2332 papers
Mathematics of Oceanography and Climate, often abbreviated as Math-Oc, sits at the vibrant intersection where complex equations meet the dynamic reality of our planet's waters. This field uses rigorous mathematical modeling to decode the swirling currents of the ocean, predict shifting weather patterns, and understand how heat moves through our climate system. It transforms abstract theory into vital insights that help scientists anticipate environmental changes and protect coastal communities.
Gist.Science curates the very latest research in this critical area directly from arXiv, the leading preprint server for the mathematical community. For every new submission, we provide two distinct perspectives: a clear, plain-language summary for the curious reader and a detailed technical breakdown for experts. This dual approach ensures that groundbreaking discoveries remain accessible to everyone, from students to seasoned researchers. Below are the latest preprints in Math-Oc, freshly processed and ready for exploration.
This paper introduces a method to transform non-commutative polynomial optimization problems with differential constraints into standard forms solvable by a complete hierarchy of semidefinite programming relaxations, demonstrating its effectiveness in approximating local observable averages in quantum spin systems under Hamiltonian evolution even in the thermodynamic limit.
This paper formulates and numerically solves an optimal switching control problem for dam management under climate change by modeling clustered rainfall and dry spells with a Hawkes process, revealing that increased event clustering shifts the optimal strategy toward prioritizing flood protection over water storage.
This paper introduces iR2N, an inexact modified proximal quasi-Newton method for nonconvex regularized optimization that achieves global convergence with complexity by allowing controlled inaccuracies in function, gradient, and proximal operator evaluations to significantly reduce computational effort.
This paper introduces LyaGuide, a unified framework that stabilizes generative flow matching by formulating guidance as a Lyapunov control problem, thereby providing explicit stability guarantees and unifying various existing guidance strategies through a novel pseudo-projection operator.
This study demonstrates that adaptive Runge-Kutta step control in optimizers fails to improve generalization or training loss compared to standard Adam under strict compute-matched conditions, as its adaptivity is illusory and its benefits are either fragile, replicable by cheaper first-order methods, or limited to a small regularization effect from gradient averaging.
This paper proposes a state-dependent scaled projection neural network (SD-SPNN) that embeds continuous-time preconditioning into the projection operator to improve convergence and conditioning for solving variational inequalities, while rigorously establishing its existence, equilibrium correspondence, and stability properties.
This paper proves the conjecture that bounded second-order heterogeneity enables improved convergence rates for Local SGD on general convex objectives, establishes nearly tight upper and lower bounds to refine the theoretical understanding of the algorithm, and extends these techniques to derive new lower bounds for serial SGD with replacement.
This paper proposes a novel slow-fast stochastic framework for distributed time-varying optimization in multi-agent systems using only zero-order information, which employs auxiliary fast subsystems to generate smooth gradient estimates while ensuring the slow subsystem achieves practical fixed-time consensus and asymptotically bounded tracking of the optimal trajectory.
This paper proposes a training-free steering method called WA-LQR that leverages mechanistic interpretability and optimal control to enhance the robustness of World Action Models against distribution shifts by exploiting low-dimensional linear separability in their activation spaces.
This paper establishes certified global optimal configurations for Heilbronn's triangle problem in a unit right triangle for up to points by proving a boundary-structure theorem and employing a mixed-integer model, thereby resolving previously open cases and confirming the conjectured optimum while demonstrating its non-expressibility in radicals.