The Spruce Budworm and Forest: A Qualitative Comparison of ODE and Boolean Models

Boolean and polynomial models of biological systems have emerged recently as viable companions to differential equations models. It is not immediately clear however whether such models are capable of capturing the multi-stable behaviour of certain biological systems: this behaviour is often sensitive to changes in the values of the model parameters, while Boolean and polynomial models are qualitative in nature. In the past few years, Boolean models of gene regulatory systems have been shown to capture multi-stability at the molecular level, confirming that such models can be used to obtain information about the system’s qualitative dynamics when precise information regarding its parameters may not be available. In this paper, we examine Boolean approximations of a classical ODE model of budworm outbreaks in a forest and show that these models exhibit a qualitative behaviour consistent with that derived from the ODE models. In particular, we demonstrate that these models can capture the bistable nature of insect population outbreaks, thus showing that Boolean models can be successfully utilized beyond the molecular level

On the Equality of Sharp and Germ - Fields for Gaussian Processes and Fields

2000 Mathematics Subject Classification: 60G15, 60G60; secondary 31B15, 31B25, 60H15We investigate the relationship between the sigma-field and the infinitesimal or germ sigma-field

Can We Bridge the Gap? Mathematics and the Life Sciences: Part 2–Discrete Models, Statistics, Co-Curricular Opportunities

This editorial serves as an introduction to Part 2 of the Special Issue Mathematics and the Life Sciences–a collection of articles showcasing ideas, examples, pedagogical frameworks, and curricular materials aiming to bridge the stubbornly persistent gap at the undergraduate level between the mathematical and the life sciences. The special issue features authors from public and private institutions of diverse types, sizes, and geographic locations: community colleges, liberal arts colleges, and research-oriented universities. We hope this special issue will serve as a resource to faculty who seek to make changes to their own course(s) or initiate curriculum reforms at their own schools. This Part 2 special issue features course materials and programs based on discrete mathematics, computational approaches, and statistics. It also includes articles on internship programs and co-curricular opportunities. Part 1 focuses on educational initiatives that are appropriate for calculus classes or require calculus as a prerequisite

Can We Bridge the Gap? Mathematics and the Life Sciences, Part 1–Calculus-Based Modules, Programs, Curricula

This editorial serves as an introduction to Part 1 of the Special Issue Mathematics and the Life Sciences–a collection of articles showcasing ideas, examples, pedagogical frameworks, and curricular materials aiming to bridge the stubbornly persistent gap at the undergraduate level between the mathematical and the life sciences. The special issue features authors from public and private institutions of diverse types, sizes, and geographic locations: community colleges, liberal arts colleges, and research-oriented universities. We hope this special issue will serve as a resource to faculty who seek to make changes to their own course(s) or initiate curriculum reforms at their own schools. Part 1 focuses on educational initiatives that are appropriate for Calculus classes or require calculus as a prerequisite. Part 2 of the special issue features course materials and programs based on discrete mathematics, computational approaches, and statistics. Part 2 also includes articles on internship programs and co-curricular opportunities

Editorial: Machine Learning in Natural Complex Systems

International audienc