1,770 research outputs found
A geometric description of the extreme Khovanov cohomology
We prove that the hypothetical extreme Khovanov cohomology of a link is the cohomology of the independence simplicial complex of its Lando graph. We also provide a family of knots having as many non-trivial extreme Khovanov cohomology modules as desired, that is, examples of H-thick knots which are as far of being H-thin as desired.Ministerio de Economía y CompetitividadFondo Europeo de Desarrollo Regiona
The effective strength of selection in random environment
We analyse a family of two-types Wright-Fisher models with selection in a
random environment and skewed offspring distribution. We provide a calculable
criterion to quantify the impact of different shapes of selection on the fate
of the weakest allele, and thus compare them. The main mathematical tool is
duality, which we prove to hold, also in presence of random environment
(quenched and in some cases annealed), between the population's allele
frequencies and genealogy, both in the case of finite population size and in
the scaling limit for large size. Duality also yields new insight on properties
of branching-coalescing processes in random environment, such as their long
term behaviour.Comment: 36 pages; v2 corrects an error in the proof of Thm 3.
An individual-based model for the Lenski experiment, and the deceleration of the relative fitness
The Lenski experiment investigates the long-term evolution of bacterial
populations. Its design allows the direct comparison of the reproductive
fitness of an evolved strain with its founder ancestor. It was observed by
Wiser et al. (2013) that the relative fitness over time increases sublinearly,
a behaviour which is commonly attributed to effects like clonal interference or
epistasis. In this paper we present an individual-based probabilistic model
that captures essential features of the design of the Lenski experiment. We
assume that each beneficial mutation increases the individual reproduction rate
by a fixed amount, which corresponds to the absence of epistasis in the
continuous-time (intraday) part of the model, but leads to an epistatic effect
in the discrete-time (interday) part of the model. Using an approximation by
near-critical Galton-Watson processes, we prove that under some assumptions on
the model parameters which exclude clonal interference, the relative fitness
process converges, after suitable rescaling, in the large population limit to a
power law function.Comment: minor changes, additional references, some comments on the notion of
relative fitness and on the modelling assumptions adde
- …