The Geometry of Biological Time by Arthur T. Winfree

By Arthur T. Winfree

Facing dynamics of methods that repeat themselves on a regular basis, this revised and up-to-date variation extends the thread from 1980 to the current day, targeting components of curiosity the place there'll be a lot job sooner or later. This includes facing spatial biochemical, electrophysiological, and organismic dynamical structures and styles that have been came across through pursuing the subject of section singularities brought within the unique e-book. particularly the paintings on excitability in mobilephone membranes might be completely up to date as will the references in the course of the ebook.

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Five more such appear on p. 304 of The Handbook of Behavioral Neurobiology volume 4 (1981), ed. J. Aschoff. B: MAPPINGS 21 w Figura 20. Eaeh point of the frontier ring of arhythmie fungus maps to the phase of the loeal rhythm at that point. In this example every point maps within about one-fifth of the eyde. Points at the same north-south latitude are mapped to the same phase. Figura 21. A eatalog advertisement for a Dove prism and , ..... _- a seene viewed through a Dove prism image rotator. Example H.

In fact the wondrous deviee is nothing more than a mirror with refraeting prisms to straighten out the refleeted optical axis (Figure b, bottom). different properties. Such maps and their winding numbers play an essential role in much that follows. We begin with four examples: Example A. , glycolysis in yeast cells (Chapter 12), is going on in each of two equal volumes. Ghosh et al. (1971) made the intriguing discovery that when such volumes are abruptly combined, the hybrid B: MAPPINGS -9 RING OF TISSUE U'J$distance) IMAGED ON 23 '" CIRCLE OF STATES (9-= time) 9 :s; rP <1.

9. ßl -t §1: Input a number between 0 and 1, output a point on a cirele or ring. An example is the inverse of map 6, which necessarily suffers the same discontinuity though in reverse: While nearby numbers always map to nearby points on the ring, so do some quite different numbers near the extremes of the interval. This underlies the necessity of an International Date Line (see Box A) and accounts for the principal annoying feature of compasses and protractors: We have to remember that 360 0 is the same as 00 • Figure 9 depicts this map as an image of 01 in the product cylinder 01 x § 1• This picture is equivalent to Figure 6.

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