English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

Evolutionary graph theory studies the evolutionary dynamics in a populationstructure given as a connected graph. Each node of the graph represents anindividual of the population, and edges determine how offspring are placed. Weconsider the classical birth-death Moran process where there are two types ofindividuals, namely, the residents with fitness 1 and mutants with fitness r.The fitness indicates the reproductive strength. The evolutionary dynamicshappens as follows: in the initial step, in a population of all residentindividuals a mutant is introduced, and then at each step, an individual ischosen proportional to the fitness of its type to reproduce, and the offspringreplaces a neighbor uniformly at random. The process stops when all individualsare either residents or mutants. The probability that all individuals in theend are mutants is called the fixation probability. We present fasterpolynomial-time Monte-Carlo algorithms for finidng the fixation probability onundirected graphs. Our algorithms are always at least a factor O(n^2/log n)faster as compared to the previous algorithms, where n is the number of nodes,and is polynomial even if r is given in binary. We also present lower boundsshowing that the upper bound on the expected number of effective steps wepresent is asymptotically tight for undirected graphs.

Faster Monte-Carlo Algorithms for Fixation Probability of the Moran Process on Undirected Graphs