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In reading garden-path sentences, people must resolve competing interpretations, though initial misinterpretations can linger despite reanalysis. This study examines the role of inhibitory control (IC) in managing these misinterpretations among Chinese-English bilinguals. Using self-paced reading tasks, we investigated how IC influences recovery from garden-path sentences in Chinese (L1) and its interaction with language proficiency during English (L2) processing. Results indicate that IC does not affect garden-path recovery in Chinese, suggesting reliance on semantic context may reduce the need for IC. In contrast, findings for English L2 learners reveal a complex relationship between language proficiency and IC: Participants with low L2 proficiency but high IC showed lingering misinterpretations, while those with high proficiency exhibited none. These results support and extend the Model of Cognitive Control (Ness et al., 2023). Moreover, our comparison of three Stroop task versions identifies L1 colour-word Stroop task as the preferred measure of IC in bilingual research.

Little seems to be known about the invariant manifolds for stochastic partial differential equations (SPDEs) driven by nonlinear multiplicative noise. Here we contribute to this aspect and analyze the Lu-Schmalfu{\ss} conjecture [Garrido-Atienza, et al., J. Differential Equations, 248(7):1637--1667, 2010] on the existence of stable manifolds for a class of parabolic SPDEs driven by nonlinear mutiplicative fractional noise. We emphasize that stable manifolds for SPDEs are infinite-dimensional objects, and the classical Lyapunov-Perron method cannot be applied, since the Lyapunov-Perron operator does not give any information about the backward orbit. However, by means of interpolation theory, we construct a suitable function space in which the discretized Lyapunov-Perron-type operator has a unique fixed point. Based on this we further prove the existence and smoothness of local stable manifolds for such SPDEs., Comment: To appear in Journal of Functional Analysis