Interdisciplinary Mathematics Applications in Biology, Environment, and Engineering
Key Questions
What interdisciplinary applications of mathematics are featured?
Contributions span biology, environment, and engineering, including Lie symmetries for physiological systems, data-driven wildfire models using wSINDy, elk-wolf predator-prey dynamics, and magnetic-particle vesicle rupture for drug delivery.
How is mathematics improving environmental and ecological modeling?
Examples include diffusion kinetics for liquid hydrogen, symbolic dynamics in tent maps, dengue forecasting models, and EcoBOT Gaussian processes that boost plant biology reproducibility by 30%. A 140-year oncology modeling review is also noted.
What is the Mean Field Games approach for public sentiment forecasting?
It applies rigorous game theory and PDEs to forecast sentiments, using convexification methods and global convergence proofs. This SIAM work bridges applied math with social science applications.
Are there engineering-focused mathematical advances mentioned?
Yes, such as numerical methods for Hamilton-Jacobi equations, fractional Chen financial systems with memory, and priority-queue-free Hausdorff distance for mesh simplification. Optimal water distribution models for multi-level systems are also covered.
How does physiology integrate with mathematical modeling here?
Bayesian data-driven approaches incorporate physiology to refine estimates in complex processes. Lie symmetries help identify conservation laws in physiological differential equation systems.
A growing stream of applied math contributions with clear real-world impact. Recent papers include: Lie symmetries for identifying conservation laws in physiological systems (differential equations + systems medicine); diffusion kinetics in liquid hydrogen; shape space analysis; numerical methods for Hamilton-Jacobi equations; data-driven wildfire spread models (wSINDy); symbolic dynamics in tent maps; 140-year review of oncology modeling; elk-wolf predator-prey model in Yellowstone; EcoBOT using Gaussian processes for plant biology (30% reproducibility improvement); magnetic-particle-driven vesicle rupture for drug delivery (PRL 2026); fractional Chen financial system with memory; dengue/chikungunya forecasting models; and more. New: Forecasting Public Sentiments via Mean Field Games (SIAM) — rigorous applied math bridging game theory, PDEs, and social science with convexification method and global convergence proof. These demonstrate strong math-bio/environment/engineering intersections.