Rigorous derivation of the 4-wave kinetic equation for the full beta-FPUT system in the joint limit N to infinity and beta to zero under weakly nonlinear scalings, reaching times up to the kinetic timescale to the power 2/3, by directly incorporating non-resonant terms in a diagrammatic expansion.
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HilbNets define convolutions via Hilbert bundle connection Laplacians, prove that sampled Hilbert cellular sheaf Laplacians converge to the continuous operator, and show that discretized networks are consistent and transferable across samplings.
Mode stability without symmetry assumptions is proved for self-similar wave map blowups in all dimensions d ≥ 4.
The fractional Massari functional Gamma-converges to the classical Massari functional, preserving minimizers, and yields limiting information for inhomogeneous Allen-Cahn equations together with the new notion of non-local hybrid mean curvature.
Comet-type periodic orbits exist in the CR3BP and undergo vertical self-resonant bifurcations up to multiplicity six in the Earth-Moon system.
Proposes six variants of individual minima-informed DM for MOMPC, including two novel ones, and embeds them in a stabilizing framework with a less restrictive descent condition than prior work.
Continued AI scaling remains feasible only if efficiency doublings recur repeatedly to keep logical compute affordable.
The survey organizes topological methods for counting solutions to Allen-Cahn equations and systems, connecting them to minimal hypersurfaces and multi-phase isoperimetric problems via Gamma-convergence.
citing papers explorer
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Rigorous Derivation of the Wave Kinetic Equation for full $\beta$-FPUT System
Rigorous derivation of the 4-wave kinetic equation for the full beta-FPUT system in the joint limit N to infinity and beta to zero under weakly nonlinear scalings, reaching times up to the kinetic timescale to the power 2/3, by directly incorporating non-resonant terms in a diagrammatic expansion.
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Consistent Geometric Deep Learning via Hilbert Bundles and Cellular Sheaves
HilbNets define convolutions via Hilbert bundle connection Laplacians, prove that sampled Hilbert cellular sheaf Laplacians converge to the continuous operator, and show that discretized networks are consistent and transferable across samplings.
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Mode stability of self-similar wave maps without symmetry in higher dimensions
Mode stability without symmetry assumptions is proved for self-similar wave map blowups in all dimensions d ≥ 4.
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$\Gamma$-convergence of the non-local Massari functional and applications to inhomogeneous Allen-Cahn equations
The fractional Massari functional Gamma-converges to the classical Massari functional, preserving minimizers, and yields limiting information for inhomogeneous Allen-Cahn equations together with the new notion of non-local hybrid mean curvature.
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Comet-type periodic motions and their out-of-plane bifurcations in the Earth-Moon CR3BP: a computational symplectic analysis
Comet-type periodic orbits exist in the CR3BP and undergo vertical self-resonant bifurcations up to multiplicity six in the Earth-Moon system.
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Individual Minima-Informed Multi-Objective Model Predictive Control for Fixed Point Stabilization
Proposes six variants of individual minima-informed DM for MOMPC, including two novel ones, and embeds them in a stabilizing framework with a less restrictive descent condition than prior work.
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Continued AI Scaling Requires Repeated Efficiency Doublings
Continued AI scaling remains feasible only if efficiency doublings recur repeatedly to keep logical compute affordable.
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Survey on topological methods for Allen--Cahn equations and systems
The survey organizes topological methods for counting solutions to Allen-Cahn equations and systems, connecting them to minimal hypersurfaces and multi-phase isoperimetric problems via Gamma-convergence.