16,922 research outputs found
Asymptotic expression for the fixation probability of a mutant in star graphs
We consider the Moran process in a graph called the "star" and obtain the
asymptotic expression for the fixation probability of a single mutant when the
size of the graph is large. The expression obtained corrects the previously
known expression announced in reference [E Lieberman, C Hauert, and MA Nowak.
Evolutionary dynamics on graphs. Nature, 433(7023):312-316, 2005] and further
studied in [M. Broom and J. Rychtar. An analysis of the fixation probability of
a mutant on special classes of non-directed graphs. Proc. R. Soc. A-Math. Phys.
Eng. Sci., 464(2098):2609-2627, 2008]. We also show that the star graph is an
accelerator of evolution, if the graph is large enough.Comment: 9 pages, 2 figure
The quantum duality principle
The "quantum duality principle" states that the quantization of a Lie
bialgebra - via a quantum universal enveloping algebra (QUEA) - provides also a
quantization of the dual Lie bialgebra (through its associated formal Poisson
group) - via a quantum formal series Hopf algebra (QFSHA) - and, conversely, a
QFSHA associated to a Lie bialgebra (via its associated formal Poisson group)
yields a QUEA for the dual Lie bialgebra as well; more precisely, there exist
functors QUEA --> QFSHA and QFSHA --> QUEA, inverse of each other, such that in
either case the Lie bialgebra associated to the target object is the dual of
that of the source object. Such a result was claimed true by Drinfeld, but
seems to be unproved in literature: we give here a complete detailed proof of
it.Comment: 19 pages, AMS-TeX file. The paper has been entirely re-written: in
particular, we add a discussion of the possible generalisation of the main
result to the infinite dimensional case. This is the author's file of the
final version (after the refereeing process), as sent for publicatio
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