a sciogliere nella metaciotola l' eccessivo rigido neurodistico ...', in: Voli in codice quasistocastico. Notes (quasistochastic poetry). Dec 09, 2004.

https://inkpi.blogspot.com/2004/12/1798-voli-in-codice-quasistocastico.html

Also: Anagrammanti neurali. Notes (quasistochastic poetry). Sep 09, 2006.

https://inkpi.blogspot.com/2006/09/2056-anagrammanti-neurali.html

Also: self-assembly, elastic, disorder, swarm, swarmalators, ai (artificial intell) (bot), brain, game, in https://www.inkgmr.net/kwrds.html 

Keywords: life, self-assembly, elasticity, disorder, swarm, swarmalators, ai,  artificial intelligence, bot, brain, games, active matter, collective states, anomalous responses, odd elasticity, nonreciprocal couplings, nonconservative elastic response, spontaneous collective dynamics, task-driven functionality, learning as a specific form of emergence, learning & adaptation without a brain.

# 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.