276 papers
This paper proposes a regularization-free variance component estimation framework for linear ill-posed models that utilizes null-space projections to eliminate unknown parameters and estimate variances directly from unbiased misclosures, thereby overcoming the bias, instability, and computational inefficiency inherent in conventional regularization-dependent approaches.
This descriptive-evaluative study audits ChatGPT and Gemini's performance in applied differential calculus, revealing that while both models can execute isolated procedures, they frequently fail in translating narrative conditions to functions, handling boundary constraints, and maintaining arithmetic consistency, thereby suggesting their solutions should be used as critique artifacts rather than unquestioned answers in education.
This paper demonstrates that spectral localization in complex networks fundamentally shifts the understanding of macroscopic dynamics from global eigenmodes to the local behavior of dominant nodes, thereby enabling a node-resolved framework that identifies microscopic drivers and predicts transitions in heterogeneous systems where classical stability theories fail.
This paper introduces a nonlocal variational model for thin films and establishes the -convergence of convolution-type functionals to a local integral functional on a lower-dimensional domain, characterizing the limit energy density through an asymptotic formula that reveals a scale separation effect under periodic homogenization.
This paper introduces a discriminant-guided preprocessing method implemented in Macaulay2 that accelerates the computation of local solutions for second-order Euler-type differential operators near x = 0 by detecting complex conjugate indicial roots to construct an oscillatory basis, thereby reducing symbolic branch-management overhead and execution time without impacting non-oscillatory cases.
This paper demonstrates that processing delays in institutional regulation alone can destabilize otherwise stable multi-agent systems through a supercritical Hopf bifurcation, causing large-amplitude oscillations in reactive agents while fixed-policy agents remain immune and Q-learning agents exhibit partial resilience due to memory-based damping.
This paper introduces a new generalized Fermat–Torricelli–Weber problem and a corresponding subgradient algorithm within a unified Hilbert space framework that connects it to mixed split feasibility problems, establishing convergence results and demonstrating practical applications in image deblurring.
This paper establishes the global well-posedness and threshold dynamics of a spatially heterogeneous SVEIAR-B reaction-diffusion epidemic model incorporating media intervention, demonstrating that disease extinction or persistence is determined by the basic reproduction number while highlighting the critical roles of media intensity, vaccination, and spatial heterogeneity in shaping epidemic outcomes.
This paper introduces and validates a scalar order parameter that quantifies the splitting between Lyapunov branches in non-Abelian oscillator networks, demonstrating its utility as a robust measure of non-Abelian synchronization effects in systems even under non-Hermitian perturbations.
This paper proposes a unified regularized multiwavelet collocation framework for solving ill-posed Fredholm integral equations of the first kind, demonstrating that basis selection is a critical component of the regularization strategy that directly influences stability, noise sensitivity, and reconstruction accuracy across different smoothness regimes.