Origin and evolution of circular waves and spirals in Dictyostelium discoideum territories.

Randomly distributed Dictyostelium discoideum cells form cooperative territories by signaling to each other with cAMP. Cells initiate the process by sending out pulsatile signals, which propagate as waves. With time, circular and spiral patterns form. We show that by adding spatial and temporal noise to the levels of an important regulator of external cAMP levels, the cAMP phosphodiesterase inhibitor, we can explain the natural progression of the system from randomly firing cells to circular waves whose symmetries break to form double- and single- or multi-armed spirals. When phosphodiesterase inhibitor is increased with time, mimicking experimental data, the wavelength of the spirals shortens, and a proportion of them evolve into pairs of connected spirals. We compare these results to recent experiments, finding that the temporal and spatial correspondence between experiment and model is very close.

Laws made and past by William Penn: Absolute Proprietary and Governour in Chief of the province of Pennsylvania and territories thereunto belonging, with the advice and consent of the freemen thereof in genrall assembly met at Newcastle...1700....and [as amended] at Philadelphia...1701

Contains one of the few original copies of Penn's laws as first passed and as revised and extended in the following year. During the interval between the two Assemblies, while Penn was absent in England, the first series of laws were found to be impracticable, and new amendments were made for which Penn had no choice but to agree to.

The terrestrial air-breathing mollusks of the United States, and the adjacent territories of North America: described and illustrated by Amos Binney. Ed. by Augustus A. Gould ...

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The Turkish Empire in Europe, Asia, and Africa: dividid into all its governments, together with the other territories that are tributary to it, as also the dominions of ye Emperor of Marocco [sic] according to the newest and most exact observations

by H. Moll.