arXiv subjects

Uzay Çetin

Publications and source records attributed to Uzay Çetin.

2 recordsLinked to original sources

arXiv2026

Worst-Case Examples for the Computation of Persistent Homology

We construct worst-case examples for the standard reduction algorithm for computing persistent homology. Our constructions are similar to the worst-case examples introduced by Morozov, but we replace the single-triangle arrangement with a strip of base and fin triangles. This structure allows us to give an explicit algorithm for their construction and to perform experiments comparing the runtime of different versions of the reduction algorithm. We further show that, after suitable edge and triangle subdivisions, these strip examples remain worst-case and can be realized as clique complexes of filtered graphs, and hence as Vietoris--Rips complexes of finite point clouds for a sequence of scale parameters.

math.AT↗

arXiv2014

Iterated Prisoners Dilemma with limited attention

How attention scarcity effects the outcomes of a game? We present our findings on a version of the Iterated Prisoners Dilemma (IPD) game in which players can accept or refuse to play with their partner. We study the memory size effect on determining the right partner to interact with. We investigate the conditions under which the cooperators are more likely to be advantageous than the defectors. This work demonstrates that, in order to beat defection, players do not need a full memorization of each action of all opponents. There exists a critical attention capacity threshold to beat defectors. This threshold depends not only on the ratio of the defectors in the population but also on the attention allocation strategy of the players.

cs.GT↗