Bulletin of the Japan Society for Industrial and Applied Mathematics
Online ISSN : 2432-1982
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  • Advancements in Glucose Control Systems Based on Mathematical Models and Data-Driven Computations
    Yoshiki Sugitani, Hisatoshi Kodani
    2023 Volume 33 Issue 4 Pages 181-189
    Published: December 25, 2023
    Released on J-STAGE: March 30, 2024
    DOIhttps://doi.org/10.11540/bjsiam.33.4_181
    JOURNAL FREE ACCESS
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    This survey reviews glucose regulatory systems using mathematical methods. We discuss the utilization of various minimal and comprehensive models of glucose metabolism combined with model predictive control, data assimilation, and physics-informed neural networks to develop decision support systems. These systems will help doctors and nurses administrating insulin levels in patients with diabetes and those in intensive care units.

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  • Reaction-Diffusion Equations on Metric Graphs
    Satoru Iwasaki
    2023 Volume 33 Issue 4 Pages 190-200
    Published: December 25, 2023
    Released on J-STAGE: March 30, 2024
    DOIhttps://doi.org/10.11540/bjsiam.33.4_190
    JOURNAL FREE ACCESS
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    Partial differential equations on metric graphs represent a set of one-dimensional partial differential equations with appropriate boundary conditions. This article aims to define the concept of metric graphs and partial differential equations on such graphs. Additionally, we review some mathematical studies concerning reaction-diffusion equations on metric graphs. Notably, the behavior of solutions for these equations on metric graphs differs considerably from that in the one-dimensional case. Finally, we discuss the findings regarding a single reaction-diffusion equation on star-shaped metric graphs and propose an approach to investigate all stationary solutions for a single reaction-diffusion equation on arbitrary metric graphs.

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