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  5. Answering complex questions about textual narratives requires reasoning over both stated context and the world knowledge that underlies it. However, pretrained language models (LM), the foundation of most modern QA systems, do not robustly represent latent relationships between concepts, which is necessary for reasoning. While knowledge graphs (KG) are often used to augment LMs with structured representations of world knowledge, it remains an open question how to effectively fuse and reason over the KG representations and the language context, which provides situational constraints and nuances. In this work, we propose GreaseLM, a new model that fuses encoded representations from pretrainedmore »LMs and graph neural networks over multiple layers of modality interaction operations. Information from both modalities propagates to the other, allowing language context representations to be grounded by structured world knowledge, and allowing linguistic nuances (e.g., negation, hedging) in the context to inform the graph representations of knowledge. Our results on three benchmarks in the commonsense reasoning (i.e., CommonsenseQA, OpenbookQA) and medical question answering (i.e., MedQA-USMLE) domains demonstrate that GreaseLM can more reliably answer questions that require reasoning over both situational constraints and structured knowledge, even outperforming models 8x larger.« less
    Free, publicly-accessible full text available January 1, 2023
  6. Immersed finite element methods are designed to solve interface problems on interface- unfitted meshes. However, most of the study, especially analysis, is mainly limited to the two-dimension case. In this paper, we provide an a priori analysis for the trilinear immersed finite element method to solve three-dimensional elliptic interface problems on Cartesian grids consisting of cuboids. We establish the trace and inverse inequalities for trilinear IFE functions for interface elements with arbitrary interface-cutting configuration. Optimal a priori error estimates are rigorously proved in both energy and L2 norms, with the constant in the error bound independent of the interface locationmore »and its dependence on coefficient contrast explicitly specified. Numerical examples are provided not only to verify our theoretical results but also to demonstrate the applicability of this IFE method in tackling some real-world 3D interface models.« less
    Free, publicly-accessible full text available September 15, 2022
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  10. This paper addresses peristaltic flow induced in a non-axisymmetric annular tube by a periodic small-amplitude wave of arbitrary shape propagating axially along its inner surface, assumed to be a circular cylinder. The study is motivated by recent in vivo experimental observations pertaining to the flow of cerebrospinal fluid along the perivascular spaces of cerebral arteries. The analysis employs the lubrication approximation, describing low-Reynolds-number peristaltic flow in the long-wavelength approximation. Closed-form analytic expressions are derived for the average pumping rate in infinitely long tubes and also in tubes of finite length. Consideration is also given to the transverse motion arising inmore »non-axisymmetric tubes. For small-amplitude waves, the solution is reduced to the integration of a parameter-free Stokes-flow problem, which is solved for relevant cross-sectional shapes, with closed-form analytical results derived for thin canals.« less
    Free, publicly-accessible full text available August 25, 2022