Reply to Michael Harrington

Reply to Christopher M . Jones and Michael Niederweis

Repeated evolution of digital adhesion in geckos: a reply to Harrington and Reeder.

We published a phylogenetic comparative analysis that found geckos had gained and lost adhesive toepads multiple times over their long evolutionary history (Gamble et al., PLoS One, 7, 2012, e39429). This was consistent with decades of morphological studies showing geckos had evolved adhesive toepads on multiple occasions and that the morphology of geckos with ancestrally padless digits can be ...

Neighbourhood effects and the real world beyond randomized community trials: a reply to Michael J Oakes.

We appreciate the positive opinion of Michael J Oakes 1 on our article 2 and his recognition of the contribution of our research group to the field of contextual epidemiology. We also understand that Oakes’ critics are not specifically directed at our publication but express a general concern on the use of observational approaches in research on neighbourhood and health. In the absence of rando...

The Paris-Harrington Theorem

In Ramsey theory, very large numbers and fast-growing functions are more of a rule than an exception. The classical Ramsey numbers R(n,m) are known to be of exponential size: the original proof directly gives the upper bound R(n,m) ≤ ( m+n−2 n−1 ) , and an exponential lower bound is also known. For the van der Waerden numbers, the original proof produced upper bounds that were not even primitiv...

2 Leo Harrington And

1. Introduction A set A of nonnegative integers is computably enumerable (c.e.), also called recursively enumerable (r.e.), if there is a computable method to list its elements.