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Implementing the discontinuous-Galerkin finite element method using graph neural networks with application to diffusion equations.

Neural Netw

December 2024

Department of Earth Science and Engineering, Imperial College London, Prince Consort Road, London SW7 2BP, UK; Centre for AI-Physics Modelling, Imperial-X, White City Campus, Imperial College London, W12 7SL, UK.

Machine learning (ML) has benefited from both software and hardware advancements, leading to increasing interest in capitalising on ML throughout academia and industry. There have been efforts in the scientific computing community to leverage this development via implementing conventional partial differential equation (PDE) solvers with machine learning packages, most of which rely on structured spatial discretisation and fast convolution algorithms. However, unstructured meshes are favoured in problems with complex geometries.

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Introduction: The incorporation of health-related sensors in wearable devices has increased their use as essential monitoring tools for a wide range of clinical applications. However, the signals obtained from these devices often present challenges such as artifacts, spikes, high-frequency noise, and data gaps, which impede their direct exploitation. Additionally, clinically relevant features are not always readily available.

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Reducing the environmental pressures stemming from food production is central to meeting global sustainability targets. Shifting diets represents one lever for improving food system sustainability, and identifying sustainable diet opportunities requires computational models to represent complex systems and allow users to evaluate counterfactual scenarios. Despite an increase in the number of food system sustainability models, there remains a lack of transparency of data inputs and mathematical formulas to facilitate replication by researchers and application by diverse stakeholders.

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A potential bio-adsorbent material for removing Rhodamine B (RB) from aqueous solution is Ru-MOF@FGA/CA beads. The adsorption capability of the material is probably enhanced by the use of a natural substance made of food-grade algae (FGA) and calcium alginate (CA), which has been cross-linked and loaded with ruthenium metal-organic frameworks (Ru-MOF). The Ru-MOF@FGA/CA beads were analyzed by XPS, PXRD, FT-IR, and SEM.

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Objective: To evaluate changes in opioid prescribing and patient-reported outcomes after surgery following implementation of Michigan's prescription drug monitoring program (PDMP) use mandate in June 2018.

Background: Most states mandate clinicians to query prescription drug monitoring program (PDMP) databases before prescribing controlled substances. Whether these PDMP use mandates affect opioid prescribing and patient-reported outcomes after surgery is unclear, especially among patients with elevated "Narx" scores, a risk score for overdose death used in most PDMPs.

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