1,714 research outputs found
Knot Floer homology, genus bounds, and mutation
In an earlier paper, we introduced a collection of graded Abelian groups
\HFKa(Y,K) associated to knots in a three-manifold. The aim of the present
paper is to investigate these groups for several specific families of knots,
including the Kinoshita-Terasaka knots and their ``Conway mutants''. These
results show that \HFKa contains more information than the Alexander
polynomial and the signature of these knots; and they also illustrate the fact
that \HFKa detects mutation. We also calculate \HFKa for certain pretzel
knots, and knots with small crossing number (). Our calculations prove
that many of the knots considered here admit no Seifert fibered surgeries.Comment: minor revisions, updated reference
On the Role of External Constraints in a Spatially Extended Evolutionary Prisoner's Dilemma Game
We study the emergency of mutual cooperation in evolutionary prisoner's
dilemma games when the players are located on a square lattice. The players can
choose one of the three strategies: cooperation (C), defection (D) or "tit for
tat" (T), and their total payoffs come from games with the nearest neighbors.
During the random sequential updates the players adopt one of their neighboring
strategies if the chosen neighbor has higher payoff. We compare the effect of
two types of external constraints added to the Darwinian evolutionary
processes. In both cases the strategy of a randomly chosen player is replaced
with probability P by another strategy. In the first case, the strategy is
replaced by a randomly chosen one among the two others, while in the second
case the new strategy is always C. Using generalized mean-field approximations
and Monte Carlo simulations the strategy concentrations are evaluated in the
stationary state for different strength of external constraints characterized
by the probability P.Comment: 19 pages, 10 figure
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