# life: learning by confusion locates a parametrization-dependent Fisher information maximum.

<< ️Learning by confusion (LBC) is a machine-learning method for locating phase transitions without assuming a known order parameter. Its characteristic accuracy curve contains a central maximum that is interpreted as the transition point, but what determines the location and finite-size scaling of this maximum has remained unclear. >>

<< ️(AA) derive an exact balance condition for the Bayes-optimal confusion peak and show that, for equilibrium systems with a single swept parameter, the peak closely follows the maximum of the corresponding Fisher information. This immediately gives its finite-size scaling and reveals an unexpected dependence on how the data are sampled: the same configurations arranged on grids uniform in T, lnT, or β=1/T can yield different finite-size pseudocritical trajectories. >>

<< Tests on the Ising, Blume-Capel, Potts, and Baxter-Wu models confirm the prediction across continuous, tricritical, and first-order transitions. (AA) results identify the statistical quantity measured by LBC and show that finite-size machine-learning estimates can depend on the parametrization of the training data as well as on the underlying physics. >>

George Issa, Richard Scalettar. Learning by Confusion Locates a Parametrization-Dependent Fisher Information Maximum. arXiv: 2610.34769v2 [cond-mat.stat-mech]. Nov 2, 2026.

https://arxiv.org/abs/2610.34769

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

Keywords: ai, artificial intelligence, machine-learning, learning by confusion, Bayes-optimal confusion peak, finite-size pseudocritical trajectories, transitions.

# gst: apropos of dispersed flowing droploids, microfluidic oscillatory rheology of transported soft entities.

<< ️Microfluidic channels have emerged as useful tools to control dynamic forcing on transported microscale objects, as encountered in emulsions, biological flows, and other soft-matter systems. Tailored channel designs enable precise interfacial and bulk rheological measurements of complex materials over a wide range of forcing timescales. >>

<< ️(AA) discuss perspectives for future research in this direction, including the study of lubrication films in highly confined droplets, the measurement of fast relaxation dynamics of complex interfaces, and the high-throughput rheological characterization of microscopic soft-matter systems ranging from single macromolecules to cells. >>

Matteo Milani, Joshua D. McGraw, Anke Lindner, et al. Microfluidic oscillatory rheology of transported soft particles. Phys. Rev. E 114, 041005. Oct 22, 2026.

https://journals.aps.org/pre/abstract/10.1103/sn3p-jrq5

arXiv: 2605.29842v2 [cond-mat.soft]. May 28, 2026.

https://arxiv.org/abs/2605.29842

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

Keywords: gst, particles, drops, droplets, droploids, microfluidics, rheology. 

# gst: ordered patches cap the stability of disordered frameworks.

<< ️Structural disorder can stabilize frameworks against pressure-induced failure, yet the ordered regions it contains limit this gain. (AA) show that, in rigid-jointed frames under hydrostatic pressure, an ensemble containing arbitrarily large patches of a crystal at positive density, whose centres carry a scaled crystal prestress, cannot stay linearly stable once those patches are stressed beyond the crystal's threshold for localizable instabilities. >>

<< ️A homogeneous loss of positive definiteness while all Bloch modes, including the acoustic limit, remain stable cannot localize, leaving a window for stabilization. Extending an acoustic criterion to prestress, (AA) show for all point groups that such a window requires a strain that keeps the crystal's symmetry. Unless the patches are shielded from stress, disorder cannot protect a crystal against a failure that breaks its symmetry, and protects a cubic crystal at most against volume collapse. >>

<< ️In two-dimensional Truchet frames, planted ordered domains bring the threshold within 1% of the bound, and correlations short of long-range order localize failure on ordered clusters. Across 876 slender-strut nets, 798 fail first by a localizable instability; the other 78 have a median window of 7.6%. Stability gained through disorder is capped by the localizable instabilities of the local order it permits. >>

Joohan Nam. Ordered patches cap the stability of disordered frameworks. arXiv: 2610.38501v1 [cond-mat.mtrl-sci]. Oct 28, 2026.

https://arxiv.org/abs/2610.38501

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

Keywords: gst, disorder, instability, collapse, structural disorder, pressure-induced failure, prestress acoustic criterion, volume collapse.

# gst: directed extended-range percolation.

<< ️For standard percolation, directionality is known to increase the complexity of percolation, requiring the distinct statistical treatment of in messages and out messages for determining the percolation order parameters. >>

<< ️Here (AA) show that when connectivity is ensured by paths of length 𝑅≥2, network directionality, impeding backtracking, can significantly reduce the complexity of percolation. To illustrate this finding, (AA) introduce directed extended-range percolation (DERP), defined on directed networks with nonreciprocal edges and motivated by applications in quantum communication. >>

<< ️In this framework, message transmission is enabled between trusted nodes separated by a directed path of length at most 𝑅. Using a message-passing approach, (AA) show that, on locally treelike structures, directionality enables an exact determination of the percolation threshold and the anomalous critical indices with a number of distinct statistical messages smaller than the naive expectation, which would require twice as many messages as in the undirected version. This reduction arises because directionality suppresses backtracking paths, thereby considerably simplifying the resulting equations. >>

<< ️On random directed networks (AA) find that the critical behavior of DERP depends sensitively on degree correlations. These analytical predictions are corroborated by extensive Monte Carlo simulations, highlighting the profound impact of directionality and correlations on long-range connectivity in complex networks. >>

Wenbo Liu, Yiwen Zeng, Xueming Liu, et al. Directed extended-range percolation. Phys. Rev. E 114, L042301. Oct 26, 2026.

https://journals.aps.org/pre/abstract/10.1103/hs2n-6rsn

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

Keywords: gst, networks, transitions, percolation, directed extended-range percolation, percolation threshold, percolation phase transition, random directed networks, network phase transitions, long-range connectivity, critical phenomena.

# gst: is vorticity amplification essential for anomalous dissipation and intermittency in turbulence?

<< ️The distinct dynamical roles of vorticity amplification (VA) and vortex tilting (VT) in three-dimensional homogeneous isotropic turbulence are investigated using direct numerical simulations of a modified Navier-Stokes system. >> 

<< ️By selectively suppressing VA while retaining VT, (AA) demonstrate that gradient amplification by VA is strictly required to sustain the classical forward energy cascade.  Progressively suppressing VA weakens small-scale velocity gradients, heavily depletes extreme fluctuations, and entirely eliminates the classical energy dissipative anomaly, causing the normalized energy dissipation to decay as Re_(𝜆)^(−1). In the limit of complete VA suppression, enstrophy emerges as the relevant inviscid invariant. >>

<< Scale-by-scale budget analyses confirm that the dynamics transition to a purely forward enstrophy cascade, characterized by an anomalous enstrophy dissipation and a robust 𝐸⁡(𝑘)∼𝑘^(−3) intermediate energy spectrum. (AA) verify that these asymptotic scaling limits—including a Re_(𝜆)^(−1/2) finite-Reynolds-number correction for the enstrophy anomalous dissipation—are universal properties of the VA-suppressed dynamics, independent of whether the large-scale forcing is helical or nonhelical. >> 

<< ️Remarkably, despite the smoothing of the velocity field and the elimination of the energy dissipative anomaly, anomalous structural scaling and a broad multifractal spectrum persist. These (AA) results reveal a fundamental mechanistic separation: Although VA is responsible for amplifying intense localized fluctuations, geometric reorganization by VT alone is mechanically sufficient to sustain multifractal intermittency. >>

Alessandro Chiarini. Is vorticity amplification essential for anomalous dissipation and intermittency in turbulence? Phys. Rev. Fluids 11, 104607. Oct 21, 2026.

https://journals.aps.org/prfluids/abstract/10.1103/jc6g-p9jk

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

Keywords: gst, vortex, turbulence, fluctuations, transitions, vorticity amplification, vortex tilting, enstrophy, enstrophy anomalous dissipation, multifractal intermittency.

# gst: enhanced turbulent clustering of time-varying particles in random flow fields.

<< ️Particles suspended in turbulent flows tend to cluster within specific regions of the flow field. Previous research consistently reported that clustering is reduced at both very small and very large Stokes numbers for moderate Reynolds numbers. However, understanding how clustering evolves with varying Stokes numbers remains elusive. >> 

<< ️This (AA) work utilizes kinematic simulations to explore clustering of particles with varying inertia at high Reynolds numbers. (Their) results show that when the Stokes number varies over time, noticeable clusters form, even for low-Stokes-number particles that typically exhibit negligible clustering. This suggests that transient effects associated with evolving particle inertia can significantly enhance clustering behavior beyond what would be predicted based on a constant Stokes number alone. >>

<< ️(AA) findings may suggest a different outlook on the enhanced clustering observed in many applications, including natural and atmospheric science, and cloud microphysics. >>

Boaz Ofarim, Yuval Dagan. Enhanced turbulent clustering of time-varying particles in random flow fields. Phys. Rev. E 114, 045104. Oct 21, 2026.

https://journals.aps.org/pre/abstract/10.1103/kdm3-spck

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

Keywords: gst, particles, turbulence, fluid-particle interactions, homogeneous turbulence, isotropic turbulence, multiphase flows, particle-laden flows, turbulent multiphase flows.

# brain: minimal network of brain dynamics; hierarchy of approximations to quasicritical neural network dynamics.

<< ️(AA) present an interacting model of neural network dynamics that incorporates key biological features, including multiple forms of inhibitory interactions. (They) develop a hierarchy of analytical mean-field approximations to characterize nonequilibrium phase transitions between ordered, disordered, and chaotic regimes, complemented by a detailed stability analysis. >> 

<< ️(AA) show that inhibition generically enhances the stability of network dynamics. The model is consistent with the quasicriticality hypothesis, exhibiting regions of maximal dynamical susceptibility and mutual information, modulated by the strength of external stimuli. (They) further demonstrate that, at the mean-field level, the critical transition belongs to the mean-field directed percolation universality class, in agreement with prior experimental and theoretical studies. More broadly, (Their) framework may offer insights into neurological disorders, with the unstable regime exhibiting chaotic dynamics that may be associated with epileptic seizures. >>

Jeremy B. Goetz, Naruepon Weerawongphrom, Rashid V. Williams-García, et al. Minimal network of brain dynamics: Hierarchy of approximations to quasicritical neural network dynamics. Phys. Rev. E 114, 044321. Oct 22, 2026.

https://journals.aps.org/pre/abstract/10.1103/64b7-qb8p

arXiv: 2512.22093v2 [cond-mat.dis-nn]. Jul 15, 2026.

https://arxiv.org/abs/2512.22093

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

Keywords: brain, neurons, networks, transitions, neuronal network activity, percolation phase transition, cortical networks, criticality.