Reaction-diffusion models have been used to describe pattern formation on the cellular scale, and traditionally do not include feedback between cellular shape changes and biochemical reactions. We introduce here a distinct reaction-diffusion-elasticity approach: The reaction-diffusion part describes bistability between two actin orientations, coupled to the elastic energy of the cell membrane deformations. This coupling supports spatially localized patterns, even when such solutions do not exist in the uncoupled self-inhibited reaction-diffusion system. We apply this concept to describe the nonlinear (threshold driven) initiation mechanism of actin-based cellular protrusions and provide support by several experimental observations.

We investigate the manual selection of numbers by lottery participants, with a database consisting of over 800 million selections from 118 consecutive draws of the national lottery in Israel. Our findings replicate results from prior research and introduce novel discoveries. (1) Preference for, and avoidance of, specific numbers 1 through 37 are consistent throughout all the drawings. Strong, but differing preferences are observed in the selection of the “power” number ranging from 1 to 7. (2) The number of guesses entered per draw correlates with the size of the prize, with each additional million in prize money generating 33,000 additional manual guesses. (3) Number preferences are strongly influenced by their location on the form. Numbers in the first of the four horizontal rows are consistently the most popular, while numbers in the fourth rows are consistently unpopular. (4) As the number of guesses increases, popularly chosen numbers tend to become slightly less popular, while unpopular numbers tend to become less unpopular.

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