All the mouse embryos above belong to the same litter but half of them have inherited a transgene from their father (the green fluorescent adult mouse on the right) that causes them to glow yellowish green under fluorescent light. In these transgenic mice, the enhanced green fluorescent protein (EGFP) is expressed in all cells except hair and erythrocytes. The fact that there are equal numbers ...

Let d > 2 be an integer number, and let fk, k ∈ {1, . . . , d}, be Ck commuting circle diffeomorphisms, with τk ∈ ]0, 1[ and τ1 + · · · + τd > 1. We prove that if the rotation numbers of the fk’s are independent over the rationals (that is, if the corresponding action of Z n on the circle is free), then they are simultaneously (topologically) conjugate to rotations. 2000 Math. Subj. Class. 22F0...

A circle graph is the intersection graph of a set of chords of a circle. The class of circle graphs is closed under pivotminors. We determine the pivot-minor-minimal non-circle-graphs; there 15 obstructions. These obstructions are found, by computer search, as a corollary to Bouchet’s characterization of circle graphs under local complementation. Our characterization generalizes Kuratowski’s Th...

One of the most famous problems of classical geometry is the Apollonius' problem asks construction of a circle which is tangent to three given objects. These objects are usually taken as points, lines, and circles. This well known problem was posed by Apollonius of Perga ( about 262 - 190 B.C.) who was a Greek mathematician known as the great geometer of ancient times after Euclid and Archimede...

(a) If we consider the intersections of the circle Hi(O) (center Hi and radius HiO) with the line Ai+1Ai+2, then we obtain six points which all lie on a circle with center H (first Droz-Farny circle). (b) If we consider the intersections of the circle Mi(H) (center Mi and radius MiH) with the line AiAi+1, then we obtain six points which all lie on a circle with center O (second Droz-Farny circl...