141 papers
This paper introduces MELMO, a Moreau envelope smoothing algorithm utilizing linear minimization oracles that achieves explicit convergence trade-offs and establishes rates for composite stationarity in weakly convex optimization problems with non-Euclidean structures.
This paper presents a novel 1D coupling method for local and nonlocal diffusion problems that exclusively utilizes local boundary conditions to achieve a seamless, natural integration with quantifiable convergence, verified through finite element and Galerkin projection discretizations.
This paper establishes fundamental theoretical limits on Hessian recovery from one-sided directional curvature measurements—including identifiability, conditioning, and parity constraints—and provides a rigorously controlled comparison of eight estimators under oracle-optimal sampling conditions.
This paper distinguishes between genuine Lie point symmetries and equivalence transformations in a three-compartment HIV model, demonstrating that while only time translation is a true symmetry, rescaling parameters alongside populations yields an equivalence group that reduces the system to a dimensionless form while preserving its key dynamical properties.
This paper demonstrates that machine learning techniques, including unsupervised clustering, supervised classification, and symbolic regression, can effectively uncover the phase structures, algebraic invariants, and transferable dynamical fingerprints of Clifford- and Grassmann-valued cellular automata, revealing how metric signatures and normalization protocols influence the emergence of order, chaos, and algebraic diversity.
This paper investigates the steady-state bifurcation and pattern formation in a three-component immune chemotaxis model with volume-filling effects by establishing the existence, direction, and stability of nonconstant solutions and demonstrating how cellular crowding influences spatial dynamics.
This paper presents a stable, adaptive RBF-meshless collocation framework with a posteriori error control that effectively solves nonlinear elliptic boundary value problems on irregular geometries, demonstrating superior accuracy and efficiency compared to uniform methods through local scaling, poly-augmentation, and an automated refinement loop.
This paper establishes decidable necessary-and-sufficient conditions for the existence of finite-support periodic highways in Langton's Ant, proving that diagonal drifts require a minimum width of six and excluding all periods up to 48 through a combination of theoretical rigidity theorems and computer-assisted verification.
This paper proposes a block Paige-Saunders bidiagonalization framework that projects large-scale nuclear norm regularized least squares problems onto a block Krylov subspace for efficient solution via the primal accelerated proximal gradient method, featuring proven linear convergence, a restarted variant to manage memory, and demonstrated superior computational efficiency in numerical experiments.
This paper presents a theoretically guaranteed, sparse randomized compression algorithm for normal cycles using Nystrom approximation and Ridge Leverage Score sampling, which significantly accelerates large-scale nonlinear shape registration tasks within the LDDMM framework while maintaining high accuracy even at extreme compression ratios.