A shape theorem for an epidemic model in dimension d≥3d\ge 3

We prove a shape theorem for the set of infected individuals in a spatial epidemic model with 3 states (susceptible-infected-recovered) on ${\mathbb Z}^d,d\ge 3$, when there is no extinction of the infection. For this, we derive percolation estimates (using dynamic renormalization techniques) for a locally dependent random graph in correspondence with the epidemic model.Comment: 39 pages; soumi

Circatidal and Circadian Rhythms of Locomotion in Limulus polyphemus

The nocturnal increases in the sensitivity of the lateral eye of Limulus polyphemus, the species of horseshoe crab found along the Atlantic coast, have been firmly established as being controlled by an endogenous circadian clock (1,2,3) located in the brain (4). Virtually nothing is known, however, about the control of the animal’s behavioral rhythms of mating and spawning that are observed in the intertidal zone during high tides in late spring (5,6,7). Many other marine species, especially intertidal crabs, exhibit similar rhythmic behaviors that have been demonstrated to be under the control of endogenous clocks that are circatidal (8,9,10,11,12), circadian (10,12), or both. While there is some evidence that the activity of juvenile horseshoe crabs is primarily nocturnal (13,14), and possibly controlled by a circadian clock (14), we know of no published work showing that locomotor activity in the adult is endogenously controlled on either a 12.4-h (circatidal) or 24-h (circadian) basis. We report here that locomotor activity in adult individuals of L. polyphemus is endogenously modulated on both a circatidal and a circadian basis and that when the animals are subjected to a light-dark (LD) cycle, most activity occurs at night