math papers | Gist.Science

A Stable Adaptive RBF-Meshless Collocation Framework for Nonlinear Elliptic Boundary Value Problems in Irregular Geometries with A Posteriori Error Control

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.

alaa alwan, Haeder Jasem2026-07-30

🔢 mathematics

Finite-Support Periodic Highways of Langton's Ant: Necessary Conditions, Transverse Exclusions, and Exact Search

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.

Atharva Jillhewar2026-07-30

🔢 mathematics

A Block Paige-Saunders Bidiagonalization Framework for Large-Scale Nuclear Norm Regularized Least Squares Problems

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.

Bo Feng2026-07-29

🔢 mathematics

Sparse Randomised Approximation of Normal Cycles

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.

Allen Paul, Neill Campbell, Tony Shardlow2026-07-29

🔢 mathematics

Algebraic Expressions for Directed Grid Graphs with Diagonal Edges: Decomposition Bounds, Lower Bounds, and Algebraic-Branching-Program Methods

This paper investigates formal path expressions for directed triangulated grid graphs and king graphs by establishing optimal upper and lower bounds on expression length through decomposition techniques and algebraic-branching-program methods, while also linking path-polynomial factorizations to min-cuts and two-terminal reliability.

Mark Korenblit, Vadim E. Levit2026-07-29

🔢 mathematics

Near-optimal scheduling with general service times and IHR abandonment times

This paper addresses the dynamic scheduling problem in an M/G/N queue with general service times and IHR abandonment times by proving the indexability of the associated discrete-time problem, deriving an explicit Whittle index, and demonstrating through simulations that the resulting policy systematically outperforms the standard $c\mu/\theta$ -rule.

Samuli Aalto2026-07-28

🔢 mathematics

Predictive Geometric Analysis of Even Perfect Numbers

This paper proposes a predictive geometric framework that models the structural regularities and macroscopic spacing of even perfect numbers using a characteristic quadratic mapping, offering a method to estimate higher-order candidates beyond the limits of traditional primality testing.

Shang Yu Chen2026-07-28

🔢 mathematics

Coupled Nonlinear Dynamics of Reservoir Volume and Governance Quality: Stability Analysis and Reinforcement-Learning-Based Management

This paper presents a nonlinear dynamical model coupling reservoir volume and governance quality to analyze stability and demonstrate that a reinforcement-learning-based management policy significantly reduces control costs compared to fixed-effort strategies, albeit with increased near-depletion risks, thereby highlighting the critical impact of treating governance as an endogenous state in reservoir management.

Milad tahavor, Mohsen Rabdoost Motlagh, Mohammad Mehdipour Zarrinkamar, Hossein Hosseini2026-07-28

📄 other

Stable reconstruction of a spatial source term in a time-space fractional diffusion equation using Tikhonov regularization and final-time measurements

This paper addresses the ill-posed inverse problem of reconstructing a space-dependent source term in a time-space fractional diffusion equation from noisy final-time data by establishing the well-posedness of the direct problem, formulating the inverse problem as an optimization task, and applying Tikhonov regularization with a gradient descent algorithm to achieve stable and accurate numerical reconstructions.

Ihya Talibi, Abdessamad Oulmelk2026-07-27

📄 other

Operator-based Analysis of Numerical Projection Perturbations in Grassmann Manifold Optimization

This paper establishes a complete operator-based perturbation analysis for orthogonal projectors on the Grassmann manifold, proving that tangent-structured perturbations yield an intrinsically quadratic idempotency defect with sharp spectral bounds and stability criteria, in contrast to the linear defects caused by non-tangent perturbations.

Pascal KUBWIMANA, B. Prabhakar Reddy, Jason M. Mkenyeleye2026-07-27

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