The traditional forms of role-playing include tabletop roleplaying, larp and online role-playing. In this paper I describe a fourth form, pervasive role-playing, which often follows many conventions of larp, but break out of the magic circle of gameplay in order to interact with surrounding society. The central pleasures of pervasive role-playing are related to playing for real, with the enviro...

A circle packing is a configuration P of circles realizing a specified pattern of tangencies. Radii of packings in the euclidean and hyperbolic planes may be computed using an iterative process suggested by William Thurston. We describe an efficient implementation, discuss its performance, and illustrate recent applications. A central role is played by new and subtle monotonicity results for “f...

T he essence of harmonic analysis is to decompose complicated expressions into pieces that reflect the structure of a group action when there is one. The goal is to make some difficult analysis manageable. In the seventeenth and eighteenth centuries, the groups that arose in this connection were the circle R/2πZ , the line R , and finite abelian groups. Embedded in applications were decompositi...

In this paper, the use of two modals (can and may) in four varieties of English (British, India, Philippines, and USA) was compared and the characteristics of each variety were statistically analyzed. After all the sample sentences were extracted from each component of the ICE corpus, a total of twenty linguistic factors were encoded. Then, the collected data were statistically analyzed with R....

Let G denote a graph and let K be a subset of vertices that are a set of target vertices of G. The Kterminal reliability of G is defined as the probability that all target vertices in K are connected, considering the possible failures of non-target vertices of G. The problem of computing K-terminal reliability is known to be #P-complete for polygon-circle graphs, and can be solved in polynomial...

Given an essential semilattice congruence \(\equiv\) on the left weak order of a \linebreak Coxeter group \(W\), we define stack-sorting operator \({\bf S}_\equiv:W\to W\) by \({{\bf S}_\equiv(w)=w\big(\pi_\downarrow^\equiv(w)\big)^{-1}}\), where \(\pi_\downarrow^\equiv(w)\) is unique minimal element class containing \(w\). When sylvester symmetric \(S_n\), S}_\equiv\) West's map. descent pop-s...

We provide an overview of the connections between circle packings and quasiconformal mappings, with particular attention to applications to string theory and image recognition.

T he essence of harmonic analysis is to decompose complicated expressions into pieces that reflect the structure of a group action when there is one. The goal is to make some difficult analysis manageable. In the seventeenth and eighteenth centuries, the groups that arose in this connection were the circle R/2πZ , the line R , and finite abelian groups. Embedded in applications were decompositi...

A discrete analogue of the holomorphic map z γ is studied. It is given by Schramm's circle pattern with the combinatorics of the square grid. It is shown that the corresponding circle patterns are imbedded and described by special separatrix solutions of discrete Painlevé equations. Global properties of these solutions, as well as of the discrete z γ , are established.

For a given positive integer v with v ≡ 4(mod 6) and v > 4, let CKPD(v) denote a canonical Kirkman packing design of order v. It is proved in this paper that any CKPD(v) can be embedded in a CKPD(u) if u ≡ v ≡ 4 (mod 6), v ≥ 82 and u ≥ 3.5v.