# gst: randomness with constraints: constructing minimal models for high-dimensional biology.

<< ️Biologists and physicists have a rich tradition of modeling living systems with simple models composed of a few interacting components. Despite the remarkable success of this approach, it remains unclear how to use such finely tuned models to study complex biological systems composed of numerous heterogeneous, interacting components. >>

<< ️One possible strategy for taming this biological complexity is to embrace the idea that many biological behaviors we observe are ``typical'' and can be modeled using random systems that respect biologically-motivated constraints. Here, (AA) review recent works showing how this approach can be used to make close connection with experiments in biological systems ranging from neuroscience to ecology and evolution and beyond. Collectively, these works suggest that the ``random-with-constraints'' paradigm represents a promising new modeling strategy for capturing experimentally observed dynamical and statistical features in high-dimensional biological data and provides a powerful minimal modeling philosophy for biology. >>

Ilya Nemenman, Pankaj Mehta. Randomness with constraints: constructing minimal models for high-dimensional biology. arXiv: 2509.03765v1 [physics.bio-ph]. Sep 3, 2025.

https://arxiv.org/abs/2509.03765

Also: random, transition, disorder & fluctuations, fly at random, quasi-stochastic poetry, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, randomness, transitions, disorder & fluctuations, random-with-constraints, fly at random, quasi-stochastic poetry.

# gst: dual role for heterogeneity in dynamic fracture.

<< ️(AA) approach the problem of heterogeneous dynamic fracture by considering spatiotemporal perturbations to planar crack fronts. Front propagation is governed by local energy balance between the elastic energy per unit area available to fracture 𝐺 and the dissipation in creating new surfaces. 𝐺 is known analytically as a perturbation series in the crack front fluctuation. >>

<< ️For dissipation that monotonically increases with the crack speed, (AA) derive an equation of motion for crack fronts that is second-order accurate. In the linear order, heterogeneity does not change the net speed of fracture. In the second order, nonlinear interactions of the front and the heterogeneous landscape populate an intermediate-scale fluctuation spectrum. >>

<< ️(AA) find that, when dissipation weakly grows with velocity, nonlinearities globally amplify dissipation and reduce the crack speed. Strong velocity dependence, however, mitigates toughening effects and may facilitate fracture. >>

Itamar Kolvin, Mokhtar Adda-Bedia, Dual Role for Heterogeneity in Dynamic Fracture. Phys. Rev. Lett. 135, 106201. Sep 3, 2025.

https://journals.aps.org/prl/abstract/10.1103/j4vb-y1ng 

arXiv: 2407.02347v1 [cond-mat.mtrl-sci]. Jul 2,  2024.

https://arxiv.org/abs/2407.02347 

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

Keywords: gst, fracture, crack, front propagation

# gst: intensity landscapes in elliptic and oval billiards with a circular absorbing region.

<< ️Billiard models of single particles moving freely in two-dimensional regions enclosed by hard walls have long provided ideal toy models for the investigation of dynamical systems and chaos. Recently, billiards with (semi)permeable walls and internal holes have been used to study open systems. >>

<< ️Here (AA) introduce a billiard model containing an internal region with partial absorption. The absorption does not change the trajectories but instead reduces an intensity variable associated with each trajectory. The value of the intensity can be tracked as a function of the initial configuration and the number of reflections from the wall and depicted in intensity landscapes over the Poincaré phase space. >>

<< ️This is similar in spirit to escape time diagrams that are often considered in dynamical systems with holes.  >>

<< ️(AA) analyze the resulting intensity landscapes for three different geometries: a circular, elliptic, and oval billiard, respectively, all with a centrally placed circular absorbing region. The intensity landscapes feature increasingly more complex structures, organized around the sets of points in phase space that intersect the absorbing region in a given iteration, which (They) study in some detail. On top of these, the intensity landscapes are enriched by effects arising from multiple absorption events for a given trajectory. >>

Katherine Holmes, Joseph Hall, Eva-Maria Graefe. Intensity landscapes in elliptic and oval billiards with a circular absorbing region. Phys. Rev. E 112, 034202. Sep 2, 2025.

https://journals.aps.org/pre/abstract/10.1103/9bv6-4npn 

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

Keywords: gst, billiard, particle, escape.

# gst: shock waves in classical dust collapse.

<< ️During gravitational collapse of dust in spherical symmetry, matter particles may collide forming shell crossing singularities (SCSs) at which the Einstein equations become indeterminate. >>

<< ️(AA) show that in the case of marginally bound dust collapse, there is a unique evolution beyond SCSs such that a propagating shock wave forms, the metric remains continuous, and the stress-energy tensor dynamically becomes that of a thin shell. (They) give numerical simulations that exhibit this result. >>

Viqar Husain, Hassan Mehmood. Shock waves in classical dust collapse. Phys. Rev. Research 7, 033215. Sep 3, 2025.

https://journals.aps.org/prresearch/abstract/10.1103/b317-86qs

arXiv: 2504.14883v1 [gr-qc]. Apr 21, 2025.

https://arxiv.org/abs/2504.14883

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

Keywords: gst, particles, singularity, shell crossing singularities, waves, shock waves, gravitational waves, collapse, dust collapse, gravitational collapse. 

# ecol: stabilization of macroscopic dynamics by fine-grained disorder in many-species ecosystems.

<< ️Models for complex, heterogeneous systems such as ecological communities vary in the level of organization they describe. When the dynamics at the species level is unknown, one typically resorts to heuristic "macroscopic" models that capture relationships among a few degrees of freedom, e.g., groups of similar species, and commonly display out-of-equilibrium dynamics. These models, however, exactly reflect the species-level "microscopic" dynamics only when microscopic heterogeneity can be neglected. >>

<< ️Here, (AA) address the robustness of such macroscopic descriptions to the addition of disordered microscopic interactions. While disorder is known to destabilize equilibria at the microscopic level, leading to asynchronous (typically chaotic) fluctuations, (They) show that it can also stabilize synchronous species fluctuations driven by macroscopic structure. >>

<< ️(AA) analytically find the conditions for the existence of heterogeneity-stabilized equilibria and relate their stability to a mismatch in the time scales of individual species. This may shed light on the empirical observation that many-species ecosystems often appear stable despite highly diverse and potentially destabilizing interactions between species and functional groups. >>

Juan Giral Martínez, Silvia De Monte, Matthieu Barbier. Stabilization of macroscopic dynamics by fine-grained disorder in many-species ecosystems. Phys. Rev. E 112, 034305. Sep 4, 2025.

https://journals.aps.org/pre/abstract/10.1103/5w5x-b1c2

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

Keywords: gst, disorder, disorder & fluctuations, chaos, ecological communities, disordered microscopic interactions, asynchronous fluctuations, heterogeneity-stabilized equilibria.

# brain: self-organized learning emerges from coherent coupling of critical neurons.

<< ️Deep artificial neural networks have surpassed human-level performance across a diverse array of complex learning tasks, establishing themselves as indispensable tools in both social applications and scientific research. >>

<< ️Despite these advances, the underlying mechanisms of training in artificial neural networks remain elusive. >>

<< ️Here, (AA) propose that artificial neural networks function as adaptive, self-organizing information processing systems in which training is mediated by the coherent coupling of strongly activated, task-specific critical neurons. >>

<< ️(AA) demonstrate that such neuronal coupling gives rise to Hebbian-like neural correlation graphs, which undergo a dynamic, second-order connectivity phase transition during the initial stages of training. Concurrently, the connection weights among critical neurons are consistently reinforced while being simultaneously redistributed in a stochastic manner. >>

<< ️As a result, a precise balance of neuronal contributions is established, inducing a local concentration within the random loss landscape which provides theoretical explanation for generalization capacity. >>

<< ️(AA) further identify a later on convergence phase transition characterized by a phase boundary in hyperparameter space, driven by the nonequilibrium probability flux through weight space. The critical computational graphs resulting from coherent coupling also decode the predictive rules learned by artificial neural networks, drawing analogies to avalanche-like dynamics observed in biological neural circuits. >>

<< ️(AA) findings suggest that the coherent coupling of critical neurons and the ensuing local concentration within the loss landscapes may represent universal learning mechanisms shared by both artificial and biological neural computation. >>

Chuanbo Liu, Jin Wang. Self-organized learning emerges from coherent coupling of critical neurons. arXiv: 2509.00107v1 [cond-mat.dis-nn]. Aug 28, 2025.

https://arxiv.org/abs/2509.00107

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

Keywords: gst, brain, neurons, networks, randomness, transitions, ai (artificial intell) (bot), learning mechanisms, self-organized learning, artificial neural networks, deep learning, neuronal coupling, criticality, stochasticity, avalanche-like dynamics.

# gst: a journey into billiard systems

<< ️Have you ever played or watched a game of pool? If so, you have already seen a billiard system in action. In mathematics and physics, a billiard system describes a ball that moves in straight lines and bounces off walls. Despite these simple rules, billiard systems can produce remarkably rich behaviors: some table shapes generate regular, periodic patterns, while others give rise to complete chaos. >>

<< Scientists also study what happens when (They) shrink the ball down to the size of an electron to a world where quantum effects take over and the familiar reflection rules no longer apply. >>

<< ️In this article, (AA) discuss billiard systems in their many forms and show how such a simple setup can reveal fundamental insights into the behavior of nature at both classical and quantum scales. >>

Weiqi Chu, Matthew Dobson. What Do Bouncing Balls Tell Us About the Universe? A Journey into Billiard Systems. arXiv: 2508.18519v1 [math.DS]. Aug 25, 2025.

https://arxiv.org/abs/2508.18519

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

Keywords: gst, billiard, transition, chaos.