A notion of random walks for circle packings is introduced. The geometry behind this notion is discussed, together with some applications. In particular, we obtain a short proof of a result regarding the type problem for circle packings, which shows that the type of a circle packing is closely related to the type of its tangency graph.

In this paper we describe various applications of the RiemannHilbert method to the theory of orthogonal polynomials on the line and on the circle.

The cyclohedron Wn, known also as the Bott-Taubes polytope, arises both as the polyhedral realization of the poset of all cyclic bracketings of the word x1x2 . . . xn and as an essential part of the Fulton-MacPherson compactification of the configuration space of n distinct, labelled points on the circle S1. The “polygonal pegs problem” asks whether every simple, closed curve in the plane or in...

The most important property of humankind is the capacity to form and maintain relationships. These relationships are absolutely necessary for any of us to survive, learn, work, love and procreate. Human relationships take many forms but the most intense, most pleasurable and most painful are those relationships with family, friends and loved ones. Within this inner circle of intimate relationsh...

Let S be a set of n points in the plane. We present a method where, using O(n log n) time and space, S can be pre-processed into a data structure such that given an axis-parallel query rectangle q, we can report the radius of the smallest enclosing disk of the points lying in S ∩ q in O(log n) time per query.

PURPOSE. Retinal nerve fiber layer (RNFL) thickness measured by optical coherence tomography (OCT) can be unreliable in the presence of a myopic tilted disc. The purpose of this study was to investigate the influence of the calculation circle location of spectral domain (SD)-OCT when measuring RNFL thickness in healthy subjects with myopic tilted disc. METHODS. Sixty-nine eyes with myopic tilte...