Gaussian basis functions provide an efficient and flexible alternative to spline activations in Kolmogorov–Arnold networks (KANs), but their performance is sensitive to the Gaussian scale parameter ϵ. We introduce the partition-of-unity Gaussian KAN (PU-GKAN), a kernel-based normalization framework that transfers the Shepard partition-of-unity principle to trainable KAN edge functions. Each Gaussian edge basis is normalized by its local sum over fixed centers, preserving the standard edge-based architecture and essentially the same trainable coefficient structure as GKAN. The resulting feature map reproduces constants exactly at the edge level and admits an explicit normalized finite-feature kernel interpretation.Numerical experiments show that PU-GKAN reduces sensitivity to ϵ, improves validation accuracy for most smooth and moderately non-smooth targets, and provides more stable training behavior. These benefits persist across variations in sample size and number of centers, higher-dimensional architectures, and Matérn RBF bases. PU-GKAN also improves physics-informed neural networks for Helmholtz and wave equations, with validation-error reductions of up to 90%. These results establish partition-of-unity normalization as a mathematically grounded and broadly applicable framework for improving the reliability and accuracy of radial basis function KANs. The implementation is available at https://github.com/AmirNoori68/PU-GKAN.
Research on left-behind regions increasingly emphasizes place-based and neo-endogenous development, yet how digital platforms as extra-regional actors trigger and the subsequent regional transformation in left-behind border regions of emerging economies remains underexplored. Drawing on qualitative fieldwork conducted between 2023 and 2025, this paper examines the digital transformation of imported fresh fruit distribution in Pingxiang, a county-level city in Guangxi Zhuang Autonomous Region of China along the border with Vietnam. It traces three phases of transformation of Pingxiang: platform-triggered grassroots adaptation, in which flexible border-trade arrangements enabled small traders to exploit digital platform-based market access; cooperative institutional experimentation, in which local authorities selectively incorporated extra-regional wholesale capabilities to stabilize distribution; and state-led infrastructural recentering, in which digital trade and distribution became increasingly organized through locally anchored, state-backed infrastructure under tighter border regulation. To explain these shifts, the paper develops cooperative experimental governance as a territorially embedded mode of governance through which state actors selectively coordinate with heterogeneous market actors to stabilize and redirect digital platform-triggered transformation in left-behind border regions. Digital platforms are thus understood as institutional triggers rather than stable developmental actors. The paper advances research on left-behind regions by showing that, in the digital era, regional transformation is shaped not simply by the formation of extra-regional connections, but by how these connections are organized, anchored, and reconfigured over time under specific border conditions.
We propose a hypernetwork-based framework for parametric optimal control of systems with parameterized dynamics and a Bolza-type cost functional. We employ Neural ODE-based optimization to train a hypernetwork that generates the parameters of control policy networks conditioned on system parameters, enabling amortized optimization across a distribution of tasks. The resulting model learns a task-conditioned family of feedback policies and enables zero-shot transfer to unseen parameter values without further optimization. Experiments show that the resulting feedback policies are consistent with Pontryagin's Maximum Principle solutions and achieve performance comparable to a multitask reinforcement learning baseline.
Efficient peroxymonosulfate (PMS)-based degradation of refractory antibiotics is still hindered by slow mass transfer and insufficient utilization of catalytic sites in heterogeneous systems. Although layered double hydroxide (LDH) membranes and oxygen vacancy (Ov) engineering have been explored separately, how Ovmediated PMS activation works together with nanoconfined transport remains unclear. Herein, we report an Ov-engineered CoFe-LDH catalytic membrane (LDH-8 MEM) for continuous-flow PMS activation and antibiotic degradation. The LDH-8 MEM/PMS system achieved rapid ofloxacin removal with high water permeance and an apparent pseudo-first-order rate constant of 65.09 s(-1) under continuous-flow operation. Density functional theory (DFT) calculations indicate that Ov facilitates PMS adsorption and initial O-O bond activation. Electron paramagnetic resonance (EPR) and quenching experiments suggest that O-1(2) is more involved in OFN oxidation under the tested conditions. Gaussian/Multiwfn analyses and molecular dynamics (MD) simulations suggest that PMS-pollutant hydrogen bonding and nanoconfined channels may favor local reactant enrichment and interfacial contact. This study provides insight into the coupled role of defect sites and confined membrane channels in PMS activation, offering guidance for designing efficient catalytic membranes for water purification.
