Clay weekly context brief for the Nonlinear Sciences category (ISO week 2026-W44).

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. Bifurcations from Weight Space: JEPAWG on Parametric Dynamical Systems
   Source: nlin.CD (Chaotic Dynamics)
   Link: https://arxiv.org/abs/2610.30847
   Trained network weights are increasingly treated as data, but there is rarely ground truth about what a population of models should encode, which hampers systematic validation of weight-space methods.
2. Modulation theory of Y- and X-wave Kadomtsev--Petviashvili solitons
   Source: nlin.PS (Pattern Formation and Solitons)
   Link: https://arxiv.org/abs/2610.31425
   The evolution of long wavelength perturbations of traveling wave 2-soliton solutions of the Kadomtsev-Petviashvili II (KP) equation are investigated using modulation theory.
3. On Borodin-Gorin presentation of Heckman-Opdam $\mathfrak{gl}_n$ hypergeometric function
   Source: nlin.SI (Exactly Solvable and Integrable Systems)
   Link: https://arxiv.org/abs/2610.30304
   We prove that Borodin-Gorin presentation for Heckman-Opdam $\mathfrak{gl}_n$ hypergeometric function by interlacing integrals is equivalent to two other integral presentations studied in arXiv:2508.18864.
4. Lifetime of the singly charged $^{229}$Th nuclear isomer
   Source: nucl-ex (Nuclear Experiment)
   Link: https://arxiv.org/abs/2610.31009
   The nucleus of thorium-229 ($^{229}$Th) has an exceptionally low-energy isomeric state ($^{229\mathrm{m}}$Th).
5. Anisotropic spin hydrodynamics in a magnetized medium: entropy-current formulation and minimal linear modes
   Source: nucl-th (Nuclear Theory)
   Link: https://arxiv.org/abs/2610.31408
   We formulate anisotropic relativistic spin hydrodynamics in a parity-even magnetized medium using an Israel--Stewart entropy-current construction.
6. Condensation and optimal targeting of repeated forcing in heterogeneous networks
   Source: nlin.AO (Adaptation and Self-Organizing Systems)
   Link: https://arxiv.org/abs/2610.29714
   Many networks receive repeated external forcing through a subset of entry nodes, for example infections imported from another population, information seeded by a campaign, or invasive species arriving through ports.
7. Idempotence criteria for lazy cellular automata
   Source: nlin.CG (Cellular Automata and Lattice Gases)
   Link: https://arxiv.org/abs/2610.11811
   A lazy cellular automaton $\tau:A^G\to A^G$ is determined by a finite neighborhood $S\subseteq G$ containing the group identity $e$, a pattern $p\in A^S$, and a writing symbol $a\in A\setminus\{p(e)\}$: its local rule is equal to the projection to $e$ except when it reads the pattern $p$, in which case it writes $a$.
8. Sparse SYK quantum batteries: Boosting quantum efficiency by reducing complexity
   Source: nlin.CD (Chaotic Dynamics)
   Link: https://arxiv.org/abs/2505.17679
   In the context of energy storage at the nanoscale, exploring the notion of quantum advantage implies walking on the thin line at the boundary between quantum mechanics and thermodynamics, which underpins our conventional understanding of battery devices.
9. Stationary and switching synchronization states in an ensemble of four nonidentical phase oscillators with repulsive couplings
   Source: nlin.PS (Pattern Formation and Solitons)
   Link: https://arxiv.org/abs/2511.16307
   This study investigates the collective dynamics (phase synchronization, instantaneous frequencies synchronization and mean frequencies synchronization) in an ensemble of four nonidentical phase oscillators with repulsive coupling.
10. Rational limit of Rains integrals of type $A_n$
   Source: nlin.SI (Exactly Solvable and Integrable Systems)
   Link: https://arxiv.org/abs/2610.30317
   We deduce the rational analogue of the elliptic Rains identity of type $A_n$ arXiv:0309252. We also derive reductions of the rational analogue and present the connection of them with well-known integrals in literature.
11. Unfolding the low-energy reactor neutrino flux from CE$\nu$NS data with a finite Dirac sum
   Source: nucl-ex (Nuclear Experiment)
   Link: https://arxiv.org/abs/2608.16107
   We present a novel method to analyze coherent elastic neutrino--nucleus scattering (CE$\nu$NS) data to extract the reactor antineutrino spectrum below the inverse beta decay threshold of 1.8 MeV, where it remains unmeasured.
12. Can Coulomb breakup of $N=Z$ clustered nuclei constrain capture cross sections? Analyzing the $\alpha(d,\gamma){}^{6}\mathrm{Li}$ case
   Source: nucl-th (Nuclear Theory)
   Link: https://arxiv.org/abs/2610.31514
   In nuclear astrophysics, it is fundamental to measure the cross section of radiative-capture reactions involving charged particles at low energy.
13. Ising-machine-like Driving Condition Restrictions in SSBM and Additional Pseudo-annealing- Driving Method for SSBM that Achieves Best Cut Value Search -
   Source: nlin.AO (Adaptation and Self-Organizing Systems)
   Link: https://arxiv.org/abs/2608.12545
   In our previous work, we proposed and experimentally demonstrated a physics-based simulator for combinatorial optimization problems (SSBM), which exploits a distinctive spontaneous symmetry breaking (SSB) phenomenon identified in a dissipative system exhibiting robust causality described by an iterative equation.
14. Frobenius Revivals in Laplacian Cellular Automata: Replication, Entropy, and Information Recovery
   Source: nlin.CG (Cellular Automata and Lattice Gases)
   Link: https://arxiv.org/abs/2511.17389
   We investigate Frobenius revivals in prime-modulus Laplacian cellular automata.
15. Digital Twins of Networked Dynamical Systems: Machine Learning Prediction of Synchronization Transitions in Coupled Chaotic Oscillators
   Source: nlin.CD (Chaotic Dynamics)
   Link: https://arxiv.org/abs/2610.30632
   Collective behaviors such as synchronization transitions are emergent properties of coupled oscillator systems, and how to reproduce them from data for large-scale systems remains an open problem.
16. Lattice Brownian bees with cooperative reproduction: steady states, collapse, and spreading
   Source: nlin.PS (Pattern Formation and Solitons)
   Link: https://arxiv.org/abs/2605.29958
   We extend the ``Brownian bees'' model of Berestycki et al.\ (2021, 2022) to cooperative reproduction, $kA\to(k{+}1)A$, of a population of $N$ symmetric random walkers with removal, at each birth event, of the particle farthest from the origin.
17. Quantum K-structure constants and cylindric Grothendieck polynomials for Grassmannians
   Source: nlin.SI (Exactly Solvable and Integrable Systems)
   Link: https://arxiv.org/abs/2610.31607
   We use the partition functions of a five-vertex exactly solvable lattice model from statistical mechanics to give new combinatorial formulae for the Schubert structure constants of torus-equivariant quantum K-theory rings of Grassmannians.
18. Track finding and particle identification performance with particle physics foundation models
   Source: nucl-ex (Nuclear Experiment)
   Link: https://arxiv.org/abs/2610.31180
   Modern high energy nuclear and particle physics experiments produce large amounts of sparse data that must be reduced significantly in size before performing physics analysis.
19. Nonconformal kinetic theory with transverse dynamics and event-by-event simulations using CoMBolt-RTA
   Source: nucl-th (Nuclear Theory)
   Link: https://arxiv.org/abs/2610.31611
   A new version of CoMBolt, called CoMBolt-RTA, is introduced to solve the Boltzmann equation for massive quasiparticles in the relaxation time approximation (RTA).
20. Predator-Prey Model: Driven Hunt for Accelerated Grokking
   Source: nlin.AO (Adaptation and Self-Organizing Systems)
   Link: https://arxiv.org/abs/2509.10562
   A machine learning method is proposed using two agents (representing two coupled replicas of the model parameters) that simulate the biological behavior of a predator and a prey.
21. When do lazy and invertible cellular automata generate all cellular automata?
   Source: nlin.CG (Cellular Automata and Lattice Gases)
   Link: https://arxiv.org/abs/2610.18480
   Let $G$ be a group and let $A$ be a set with at least two elements.
22. Physics is the Best Teacher: Consistency Learning for Time-Invariant Operators of Chaotic Dynamics
   Source: nlin.CD (Chaotic Dynamics)
   Link: https://arxiv.org/abs/2610.04108
   Accelerating the prediction of long-term behavior in chaotic systems is crucial in scientific computing.
23. Phenotype-structured nonlocal aggregation models I: signal production and response
   Source: nlin.PS (Pattern Formation and Solitons)
   Link: https://arxiv.org/abs/2610.29884
   Individuals within a cellular or ecological population can exhibit substantial variation in their traits or phenotype.
24. The gauge action on semi-discrete Lax representations, its invariants, and Lax-Miura type constructions
   Source: nlin.SI (Exactly Solvable and Integrable Systems)
   Link: https://arxiv.org/abs/2604.20830
   We introduce and study explicit invariants with respect to the action of (local) gauge transformations on the set of semi-discrete (differential-difference) matrix Lax representations (MLRs) for a given (1+1)-dimensional evolutionary differential-difference equation with any number of components.
25. Remarks on MAMI's recent determination of $B_{\Lambda}({_{\Lambda}^3}{\rm H})$
   Source: nucl-ex (Nuclear Experiment)
   Link: https://arxiv.org/abs/2604.18259
   A recent report on ${^7{\rm Li}}(e,e'K^+)$ electroproduction runs by the A1 collaboration at the Mainz Microtron (MAMI) assigns a sharp pion-momentum line at $p_{\pi^-}\approx 113.8\pm 0.1$ MeV/c to ${_{\Lambda}^3}{\rm H}\to\pi^-+{^3{\rm He}}$ weak decay, resulting in exceptionally large ${_{\Lambda}^3}{\rm H}$ binding-energy $B_{\Lambda}({_{\Lambda}^3}{\rm H})=0.523\pm 0.013\pm 0.075$ MeV.
26. Parton distribution functions of the proton in a hot isospin-asymmetric nuclear medium and finite nuclei
   Source: nucl-th (Nuclear Theory)
   Link: https://arxiv.org/abs/2610.31122
   When a nucleon is bound in a nucleus, its quark distributions are modified, and the change in the spin-dependent distributions can differ in size from that in the spin-independent ones.
27. Does a Flux-Defined Markov Blanket Screen Self-Replicating Gray--Scott Spots? A Computational Test of a Blanket Condition from the Free Energy Principle
   Source: nlin.AO (Adaptation and Self-Organizing Systems)
   Link: https://arxiv.org/abs/2610.27235
   Friston's free energy principle holds that a system separated from its environment by a Markov blanket---a boundary whose states statistically screen its interior from its exterior---can be treated as performing approximate Bayesian inference, and that such blankets arise wherever coupling is short-range.
28. Geometry-Controlled Initial-Density Dependence in Branching-Merging Exclusion Processes
   Source: nlin.CG (Cellular Automata and Lattice Gases)
   Link: https://arxiv.org/abs/2610.15333
   We study geometry-controlled, initial-density-dependent stationary states in exclusion processes with branching-merging structures.
29. Reduction of Decaying Navier--Stokes Turbulence to the Quantum Pendulum
   Source: nlin.CD (Chaotic Dynamics)
   Link: https://arxiv.org/abs/2607.05745
   The statistics of a classical flow is a problem of quantum mechanics in loop space, and not by analogy: the loop functional of any flow is the loop-ordered exponential of the covariant derivative $\partial+\mathrm{i}v/\nu$.
30. Quantum vacuum inversion and multi-kink unbinding in the non-degenerate double sine-Gordon model
   Source: nlin.PS (Pattern Formation and Solitons)
   Link: https://arxiv.org/abs/2609.24861
   Quantum fluctuations can unbind a composite soliton while the correction to its mass stays small.
31. Exact spectral integrability of a finite-channel random Schr\"odinger operator: from fermionization of the Dyson--Riccati gas to Kontsevich integral
   Source: nlin.SI (Exactly Solvable and Integrable Systems)
   Link: https://arxiv.org/abs/2610.27154
   We solve exactly, for arbitrary finite channel number $N$, the Riccati dynamics of a quasi-one-dimensional random matrix Schr\"odinger operator with Hermitian white-noise potential in the $\beta=2$ unitary symmetry class.
32. \textit{Ab initio} no-core shell model calculations of the electric dipole polarizabilities and photoabsorption cross sections of the $A=3$ mirror nuclei
   Source: nucl-ex (Nuclear Experiment)
   Link: https://arxiv.org/abs/2610.29711
   We present \textit{ab initio} no-core shell-model calculations of the electric dipole ($E1$) polarizabilities and photoabsorption cross sections of the $A=3$ mirror nuclei $^3$H and $^3$He using the Daejeon16 nucleon-nucleon interaction.
33. Mass-Dependent Non-Extensivity in Tsallis Blast-Wave Fits to Identified Hadron $p_T$ Spectra at RHIC and LHC
   Source: nucl-th (Nuclear Theory)
   Link: https://arxiv.org/abs/2606.24777
   We analyze identified-hadron transverse-momentum spectra from STAR Au+Au and ALICE Pb+Pb collisions over $\sqrt{s_{NN}} = 7.7$~GeV--$5.02$~TeV using an extended Tsallis Blast-Wave (TBW) framework, which includes a non-extensivity parameter $q$ to quantify the degree of incomplete thermal equilibrium.

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 33 of 474 available items for this weekly brief.