A neglected mathematical theory is enjoying new popularity, thanks to its relevance to network dynamics in biological systems. The beating of a leech's heart is just one example that has a mathematical basis in 'groupoid theory'. The historically uneasy relation-ship between biology and mathematics has improved markedly in recent years, as it has become increasingly clear that our understanding of biological systems can benefit from mathematical input and insight. Examples include the spatial and temporal behaviour of ecosystems, the geometry of protein folding, the informatics of DNA, the dynamics of the cytoskeleton and the mechanisms of visual perception. In such areas, biologists can accumulate the key data, delineate the important interactions and suggest possible mechanisms, but at some point the questions migrate to realms that are more congenial to physicists and mathematicians. Conversely, biology poses stimulating challenges for mathematics. A case in point is network dynamics. Networks arise naturally in many areas of science, and there are numerous examples in biology: gene regulation, protein networks, epidemiology, ecological food webs, neural networks for locomotion, vision, speciation and the synchronous flashing of fireflies.
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