A circle n-gon is the region between n non-crossing chords of a circle; the sides of a circle n-gon are either chords or arcs of the circle. A circle n-gon graph is the intersection graph of a family of circle n-gons in a circle. The family of circle trapezoid graphs is exactly the family of circle 2-gon graphs and the family of circle graphs is exactly the family of circle 1-gon graphs. The fa...

A chord deviating from the conventions of Western tonal music elicits an early right anterior negativity (ERAN) in inferofrontal brain regions. Here, we tested whether the ERAN is modulated by expertise in more than one music culture, as typical of folk musicians. Finnish folk musicians and nonmusicians participated in electroencephalography recordings. The cadences consisted of seven chords. I...

We introduce and study an infinite random triangulation of the unit disk that arises as the limit of several recursive models. This triangulation is generated by throwing chords uniformly at random in the unit disk and keeping only those chords that do not intersect the previous ones. After throwing infinitely many chords and taking the closure of the resulting set, one gets a random compact su...

The partial representation extension problem is a recently introduced generalization of the recognition problem. A circle graph is an intersection graph of chords of a circle. We study the partial representation extension problem for circle graphs, where the input consists of a graph G and a partial representation R′ giving some pre-drawn chords that represent an induced subgraph of G. The ques...

We consider a pair of isoperimetric problems arising in physics. The first concerns a Schrödinger operator in L2(R2) with an attractive interaction supported on a closed curve Γ, formally given by −∆ − αδ(x−Γ); we ask which curve of a given length maximizes the ground state energy. In the second problem we have a loop-shaped thread Γ in R3, homogeneously charged but not conducting, and we ask a...