9 papers
Replacers and their evolutionary stability in the Moran process on graphs
Michal Pecho, Jakub Svoboda, Lenka Kopfová +2
Evolutionary dynamics in finite structured populations are commonly modeled by the Moran Birth-death process. A key quantity is the fixation probability of a single invader attempt…
Fixation location in structured populations
David A. Brewster, Gabor Lippner, Josef Tkadlec +1
In stochastic evolutionary dynamics, the replacement of an existing genotype or cultural trait by a newly introduced mutant is typically characterized by the quantities of fixation…
The evolutionary advantage of replacers in the Moran process
Michal Pecho, Josef Tkadlec, Martin A. Nowak
Evolution occurs in populations of reproducing individuals. In stochastic descriptions of evolutionary dynamics, such as the Moran process, individuals are chosen randomly for birt…
Humanity's Last Exam
Long Phan, Alice Gatti, Ziwen Han +1144
Benchmarks are important tools for tracking the rapid advancements in large language model (LLM) capabilities. However, benchmarks are not keeping pace in difficulty: LLMs now achi…
Lattice and Non-lattice Piercing of Axis-Parallel Rectangles
Adrian Dumitrescu, Arsenii Sagdeev, Josef Tkadlec
Given a family of shapes in the plane, we study what is the lowest possible density of a point set that pierces (``intersects'', ``hits'') all translates of each…
Maintaining diversity in structured populations
David A. Brewster, Jakub Svoboda, Dylan Roscow +3
We examine population structures for their ability to maintain diversity in neutral evolution. We use the general framework of evolutionary graph theory and consider birth-death (b…