It has been suggested that the temporal control of rhythmic unimanual movements is different between tasks requiring continuous (e.g., circle drawing) and discontinuous movements (e.g., finger tapping). Specifically, for continuous movements temporal regularities are an emergent property, whereas for tasks that involve discontinuities timing is an explicit part of the action goal. The present e...

BACKGROUND AND OBJECTIVES The circle of Willis, an anastomotic polygon at the base of the brain, forms an important collateral network to maintain cerebral blood perfusion. The aim of this study was to investigate different anatomic variations of the circle of Willis and their prevalence. METHODS This cross-sectional study was conducted on 525 healthy participants including 205 men and 320 wo...

The Andreev-Koebe-Thurston circle packing theorem is generalized and improved in two ways. First, we get simultaneous circle packings of the map and its dual map so that, in the corresponding straight-line representations of the map and the dual, any two edges dual to each other are perpendicular. Necessary and sufficient condition for a map to have such a primal-dual circle packing representat...

We study the complexity of the colouring problem for circle graphs. We will solve the two open questions of [Un88], where first results were presented. 1. Here we will present an algorithm which solves the 3-colouring problem of circle graphs in time O(n log(n)). In [Un88] we showed that the 4-colouring problem for circle graphs is NP-complete. 2. If the largest clique of a circle graph has siz...

The intersection graph of a family of arcs on a circle is called a circular-arc graph. This class of graphs admits some interesting subclasses: proper circular-arc graphs, unit circular-arc graphs, Helly circular-arc graphs and clique-Helly circular-arc graphs. The intersection graph of a family of chords in a circle is called a circle graph. Analogously, this class of graphs admits some subcla...

The aim of the study was to investigate the distribution of the circle of Willis variants in Polish population by means of computed tomography angiography (CTA). The results were then analysed and compared with another study that used similar methods but that was carried out on an ethnically distinct population. Patients presenting with intracranial pathology were excluded from the initial stud...