Devil's staircases, ramps, humps and roller coasters

Return on Roller Coasters: A Model to Guide Investments in Theme Park Attractions

Despite the economic significance of the theme park industry and the huge investments needed to set up new attractions, no marketing models exist to guide these investment decisions. This study addresses this gap in the literature by estimating a response model for theme park attendance. The model not only determines the contribution of each attraction to attendance, but also how this contribut...

Approximation of Staircases by Staircases

| The simplest nontrivial monotone functions are \staircases." The problem arises: what is the best approximation of some monotone function f(x) by a staircase with M jumps? In particular: what if f(x) is itself a staircase with N, N > M, steps? This paper considers algorithms for solving, and theorems relating to, this problem. All of the algorithms we propose are space-optimal up to a constan...

Staircases in Z²

A staircase in this paper is the set of points in Z2 below a given rational line in the plane that have Manhattan Distance less than 1 to the line. Staircases are closely related to Beatty and Sturmian sequences of rational numbers. Connecting the geometry and the number theoretic concepts, we obtain three equivalent characterizations of Sturmian sequences of rational numbers, as well as a new ...

Dembski, Darwin and Devils

Generalized Staircases: Recurrence and Symmetry

We study infinite translation surfaces which are Z-covers of compact translation surfaces. We obtain conditions ensuring that such surfaces have Veech groups which are Fuchsian of the first kind and give a necessary and sufficient condition for recurrence of their straight-line flows. Extending results of Hubert and Schmithüsen, we provide examples of infinite non-arithmetic lattice surfaces, a...