The ob gene was cloned in 1994 using the methodology of positional cloning. Leptin, the protein encoded by the ob gene, was identified in 1995 and shown to be a hormonal signal that regulates energy balance.14 Since its discovery 15 years ago, 30,943 articles on leptin have been written (S Korres, personal communication, 2009), providing an opportunity to assess, with some hindsight, the impact...

The last theorem of Lecture 9 assures us that in any Büchi game one of the two players has a positional winning strategy. Thus, for any alternating Büchi automaton (ABA ) A and word w, either the automaton or the pathfinder has a positional winning strategy in the game G(A,w). Thus, if A accepts w there is a positional run for A on w. Consider the ABA A1 from the previous lecture. Here is a pos...

Spatial statistical analyses inevitably are affected by positional errors embedded in georeferenced data. Positional errors further propagate when observations need to be geographically aggregated. This data accuracy issue often results in unreliable statistical conclusion about attribute variables in spatial statistical modeling. This paper investigates how positional errors propagate to varia...