6 citations · 6 across the 5 of their papers we have counts for
6 papers
Testing the transcendence conjectures of a modular involution of the real line and its continued fraction statistics
Hakan Ayral, A. Muhammed Uludağ
We study the values of the recently introduced involution J (jimm) of the real line, which is equivariant with the action of the group PGL(2,Z). We test our conjecture that this in…
Parallel and in-process compilation of individuals for genetic programming on GPU
Hakan Ayral, Songül Albayrak
Three approaches to implement genetic programming on GPU hardware are compilation, interpretation and direct generation of machine code. The compiled approach is known to have a pr…
Dynamics of a family of continued fraction maps
Muhammed Uludağ, Hakan Ayral
We study the dynamics of a family of continued fraction maps parametrized by the unit interval. This family contains as special instances the Gauss continued fraction map and the F…
On the involution of the real line induced by Dyer's outer automorphism of PGL(2,Z)
A. Muhammed Uludağ, Hakan Ayral
We study the involution of the real line induced by the outer automorphism of the extended modular group PGL(2,Z). This `modular' involution is discontinuous at rationals but satis…
A subtle symmetry of Lebesgue's measure
Muhammed Uludağ, Hakan Ayral
We represent the Lebesgue measure on the unit interval as a boundary measure of the Farey tree and show that this representation has a certain symmetry related to the tree automorp…
Jimm, a Fundamental Involution
A. Muhammed Uludağ, Hakan Ayral
We study the involution of the real line induced by the outer automorphism of the extended modular group PGL(2,Z). This `modular' involution is discontinuous at rationals but satis…