This chapter describes the development of a math trail for high school students. In 2016, we developed this trail through Leiden (The Netherlands) during a student project for the Science... Show moreThis chapter describes the development of a math trail for high school students. In 2016, we developed this trail through Leiden (The Netherlands) during a student project for the Science Communication and Society specialization, a track for master students at the Faculty of Science at Leiden University. Our aim was to provide a guided trail through the city that links everyday sights to mathematical concepts within the curriculum of high school students between 13 and 15 years old. The entire project was carried out in 3 weeks. We did background research, consisting of literature reviews, target audience surveys with school children, and focus groups with teachers. Based on the conclusions from this background research, we developed questions that suited both the goal to make the math trail a fun experience that makes math less abstract and the goal to include questions from across the curriculum. In this chapter, we would like to share our insights from the background research and our experiences in developing a math trail. We moreover aim to provide those who are interested in designing a math trail in their city with a practical step-by-step plan and checklist. Show less
The cellular Potts model (CPM, a.k.a. Glazier–Graner–Hogeweg or GGH model) is a somewhat liberal extension of probabilistic cellular automata. The model is derived from the Ising and Potts models... Show moreThe cellular Potts model (CPM, a.k.a. Glazier–Graner–Hogeweg or GGH model) is a somewhat liberal extension of probabilistic cellular automata. The model is derived from the Ising and Potts models and represents biological cells as domains of CA-sites of the same state. A Hamiltonian energy is used to describe the balance of forces that the biological cells apply onto one another and their local environment. A Metropolis algorithm iteratively copies the state from one site into one of the adjacent sites, thus shifting the domain interfaces and moving the biological cells along the lattice. The approach is commonly used in applications of developmental biology, where the CPM often interacts with systems of ordinary-differential equations that model the intracellular chemical kinetics and partial-differential equations that model the extracellular chemical signal dynamics to constitute a hybrid and multiscale description of the biological system. In this chapter we will introduce the cellular Potts model and discuss its use in developmental biology, focusing on the development of blood vessels, a process called vascular morphogenesis. We will start by introducing a range of models focusing on uncovering the basic mechanisms of vascular morphogenesis: network formation and sprouting and then show how these models are extended with models of intracellular regulation and with interactions with the extracellular micro-environment. We then briefly review the integration of models of vascular morphogenesis in several examples of organ development in health and disease, including development, cancer, and age-related macular degeneration. We end by discussing the computational efficiency of the CPM and the available strategies for the validation of CPM-based simulation models. Show less
In January 1970, computer scientist Leo Geurts walked into Swart Gallery in Amsterdam, The Netherlands, to see the solo exhibition by Dutch artist Peter Struycken (The Netherlands, 1939). He was... Show moreIn January 1970, computer scientist Leo Geurts walked into Swart Gallery in Amsterdam, The Netherlands, to see the solo exhibition by Dutch artist Peter Struycken (The Netherlands, 1939). He was struck by Struycken’s black and white works “Computerstructuren” (1969), which were painted after grid patterns generated by algorithms. Geurts assumed that they must have been produced using cellular automata. He started working with Lambert Meertens at Mathematisch Centrum (now CWI) in Amsterdam to make a similar work. Show less
