Clay weekly context brief for the Nonlinear Sciences category (ISO week 2026-W37).

Clay tracks publications from the Nonlinear Sciences feed list. Below are recent items from this category, each with its source and a short description of what the publication covers when one is available in the source feed.

Recent publications:
1. Dynamic models with $p$ parameters are identified by $2p+1$ random features
   Source: nlin.CD (Chaotic Dynamics)
   Link: https://arxiv.org/abs/2607.16035
   A foundational principle in nonlinear dynamics is that the structure of a dynamical system can be recovered from a small number of generic measurements or coordinates.
2. Vortex solitons in disclination quasicrystals
   Source: nlin.PS (Pattern Formation and Solitons)
   Link: https://arxiv.org/abs/2609.03244
   Being structures characterized by discrete rotational symmetry $\mathcal{C}_\nu$ of order $\nu$, photonic quasicrystals are capable to support stable propagation of linear vortex-carrying light beams and vortex solitons.
3. Mixed superposition rules for Lie systems, compatible geometric structures, and applications
   Source: nlin.SI (Exactly Solvable and Integrable Systems)
   Link: https://arxiv.org/abs/2511.01063
   Mixed superposition rules are, in short, a method to describe the general solutions of a time-dependent system of first-order differential equations, a so-called Lie system, in terms of particular solutions of other ones.
4. Large-Language Models as a Cognitive Virus
   Source: nlin.AO (Adaptation and Self-Organizing Systems)
   Link: https://arxiv.org/abs/2609.03344
   Large-language models (LLMs) are rapidly becoming part of human culture, reshaping how information is produced, transmitted, and used.
5. Radiative and Dalitz decays of $\Upsilon(1S)$ in the light of the ATOMKI X17 anomaly
   Source: nucl-ex (Nuclear Experiment)
   Link: https://arxiv.org/abs/2609.02874
   We study the radiative decay $\Upsilon(1S)\to \eta_b\gamma$ and the Dalitz decay $\Upsilon(1S)\to \eta_b e^+ e^-$ within the framework of the Covariant Confined Quark Model.
6. Hydrodynamical Initial State in Small Systems From the Phase-Space Entropy
   Source: nucl-th (Nuclear Theory)
   Link: https://arxiv.org/abs/2511.03851
   The experimental observation of collective behavior in proton-proton and proton-nucleus collisions poses a fundamental theoretical question regarding the proper characterization of the initial state underlying hydrodynamic evolution.
7. Collision-based logic in Lenia and its composition boundary
   Source: nlin.CG (Cellular Automata and Lattice Gases)
   Link: https://arxiv.org/abs/2609.01348
   Continuous cellular automata such as Lenia spontaneously produce lifelike, self-propelling patterns, including the Orbium glider, which travels in a straight line while pulsing through a fixed breathing cycle.
8. Estimating dynamic models by matching random features
   Source: nlin.CD (Chaotic Dynamics)
   Link: https://arxiv.org/abs/2607.21916
   Scientists increasingly express their ideas as dynamic models of complex processes.
9. Three-observable measurement of the critical velocity in a paraxial superfluid of light flowing past a mobile impurity
   Source: nlin.PS (Pattern Formation and Solitons)
   Link: https://arxiv.org/abs/2609.03948
   We report the measurement of the critical velocity of a paraxial superfluid of light flowing past a mobile impurity, realized using a dual-wavelength optical scheme in a warm vapor of $^{87}\text{Rb}$.
10. Integrability and transformations in the bilinear method: An introduction
   Source: nlin.SI (Exactly Solvable and Integrable Systems)
   Link: https://arxiv.org/abs/2606.16205
   This is a partial review of the bilinear method, focusing on the integrability based on the 3-soliton-solution condition and the transformations between $\tau$ functions. \textit{Dedicated to Jarmo Hietarinta's 80th birthday}.
11. An Energy-Based Mechanism for Compositional Behavior
   Source: nlin.AO (Adaptation and Self-Organizing Systems)
   Link: https://arxiv.org/abs/2512.04745
   Flexible intelligence relies on the ability to reuse previously acquired behaviors and combine them differently as circumstances change.
12. Halo-EFT: an effective and efficient tool to study reactions with halo nuclei
   Source: nucl-ex (Nuclear Experiment)
   Link: https://arxiv.org/abs/2609.02704
   Halo nuclei are exotic nuclei, which exhibit a much larger matter radius than their isobars.
13. Magnetic-type Love number differentiating quark stars from neutron stars
   Source: nucl-th (Nuclear Theory)
   Link: https://arxiv.org/abs/2511.02236
   The quark star (QS) is a hypothetical and yet undiscovered stellar object, and its existence would mark a paradigm shift in research on nuclear and quark matter.
14. Squeezing codes: robust fluctuation-stabilized memories
   Source: nlin.CG (Cellular Automata and Lattice Gases)
   Link: https://arxiv.org/abs/2509.20730
   We introduce families of classical stochastic dynamics in two and higher dimensions which stabilize order in the absence of any symmetry.
15. An active Lorentz gas: walking droplets in periodic media
   Source: nlin.CD (Chaotic Dynamics)
   Link: https://arxiv.org/abs/2609.02419
   The Lorentz gas is a paradigmatic model in dynamical systems theory for understanding the origin of nonequilibrium transport in terms of microscopic deterministic chaos.
16. Emergence of Complex Web Structures
   Source: nlin.PS (Pattern Formation and Solitons)
   Link: https://arxiv.org/abs/2604.11481
   Complex structures often emerge from initially homogeneous or weakly correlated states.
17. An integrable semi-discretization of the two-component Hunter-Saxton equation
   Source: nlin.SI (Exactly Solvable and Integrable Systems)
   Link: https://arxiv.org/abs/2606.18701
   In this paper, we propose an integrable semi-discretization of the two-component Hunter--Saxton (2-HS) equation, the short-wave limit of the two-component Camassa--Holm (2-CH) equation.
18. A Reexamination of Noise-Driven Robustness Evolution in Gene Regulatory Networks
   Source: nlin.AO (Adaptation and Self-Organizing Systems)
   Link: https://arxiv.org/abs/2607.18645
   Gene regulatory network (GRN) models are widely used to investigate gene-expression dynamics in biological systems.
19. Towards First Detection of the Solar MSW Transition With JUNO
   Source: nucl-ex (Nuclear Experiment)
   Link: https://arxiv.org/abs/2512.14824
   Matter-induced neutrino flavor mixing (the Mikheyev-Smirnov-Wolfenstein, or MSW, effect) is a central prediction of the neutrino mixing framework, but it has not been conclusively observed.
20. Investigation into thorium sulfate as a spinless crystal for a high-performance solid-state $^{229}Th$ nuclear clock
   Source: nucl-th (Nuclear Theory)
   Link: https://arxiv.org/abs/2503.11374
   The $^{229}Th$ isotope has a laser-accessible nuclear transition allowing the construction of a solid-state nuclear clock.
21. Learning and Predicting the Nonlinear Variability of X-ray Binaries with the Koopman Operator
   Source: nlin.CD (Chaotic Dynamics)
   Link: https://arxiv.org/abs/2609.01734
   X-ray variability in compact-object binaries encodes the nonlinear dynamics of corona-jet interactions and accretion disk instabilities.
22. Chemotaxis-induced linear instabilities and pattern formation in a reaction-diffusion model
   Source: nlin.PS (Pattern Formation and Solitons)
   Link: https://arxiv.org/abs/2609.01159
   We study linear instabilities and pattern formation in a spatially extended Selkov model for glycolysis with diffusion and chemotactic interactions between two species.
23. Elliptic spin Ruijsenaars-Schneider integrable models from 5d $\mathcal{N}=1$ gauge theories
   Source: nlin.SI (Exactly Solvable and Integrable Systems)
   Link: https://arxiv.org/abs/2608.17837
   We show that the Coulomb branches of 5d $\mathcal{N}=1$ necklace quiver gauge theories on $\mathbb{R}^3 \times T^2$ are identified with the phase spaces of elliptic spin Ruijsenaars-Schneider models with dynamical inhomogeneities.
24. Criticality of nonreciprocal phase oscillators with long-range interactions
   Source: nlin.AO (Adaptation and Self-Organizing Systems)
   Link: https://arxiv.org/abs/2606.16427
   We study noisy identical Kuramoto-Sakaguchi oscillators with phase lag $\alpha\in[0,\pi/2)$, where $\alpha>0$ induces nonreciprocal interactions.
25. Dynamical correlations across momentum scales in the quark-gluon plasma
   Source: nucl-ex (Nuclear Experiment)
   Link: https://arxiv.org/abs/2512.10265
   Experimental probes of the Quark-Gluon Plasma (QGP) generated in heavy-ion collisions span a broad range in momentum scale: low transverse momentum (low $p_T$) measurements probe collective dynamics, while high $p_T$ measurements probe the response to QGP excitation by jets (jet quenching).
26. Strong decay widths of S- and P-wave singly- and doubly-heavy charm and bottom baryons
   Source: nucl-th (Nuclear Theory)
   Link: https://arxiv.org/abs/2410.09622
   We present a study of two-body decay widths of heavy baryons into another heavy baryon and a light pseudoscalar meson in the framework of the non-relativistic quark model in combination with the elementary emission model for the strong couplings.
27. Fuzzy local reduced order models (fl-ROMs)
   Source: nlin.CD (Chaotic Dynamics)
   Link: https://arxiv.org/abs/2609.00031
   Nonlinear dynamical systems often evolve on low-dimensional manifolds with intricate geometry, making them difficult to approximate with a single global reduced-order model (ROM).
28. Painleve solitons of AKNS system and irrational algebraic solitons of NLS equations
   Source: nlin.PS (Pattern Formation and Solitons)
   Link: https://arxiv.org/abs/2602.04498
   A novel symmetry decomposition approach is introduced to derive the so-called ``Painlev\'e solitons'' of the Ablowitz-Kaup-Newell-Segur (AKNS) system.
29. Collective superintegrable systems from the Guillemin--Sternberg torus action
   Source: nlin.SI (Exactly Solvable and Integrable Systems)
   Link: https://arxiv.org/abs/2608.01878
   We present a novel approach to the superintegrability of collective Hamiltonians invariant under a Hamiltonian action of a connected semisimple compact Lie group, $G$, on a symplectic manifold, $M$.
30. Emergent aggregation from collective foraging
   Source: nlin.AO (Adaptation and Self-Organizing Systems)
   Link: https://arxiv.org/abs/2608.28046
   Collective behaviour in living systems is usually modelled as the outcome of a \emph{direct} social drive: agents are rewarded, or hard-wired, to align with or approach their neighbours.
31. Locating the QCD critical point with finite-size scaling of proton cumulants
   Source: nucl-ex (Nuclear Experiment)
   Link: https://arxiv.org/abs/2405.10278
   We perform a finite-size scaling analysis of net-proton number cumulants in Au+Au collisions at center-of-mass energies between $\sqrt{s_{\rm{NN}}} = 2.4$ and $200~\rm{GeV}$ to search for evidence of a critical point in the QCD phase diagram.
32. Data-Driven Analysis for the Bottomonium Potential in the Quark-Gluon Plasma
   Source: nucl-th (Nuclear Theory)
   Link: https://arxiv.org/abs/2512.11536
   We present a data-driven analysis within a quantum evolutionary microscopic framework to constrain the in-medium bottomonium potential.

Sources in this brief: nlin.AO (Adaptation and Self-Organizing Systems); nlin.CD (Chaotic Dynamics); nlin.CG (Cellular Automata and Lattice Gases); nlin.PS (Pattern Formation and Solitons); nlin.SI (Exactly Solvable and Integrable Systems); nucl-ex (Nuclear Experiment); nucl-th (Nuclear Theory).
Selected 32 of 485 available items for this weekly brief.