# life: apropos of birth-and-death processes, framework for fluctuating times and counting observables in stochastic excursions.

<< ️Many natural systems exhibit dynamics characterized by alternating phases or recurring sets of states. Describing the fluctuations of such systems over stochastic trajectories is necessary across diverse fields, from biological motors to quantum thermal machines. >>

<< ️In an accompanying Letter, (AA) introduced the notion of stochastic excursions−a framework to analyze out of equilibrium processes via sub-trajectories. Through counting observables, this framework captures finite-time fluctuations and trajectory-level behavior, which provides insights into thermodynamical trade-offs between thermodynamic quantities of interest, such as entropy production and dynamical activity. >>

<< ️In this work, (AA) enhance this formalism by providing a suite of technical results on how to efficiently compute excursion-related quantities. (Their) analytical results provide explicit formulas for general moments of counting variables and excursion duration, as well as their covariance and conditional moments. (They) show that excursion statistics recover full counting statistics results, and uncover a relation between fluctuations of counting observables at single-excursion level and the steady state diffusion coefficient (noise). >> 

<< ️(AA) also discuss a fluctuation theorem for individual excursions and show that it implies a modified thermodynamic uncertainty relation at the excursion level. In addition, (They) explore how analyzing excursions and using the results developed here can yield insights into three problems of interest: the three-qubit absorption refrigerator, cellular sensing, and birth-and-death processes. >>

Guilherme Fiusa, Pedro E. Harunari, Abhaya S. Hegde, et al. Framework for fluctuating times and counting observables in stochastic excursions.

Phys. Rev. E 114, 024129. Aug 13, 2026.

https://journals.aps.org/pre/abstract/10.1103/jydr-1853

arXiv: 2506.05160v3 [cond-mat.stat-mech]. Aug 19, 2026.

https://arxiv.org/abs/2506.05160

Also: Guilherme Fiusa, Pedro E. Harunari, Abhaya S. Hegde, et al. Counting observables in stochastic excursions. Phys. Rev. E 114, L022102 (2026). 

https://journals.aps.org/pre/abstract/10.1103/1blp-2b27

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

Keywords: walk, walking, noise, uncertainty, behavior, fluctuations, randomness, stochasticity, stochastic excursions, Nomads. 

# gst: apropos of stretching during transitions, singularities in soft matter systems.

<< ️When a liquid thread pinches off, its neck thins as it separates into two unconnected regions. Using continuum mechanics, we can predict that the neck reaches zero radius in finite time while its curvature grows without bound. Together, the vanishing neck and diverging curvature form a finite-time singularity. >>

<< ️However, a real fluid does not realise these mathematical limits as molecular or material physics takes over once the neck becomes sufficiently small. Similar singularities arise throughout soft matter whenever a smooth continuum description is used at vanishing length scales. >>

<< ️This (AA) review asks what the shrinking region forgets, what it retains, and which material length, time, or stress cuts off the apparent divergence. The dynamics near a singularity often become self-similar, with profiles at different times collapsing onto one shape when rescaled by the shrinking local length. Sometimes that collapse is universal enough that the surrounding geometry and forcing no longer determine the local dynamics. Nonetheless, the measured output could still depend on how the shrinking region is fed by the surrounding flow and on the small-scale physics that finally replaces the ideal divergence. >>

<< ️Complex fluids and active matter change the same local balance by bringing their own timescales into the shrinking region. Beyond interfaces, the same logic applies when the localised object is a stress concentration or a defect in geometry or order rather than a moving surface. Singularities matter because they show where continuum theory stops being the relevant description and how the small-scale cutoff sets the outputs that count in printing, coating, aerosols, and stretchable solids. >>

Vatsal Sanjay. Singularities in Soft Matter Systems. arXiv: 2608.11060v1 [cond-mat.soft]. Aug 11, 2026.

https://arxiv.org/abs/2608.11060

Also: elastic, singularity, transition, collapse, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, elasticity, singularity, transitions, collapse, soft matter

# gst: stabilities in the attachment of a particle to a pendant droplet.

<< ️Attachment of a particle to a pendant drop was experimentally investigated by Feng et al. (2022)]. The attachment force on the particle, consisting of the surface tension force and the pressure force, can overcome the gravity force. The attachment in equilibrium is possibly hard to maintain in practice due to instabilities. >>

<< This (AA) paper aims to discover the condition for the particle to be successfully attached under the liquid drop (bridge) through analyzing the stabilities of the capillary system. With disturbances potentially existing for both the liquid bridge and the particle, the two corresponding types of stabilities are studied. >>

<< Considering the cases with liquid surfaces checked to be stable, (AA) find four regimes for the attachment of the particle: the regimes of stable attachment, possibly stable attachment, overloaded attachment, and nonphysical attachment. Only the first two regimes mean feasible attachments in practice. (Their) prediction of feasible attachments agrees well with Feng et al., indicating the validity of (Their) stability theory. Whether for fixed-density particles of different sizes or fixed-size particles of different densities, the attachment capability for the liquid bridge first decreases, then increases, and decreases again as the volume of the liquid bridge increases. This can guide practice for lifting particles of higher weight with the pendant drop. >>

Wanqiu Zhang, Fei Zhang, Xinping Zhou. Stabilities in the attachment of a particle to a pendant droplet. Phys. Rev. Fluids 11, 084001. Aug 7, 2026.

https://journals.aps.org/prfluids/abstract/10.1103/b63k-qk8s

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

Keywords: gst, drops, droplets, droploids, particles, stability, fluid-particle interactions, interfacial flows, liquid bridges, surface & interfacial phenomena.

# gst: escape over a saddle by colored noise.

<< ️Stochastic dynamical systems allow modeling of transitions induced by random disturbances, in particular from an attracting equilibrium and crossing the stable manifold of a saddle. While the small-noise limit is well-described by the large deviation principle, existing computational methods often struggle with stochastic forcings any more complicated than nondegenerate Gaussian white noise, and with unbounded time intervals. >>

<< ️The primary innovations of this (AA) work are extending the framework to cater for colored and degenerate forcing and unbounded time horizons—scenarios that are physically realistic but numerically challenging. (They) cater for degenerate noise by using the Hamiltonian optimal control method. (They) cater for a class of colored noises by using linear filters on white noise. (They) cater for infinite time horizon by introducing the method of division (MOD), a computational approach for approximating rare transition events, including their most likely paths and the exponential scaling laws of their transition rates. >>

<< ️The effectiveness of MOD and the above approaches to colored noise, is demonstrated by illustration on two examples: an inverted double-well potential and a simplified roll-heave model for ship capsize. >>

Jiayao Shao (邵家瑶), Tobias Grafke, Robert S. MacKay. Escape over a saddle by colored noise: Theory and numerics. Phys. Rev. E 114, 024210. Aug 12, 2026.

https://journals.aps.org/pre/abstract/10.1103/w8dd-9cqg

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

Keywords: gst, escape, noise, randomness, stochasticity, transitions, noise-induced transitions, method of division (MOD), inverted double-well potential, simplified roll-heave model, large deviation & rare event statistics.

gst: nonreciprocal dynamics with weak noise: aperiodic “Escher cycles” and their quasipotential landscape.

<< ️(AA) present an explicit construction of the Freidlin-Wentzell quasipotential of a stochastic system with two degrees of freedom and nonreciprocal interactions. This model undergoes noise-induced transitions between four metastable attractors, forming recurrent but aperiodic “Escher cycles,” similar to the cyclic nucleation dynamics observed in the nonreciprocal Ising model. >>

<< (AA) calculate the quasipotential analytically to first order in nonreciprocality. (They) characterize it along a one-dimensional reaction coordinate that connects the attractors, and (They) also obtain the full two-dimensional landscape, at leading order in perturbation theory. >>

<< ️The resulting landscapes feature flat regions and extended plateaus, together with nondifferentiable switching lines. These singular structures arise from two geometric mechanisms: the handover of dominance between competing transition paths, and the competition between basins of attraction. The system provides a rare case where the geometry of nonequilibrium rare events can be fully resolved, and a simple analytically tractable example of a quasipotential in more than one coordinate that captures a rich set of nonequilibrium features. >>

Janik Schüttler, Robert L. Jack, Michael E. Cates. Nonreciprocal dynamics with weak noise: Aperiodic “Escher cycles” and their quasipotential landscape. Phys. Rev. E 114, 024104. Aug 3, 2026.

https://journals.aps.org/pre/abstract/10.1103/slp9-rd27

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

Keywords: gst, noise, randomness, stochasticity, transitions, singularity, nonreciprocal interactions, noise-induced transitions, metastable attractors, Escher cycles, perturbation theory, escape problems, large deviation & rare event statistics. 

# gst: apropos of persistence or extinction, lag-induced critical transitions to extinction in replicating systems; the 𝜏-tipping mechanism.

<< Replicating systems sustained by error-prone enzymatic amplification can undergo critical transitions between persistence and extinction. In RNA viruses, such transitions are classically governed by mutation rates and fitness landscape topographies, giving rise to error thresholds and lethal mutagenesis. >>

<< Motivated by experimental evidence that polymerase-targeting antivirals limit replication, (AA) analyze replicating systems with explicit time lags in replication-enzyme availability by means of delay differential equations. (Their) approach is not equivalent to a simple renormalization of the rate of replication, since explicit delays introduce memory and temporal nonlocality into the dynamics. (They)  identify a lag-induced critical transition driven by the loss of temporal coordination between genome expression and replication. >>

<< At fixed mutation and replication rates ensuring persistence, populations cross an extinction threshold solely due to replication delays. In (Their) delay-extended quasispecies model, the timing of replicase availability emerges as an independent dynamical control parameter, defining a route to extinction that is fundamentally distinct from transitions driven by mutation rates or replicative fitness. >>

<< These (AA) results further suggest that perturbing the temporal coordination of viral replication may provide an alternative antiviral strategy for driving viral populations toward collapse. More generally, (They) propose that the extinction mechanism described here constitutes a form of lag-time-induced tipping, which (They) denote as 𝜏-tipping. >>

Edward A. Turner, Francisco Crespo, Joan Gimeno, et al. Lag-induced critical transitions to extinction in replicating systems: the 𝜏-tipping mechanism. Phys. Rev. E 114, 024401. Aug 5, 2026.

https://journals.aps.org/pre/abstract/10.1103/gyd9-ctnc

arXiv: 2603.02036v1 [q-bio.PE]. Mar 2, 2026. 

https://arxiv.org/abs/2603.02036

Also: transition, pause, silence, virus, collapse, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, transitions, pause, silence, virus, error, collapse, genomes, RNA virus, replication, replicating systems, enzymatic amplification, criticality, persistence, extinction, mutation rates, fitness landscape topographies, error threshold, time-delay systems, lag-time-induced tipping, lag-induced critical transition, loss of temporal coordination.

# behav: noise-induced stability of insect swarms.

<< ️Flying insect swarms exhibit cohesion without the local velocity alignment observed in flocks of birds or schools of fish. The interaction rules and channels of communication between insects that lead to collective behavior have not yet been determined. >>

<< ️(AA) propose a theoretical model based on acoustic communication between swarm members, where each individual is attracted to a weighted mean field of its neighbors. (They) demonstrate that this simple framework can describe a wide range of swarming dynamics, including a phenomenon where pairs of insects break free from the swarm in a helical orbit around each other. >>

<< ️Counterintuitively, (Their) numerical model suggests that stochastic noise enhances the stability of an insect swarm, as it interferes with pair formation. >>

<< Finally, (AA) demonstrate that a specific species of malarial mosquito produces swarms that reside on the edge of a transition to instability. (Their) study shows that fairly simple local interaction rules can be sufficient to describe the collective behavior of swarming biological systems. >>

Justin Faber, Annabelle Boots, Dolores Bozovic. Noise-induced stability of insect swarms. arXiv: 2608.00314v2 [physics.bio-ph]. Aug 7, 2026.

https://arxiv.org/abs/2608.00314

Also: swarm, behavior, noise, instability, transition, sound, jazz, dance, in https://www.inkgmr.net/kwrds.html 

Keywords: behavior, swarm, noise, instability, transitions, sound, jazz, dance, flying insects, collective behavior, acoustic communication, weighted mean field of neighbors.

# gst: survival probability of particles inside the lemon billiard.

<< ️(AA) study the escape of particles in the lemon billiard, a two-parameter family of billiard systems defined by the intersection of two identical circles. Using numerical simulations, (They) explore how the survival probability depends on the position and size of the hole, as well as on the billiard shape parameter. >>

<< ️(AA) find that the survival probability exhibits a two-stage decay pattern: an initial exponential regime followed by a long-time power-law tail, a signature of the stickiness effect. (Their) results show that the short-time exponential decay rate follows a power-law dependence on the hole size, with different scaling exponents for holes placed in chaotic regions versus mixed phase-space regions. For holes located in mixed phase-space regions, the decay exponent of the long-time power-law tail remains approximately constant, while the amplitude follows a power-law scaling with hole size. >>

<< ️(They) also examine the dependence of short-time exponential decay rate on the billiard shape parameter and observe scaling behavior for small values of this parameter, which breaks down as the parameter increases. >>

Daniel Borin, Edson Denis Leonel, Diego Fregolent Mendes de Oliveira. Survival probability of particles inside the lemon billiard. Phys. Rev. E 114, 014224. Jul 28, 2026.

https://journals.aps.org/pre/abstract/10.1103/md5j-ggyd

arXiv: 2601.13000v1 [nlin.CD]. Jan 19, 2026.

https://arxiv.org/abs/2601.13000

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

Keywords: gst, billiard, particles, chaos, transitions, survival probability, two-stage decay pattern, stickiness effect, scaling behavior, scaling laws of complex systems. 

# gst: apropos of bluff-body wakes, effect of centerline separation on a vortex dominated wake.

<< A previously undocumented Reynolds-number-dependent transition is identified in the wake of a rounded-edge slanted afterbody, from a centerline-separated to a novel centerline-attached vortex state. The transition produces a pronounced drag reduction through the collapse of the centerline recirculation region as the upstream boundary layer becomes turbulent. These (AA) findings explore experimental evidence linking laminar separation bubble dynamics, shear-layer instability, and wake-state transitions in this canonical bluff-body geometry. >> ( APS Editor, https://journals.aps.org/prfluids/recent/ )

Rhylan A. Huss, Farrukh S. Alvi. Effect of centerline separation on a vortex dominated wake. Phys. Rev. Fluids 11, 074702. Jul 28, 2026.

https://journals.aps.org/prfluids/abstract/10.1103/bn64-wtlz

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

Keywords: gst, vortex, transition, 

bubble, laminar separation bubble dynamics, shear-layer instability, wake-state transitions.

# gst: natural invariant measures for chaotic game dynamics; finding order in chaos.

<< ️(AA) study the long-term behavior of the Multiplicative Weights Update (MWU) algorithm in game settings where learning dynamics frequently fail to converge to Nash equilibria and instead exhibit Li-Yorke chaos. While such chaos precludes the prediction of specific long-term strategy profiles, it does not imply a lack of statistical structure. >>

<< ️(AA) demonstrate that natural invariant measures — a fundamental concept from ergodic theory — provide the rigorous framework necessary to find order within this chaos. Focusing on a two-strategy congestion game, (They) prove that these measures allow for a comprehensive statistical characterization of the dynamics. Crucially, (They) show that this framework extends beyond simple strategy frequencies to general observables, enabling the precise calculation of long-term time averages for broad classes of economic metrics — including payoffs, social cost, and regret — despite chaos. >>

<< ️(They) results reveal that this simple learning algorithm captures the full spectrum of behaviors found in one-dimensional dynamical systems, from unique or multiple absolutely continuous invariant measures to complex periodic attractors as well as coexisting chaotic and stable (periodic) behaviors. By bridging game theory and dynamical systems, (AA) show that statistical predictability is attainable even in the absence of pointwise convergence. >>

<< ️The intersection of game theory, dynamical systems, computer science, and statistics is rich with open questions, particularly when considering learning dynamics in games. >>

Jakub Bielawski, Thiparat Chotibut, Fryderyk Falniowski, et al. Natural Invariant Measures for Chaotic Game Dynamics: Finding Order in Chaos. arXiv: 2607.21805v1 [math.DS]. Jul 23, 2026.

https://arxiv.org/abs/2607.21805

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

Keywords: gst, game, chaos, Multiplicative Weights Update (MWU) algorithm, statistical structure, statistical predictability, two-strategy congestion game, complex periodic attractors, coexisting chaotic and stable (periodic) behaviors.

# gst: on the scaling of bubble interactions in dynamic turbulence; theoretical, numerical, and experimental study.

<< This (AA) study investigates dilute bubbly decaying homogeneous isotropic turbulence at high Reynolds number using theory, direct numerical simulation, and experiments. The turbulent kinetic energy and dissipation rate follow power-law decay, while the bubble population reorganizes relative to the evolving Hinze scale. When the dissipation decays sufficiently rapidly, the Hinze scale grows faster than the characteristic bubble diameter, driving the population from super-Hinze toward sub-Hinze sizes. The system passes through a mixed regime in which coalescence dominates but breakup remains active, followed by a pure-coalescence regime. Residual breakup in the mixed regime increases the number of small bubbles and enhances coalescence, leading to faster growth of the characteristic bubble size. DNS of dilute bubble-laden turbulence shows decay exponents close to single-phase turbulence and a bubble-size distribution that shifts toward smaller diameter relative to the Hinze scale. >>

<< Before the transition, the distribution exhibits two power-law ranges associated with capillary effects and inertial breakup; after the transition, it approaches a single capillary-dominated scaling. Theory and DNS predict distinct growth laws for bubble diameter in the mixed and pure-coalescence regimes, together with corresponding scalings for number density, interfacial area, and coalescence rate. These predictions are further assessed in a spatially developing pump-driven bubbly duct flow at higher Reynolds number. Despite confinement, inhomogeneity, and wall production, the measured trends agree with the theoretical and DNS-based scalings. >>

<< The (AA) results identify Hinze-scale drift as the organizing mechanism for bubble interactions in both idealized and practical decaying turbulent flows, and provide guidance for population-balance and interfacial-area-transport models. >>

Vivek Kumar, Prasoon Suchandra, Shivam Prajapati, et al. On the scaling of bubble interactions in dynamic turbulence: theoretical, numerical, and experimental study.  arXiv: 2607.25251v1 [physics.flu-dyn]. Jul 28, 2026.

https://arxiv.org/abs/2607.25251

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

Keywords: gst, bubble, transitions, dilute bubbly decaying, coalescence, mixed- pure-coalescence regimes, dilute bubble-laden turbulence, capillary effects, inertial breakup, decaying turbulent flows.  

# gst: emergence of minimal chimera in uncoupled oscillators under common frequency-modulated driving.

<< (AA) report the experimental realization of minimal chimera states in a system of three uncoupled oscillators driven solely by frequency-modulated forcing. Unlike conventional scenarios where chimera states emerge due to interactions among oscillators, here the coexistence of coherent and incoherent dynamics arises entirely from a common external modulation of a system parameter. By tuning the modulation amplitude and frequency, the system exhibits transitions between global synchronization, global incoherence, and minimal chimera states. >>

<< The stability of these regimes is quantified using the maximal Lyapunov exponent, while a synchronization order parameter is employed to characterize the degree of coherence. A systematic exploration of the parameter space reveals well-defined regions associated with distinct dynamical behaviors. To provide analytical understanding, (AA) employ a phase-reduction approach and derive the corresponding phase dynamics, which elucidate the mechanisms underlying phase locking and desynchronization. The robustness of the proposed mechanism is further demonstrated in a time-delayed chaotic system. >>

<< Finally, experimental results obtained from an electronic circuit realization confirm the emergence of minimal chimera states under frequency-modulated driving. These findings establish external modulation as a viable route to chimera formation without coupling, offering a new perspective on collective dynamics in driven nonlinear systems. >>

Debabrata Biswas, Tanmoy Banerjee. Emergence of minimal chimera in uncoupled oscillators under common frequency-modulated driving: theory and experiment. arXiv: 2607.25449v1 [nlin.CD]. Jul 28, 2026.

https://arxiv.org/abs/2607.25449

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

Keywords: gst, chimera, transition, chaos, three uncoupled oscillators, coherent- incoherent dynamics, frequency-modulated forcing, global synchronization, global incoherence, minimal chimera states.

# sound: origin of the sound produced by a detaching bubble.

<< ️When a bubble detaches, it produces a sound. While the frequency of this sound is well understood, there has been no consensus on what drives its amplitude. Although mechanisms based on shape oscillations, initial velocity of the bubble radius, neck collapse or Laplace pressure have been suggested, none of them has been confirmed experimentally. >>

<< (AA) performed experiments involving two methods of producing bubbles, which result in sound levels differing by two orders of magnitude. (They) results show that the sound amplitude is given by the conditions of velocity and radius of the bubble at detachment, in line with the scenario of a free harmonic oscillator proposed by Strasberg in 1956. >>

<< ️(They) refined this scenario by describing how the bubble radius velocity is affected by gas exchange though the closing neck. This “leaking bubble” model predicts that the bubble begins to produce sound prior to detachment, as observed experimentally. By feeding image analysis of the neck into the model, (AA) obtained excellent agreement between the experimental and the calculated pressure signals. >>

Vincent Gourmandie, Jeanne Chauris, Remi Fechter, et al. Origin of the sound produced by a detaching bubble. Phys. Rev. Fluids 11, 073605. Jul 29, 2026.

https://journals.aps.org/prfluids/abstract/10.1103/xshn-mnb8

Also: sound, bubble, noise, in https://www.inkgmr.net/kwrds.html 

Keywords: sound, bubble, bubble dynamics, detachment bubble, leaking bubble, noise, acoustics, hydrodynamic noise, underwater acoustics. 

# gst: breathing chimera states from purely triadic interactions.

<< ️Chimera states, characterized by the coexistence of synchronized and desynchronized dynamics in identical oscillators, are typically studied in systems with pairwise interactions. Whether higher-order interactions alone can generate such symmetry-broken collective states remains unclear. >>

<< ️Here, (AA) show that chimera states can arise solely from triadic interactions. Furthermore, exploiting the intrinsic π-symmetry of the triadic coupling leads to bimodal phase distributions. (They) construct a bimodal Ott--Antonsen reduction that incorporates an asymmetry parameter via symmetry-breaking initial conditions, thereby achieving an exact low-dimensional description of the macroscopic dynamics. This allows to derive an analytic condition for the emergence of chimera states and identify a bifurcation to a breathing chimera regime characterized by persistent oscillations. Furthermore, the reduced dynamics can be expressed as a Riccati-type equation, providing a geometric interpretation of the chimera state as a closed periodic orbit in the complex plane. >> 

<< ️(AA) results establish purely triadic coupling as a minimal mechanism for chimera formation and provide a tractable framework for studying symmetry-broken collective dynamics in systems dominated by many-body interactions. >>

Sudo Yi, Gugyoung Kim, Mi Jin Lee, et al. Breathing chimera states from purely triadic interactions. arXiv: 2607.28017v1 [physics.soc-ph]. Jul 30, 2026.

https://arxiv.org/abs/2607.28017

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

Keywords: gst, chimera, coupled oscillators, synchronized- desynchronized dynamics, pairwise interactions, symmetry-broken collective states, triadic interactions, bifurcations. 

# life: a calculus of discernment; decision-relevant insight, sequence value, and forgetting as higher-order learning.

<< ️In a world of generative AI, candidate insights are abundant; what is scarce is the capacity to discern which matter, to act on them in the right amount and order, and to forget the rest so the system can adapt. (AA) argue these scarcities are governed by one object and build a framework around it. (They) define an insight strictly as a lever with an identified, measurable effect on an objective, and rank candidates by decision-relevance via the expected value of information rather than novelty. >>

<< ️(They) show action carries an order, not only a size: under realistic belief dynamics, content "touches" are non-commuting operators, so a fixed plan delivered in different orders yields different outcomes, defining a sequence premium. (They) observe that the value of any lever is a shadow price, unifying pharmaceutical marketing, equity selection, and manufacturing as one leverage-discovery problem. >>

<< ️Most speculatively, (AA) propose APOHA, a theory in which forgetting is not the disposal of knowledge but the operator by which value is learned: the value of a retained item is the counterfactual cost of forgetting it, a learning system is the residue of maximal forgetting subject to preserved value, and higher-order value is the structure that survives repeated forgetting (a renormalisation-relevant invariant), with consolidation as its conjugate. >>

<< ️(AA) state the central open problem (a non-trivial attractor with a spectral gap) and test the forgetting theory: operationalising APOHA as an agent on a non-stationary obesity-treatment decision world over 30 seeds, adaptive forgetting cut cumulative decision-regret by 24-32% against never-forget and a fixed half-life, kept a ~6x smaller, cleaner memory, and converged stably; notably, blind forgetting was worse than never forgetting, so the benefit is specific to value-aware forgetting. A multi-disciplinary critique stress-tests the whole. >>

Suyash Mishra. A Calculus of Discernment: Decision-Relevant Insight, Sequence Value, and Forgetting as Higher-Order Learning. arXiv: 2607.18275v1 [cs.GT]. Jun 17, 2026.

https://arxiv.org/abs/2607.18275

Also: brain, pause, silence, Occam, Zen, in https://www.inkgmr.net/kwrds.html 

Keywords: life, brain, pause, silence, Occam, Zen, memory, higher-order learning, oblivion, APOHA attractor, discernment, sequencing, leverage, forgetting theory, survives repeated forgetting, never forgetting, blind forgetting, value-aware removal, value-aware forgetting, 

# gst: the origins of transient bimodality

<< Many dynamical systems exhibit diverse modes of behavior. In biology, such modes can represent individual or cell fates. While the emergence of multimodality is commonly studied, transient bimodality is much less well understood. Under transient bimodality, a system moving from a well-defined initial to a final state transiently undergoes a bifurcation into multiple probability modes. This noise-driven phenomenon can significantly impact processes such as cell differentiation and speciation in the presence of changing environmental conditions. >>

<< (AA) detail a theoretical approach for understanding transient bimodality connecting results from ecology, optics, chemical reaction networks and cell biology, propose a ``minimal model'' of transient bimodality and derive a general criterion for its presence. (They) show that fast-to-slow dynamics can lead to transient bimodality in addition to the well-known case of slow-to-fast dynamics. Finally, (AA)  discuss the role of transient bimodality across the scientific literature, with emphasis on biochemical kinetics and gene regulation. >>

Kaan Öcal, Augustinas Sukys, Aanjaneya Kumar, et al. The Origins of Transient Bimodality. arXiv: 2607.16531v1 [q-bio.SC]. Jul 17, 2026.

https://arxiv.org/abs/2607.16531

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

Keywords: gst, noise, uncertainty, transitions, transient bimodality, bifurcations, multimodality, noise-driven phenomenon, fast-to-slow dynamics. 

# gst: vortex formation around islands in random waves.

<< ️Wave vortices are fundamental topological features of interference fields, occurring at nodal points where the wave amplitude vanishes. A distinct class of vortices can instead form around it islands or `holes' in two-dimensional wavefields, where the wave intensity remains finite and may even peak at the boundary. >> 

<< ️Here (AA) develop a statistical theory of vortices around islands in random two-dimensional wavefields, with and without the Coriolis effect, and test it experimentally. (They) determine the probabilities of vortices with different topological charges as functions of island size and Coriolis parameter.  ️(They) find that island-bound vortices emerge with unexpectedly high probability, approaching 50% in non-rotating systems and nearly 100% in rotating systems. Moreover, for a broad range of parameters, the presence of a subwavelength island dramatically enhances vortex formation compared with homogeneous random wavefields. >>

<< ️(AA) results explain the formation of tidal vortices around ocean islands of particular sizes (~0.1 of the characteristic wavelength) and establish a general mechanism for generating localized high-intensity vortices around defects in diverse wave systems, from water waves to nanophotonic structures. >>

Alex J. Vernon, Junyi Ye, Wenzhe Liu, et al. Vortex formation around islands in random waves. arXiv: 2607.15938v1 [physics.flu-dyn]. Jul 17, 2026.

https://arxiv.org/abs/2607.15938

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

Keywords: gst, waves, vortex, randomness, defects, wave vortices, tidal vortices, interference fields, homogeneous random wavefields, random two-dimensional wavefields, rotating non-rotating systems.

# life: apropos of bizarre predatory behavior (even among humans?), a caterpillar patrols spiderwebs camouflaged in insect prey's body parts.

<< Lepidoptera is the most herbivorous of all the insect orders, with predatory caterpillars globally comprising less than 0.13% of the nearly 200,000 moth and butterfly species. Here, (AA) report a species in which caterpillars are carnivorous inhabitants of spider's webs, feeding on the arthropods that they find there. This Hawaiian lineage also boasts an unprecedented and macabre practice of decorating its portable larval home with the body parts of the spider prey it harvests from the web where it resides. >>

<< Phylogenomic data suggest that the origin of this unique spider cohabitant is at least six million years old, more than one million years older than Hawai"'s current high islands. After decades of searching. only one species has been discovered, and it is restricted to 15 square kilometers of a single mountain range on the island of O'ahu, meaning that other members of the lineage have disappeared from older islands. >>

<< Conservation action to save this globally unique lineage is imperative and overdue. >>

Daniel Rubinoff, Michael San Jose, Camiel Doorenweerd. Hawaiian caterpillar patrols spiderwebs camouflaged in insect prey's body parts. Science 388, 428-430. Apr 25, 2025. 

https://www.science.org/doi/10.1126/science.ads4243

https://x.com/ScienceMagazine/status/1938501366487351661

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

Keywords: behavior.

# gst: interwoven long-range order induced by random fields.

<< (AA) propose a distinct type of long-range ordered phase that can occur in classical and quantum many-particle systems. It is induced by impurities and defects that locally break a subset of the order-parameter symmetries, i.e., by random-field disorder that couples to a composite vestigial order parameter. >>

<< The proposed ``implectic'' phase is characterized by spontaneous symmetry breaking on the background of the spatially interwoven domain structure created by the random fields. (They) explicitly demonstrate the existence of this phase in a layered J1−J2 Ising magnet by means of large-scale Monte Carlo simulations. (AA) then discuss numerous potential applications in systems featuring charge and spin density wave order including frustrated magnets, cuprate and iron-based superconductors, and ultracold atoms. >>

Jeremiah Bender, Thomas Vojta. Interwoven long-range order induced by random fields. arXiv: 2607.10337v1 [cond-mat.dis-nn]. Jul 11, 2026.

https://arxiv.org/abs/2607.10337

Also: particle, waves, order, disorder, fracture, crack, random, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, particle, waves, order, disorder, fracture, crack, transitions, impurities, defects, locally break, spontaneous symmetry breaking, random-field disorder, implectic long-range ordered phases.

# gst: twisted state stability under local order parameter adaptation.

<< ️Twisted states commonly arise in nonlocally coupled ring networks. (AA) study the stability of twisted states in networks with higher-order interactions under the adaptive mechanism based on the local order parameter. >>

<< ️The adaptive feedback dynamically regulates the coupling strength and thus reshapes the collective dynamics of the system. Analytical and numerical results show that higher-order adaptivity reduces the linear stability of twisted states, whereas pairwise adaptivity enhances it. Numerical simulations further demonstrate that increasing the exponent of higher-order adaptation drives the system toward more ordered states and correspondingly enlarges the basin of twisted states. >>

<< Moreover, a larger coupling range reduces twisted-state stability, while in random hypergraphs, higher-order adaptivity enlarges the synchronization basin without significantly changing the linear stability. These findings reveal a nonequilibrium relationship between linear stability and basin stability and highlight the important role of adaptive regulation in higher-order network dynamics. >>

Xueqin Wang, Hong He, Wende Tang, et al. Twisted state stability under local order parameter adaptation. Phys. Rev. E 114, 014209. Jul 13, 2026. 

https://journals.aps.org/pre/abstract/10.1103/p2wd-nfbr

Also: network, stability, chimera, order, disorder, fluctuations, random, twist, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, networks, stability, chimera, order, disorder, fluctuations, randomness, synchronization, coupled oscillators, adaptive feedbacks, twisted states, basin stability. 

# gst: dynamical origin of extreme events in mutually coupled and networked Brusselator.

<< This (AA) study investigates the dynamical origins and statistical properties of extreme events (EEs) in a diffusively coupled theoretical Brusselator system, extending from pairwise interactions to globally coupled networks. >>

<< Statistically, the emergence of EEs is characterized by heavy-tailed probability density functions and exponential interevent interval distributions, alongside an analysis of the complementary cumulative distribution function and return periods. To elucidate the underlying generative mechanism, (They) employ invariant manifold computations and vector field divergence analysis. >>

<< (Their) results demonstrate that EEs are triggered by a critical region formed by the geometric alignment of stable and unstable manifolds near a saddle-type invariant set governed by the Shilnikov mechanism. Furthermore, extending the analysis to a globally coupled network reveals that network dimensionality does not affect the prevalence of EEs. >>

<< Finally, these numerical findings are corroborated by experimental observations from an analog electronic circuit, confirming the robustness of these dynamical phenomena in physical systems. >>

S.V. Manivelan, S.Sabarathinam, K.Thamilmaran, et al. Dynamical origin of extreme events in mutually coupled and networked Brusselator. Phys. Rev. E 114, 014217. Jul 15, 2026.

https://journals.aps.org/pre/abstract/10.1103/byp5-gxrz  

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

Keywords: gst, networks, chaos, Brusselator, coupled oscillators, extreme event statistics, criticality, saddle-type invariant set.

# life: drawing with water waves.

<< The deterministic reproduction of complex 3D wave fields remains a significant challenge in ocean engineering. This (AA) study proposes a novel methodology for drawing arbitrary 2D curves and 3D volumetric shapes on a water surface using transient multi-directional focused waves. >>

<< To overcome the limitations of conventional discrete-point focusing methods, (Their) framework integrates Bézier curve parametrisation, equal arc-length sampling, and an Iterative Amplitude Correction (IAC) algorithm. This effectively mitigates wave height overshoot and enables precise spatial superposition of spectral components. >>

<< The method's effectiveness was validated through linear wave theory and Smoothed Particle Hydrodynamics (SPH) simulations, successfully reproducing 2D characters and a 3D human face. Physical experiments in the FloWave circular wave basin further demonstrated target shape generation, such as a 2D star and 3D pyramid. Although further integration of nonlinear wave theories is necessary for high-amplitude accuracy, this technique establishes a deterministic methodology for creating arbitrary 2D and 3D surface geometries. It represents a significant advantage in wave field control for ocean engineering applications. >>

Taiga Kanehira, James Steer, Laura-Beth Jordan, et al. Drawing with water waves. arXiv: 2607.13691v1 [physics.flu-dyn]. Jul 15, 2026.

https://arxiv.org/abs/2607.13691

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

Keywords: waves

# 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.