3,281 research outputs found
Geometric Prequantization of the Moduli Space of the Vortex equations on a Riemann surface
The moduli space of solutions to the vortex equations on a Riemann surface
are well known to have a symplectic (in fact K\"{a}hler) structure. We show
this symplectic structure explictly and proceed to show a family of symplectic
(in fact, K\"{a}hler) structures on the moduli space,
parametrised by , a section of a line bundle on the Riemann surface.
Next we show that corresponding to these there is a family of prequantum line
bundles on the moduli space whose curvature is
proportional to the symplectic forms .Comment: 8 page
Prisoner's Dilemma cellular automata revisited: evolution of cooperation under environmental pressure
We propose an extension of the evolutionary Prisoner's Dilemma cellular
automata, introduced by Nowak and May \cite{nm92}, in which the pressure of the
environment is taken into account. This is implemented by requiring that
individuals need to collect a minimum score , representing
indispensable resources (nutrients, energy, money, etc.) to prosper in this
environment. So the agents, instead of evolving just by adopting the behaviour
of the most successful neighbour (who got ), also take into account if
is above or below the threshold . If an
individual has a probability of adopting the opposite behaviour from the one
used by its most successful neighbour. This modification allows the evolution
of cooperation for payoffs for which defection was the rule (as it happens, for
example, when the sucker's payoff is much worse than the punishment for mutual
defection). We also analyse a more sophisticated version of this model in which
the selective rule is supplemented with a "win-stay, lose-shift" criterion. The
cluster structure is analyzed and, for this more complex version we found
power-law scaling for a restricted region in the parameter space.Comment: 15 pages, 8 figures; added figures and revised tex
Adaptation and enslavement in endosymbiont-host associations
The evolutionary persistence of symbiotic associations is a puzzle.
Adaptation should eliminate cooperative traits if it is possible to enjoy the
advantages of cooperation without reciprocating - a facet of cooperation known
in game theory as the Prisoner's Dilemma. Despite this barrier, symbioses are
widespread, and may have been necessary for the evolution of complex life. The
discovery of strategies such as tit-for-tat has been presented as a general
solution to the problem of cooperation. However, this only holds for
within-species cooperation, where a single strategy will come to dominate the
population. In a symbiotic association each species may have a different
strategy, and the theoretical analysis of the single species problem is no
guide to the outcome. We present basic analysis of two-species cooperation and
show that a species with a fast adaptation rate is enslaved by a slowly
evolving one. Paradoxically, the rapidly evolving species becomes highly
cooperative, whereas the slowly evolving one gives little in return. This helps
understand the occurrence of endosymbioses where the host benefits, but the
symbionts appear to gain little from the association.Comment: v2: Correction made to equations 5 & 6 v3: Revised version accepted
in Phys. Rev. E; New figure adde
Stochasticity and evolutionary stability
In stochastic dynamical systems, different concepts of stability can be
obtained in different limits. A particularly interesting example is
evolutionary game theory, which is traditionally based on infinite populations,
where strict Nash equilibria correspond to stable fixed points that are always
evolutionarily stable. However, in finite populations stochastic effects can
drive the system away from strict Nash equilibria, which gives rise to a new
concept for evolutionary stability. The conventional and the new stability
concepts may apparently contradict each other leading to conflicting
predictions in large yet finite populations. We show that the two concepts can
be derived from the frequency dependent Moran process in different limits. Our
results help to determine the appropriate stability concept in large finite
populations. The general validity of our findings is demonstrated showing that
the same results are valid employing vastly different co-evolutionary
processes
Nongaussian fluctuations arising from finite populations: Exact results for the evolutionary Moran process
The appropriate description of fluctuations within the framework of
evolutionary game theory is a fundamental unsolved problem in the case of
finite populations. The Moran process recently introduced into this context
[Nowak et al., Nature (London) 428, 646 (2004)] defines a promising standard
model of evolutionary game theory in finite populations for which analytical
results are accessible. In this paper, we derive the stationary distribution of
the Moran process population dynamics for arbitrary games for the
finite size case. We show that a nonvanishing background fitness can be
transformed to the vanishing case by rescaling the payoff matrix. In contrast
to the common approach to mimic finite-size fluctuations by Gaussian
distributed noise, the finite size fluctuations can deviate significantly from
a Gaussian distribution.Comment: 4 pages (2 figs). Published in Physical Review E (Rapid
Communications
Robustness of Cooperation in the Evolutionary Prisoner's Dilemma on Complex Networks
Recent studies on the evolutionary dynamics of the Prisoner's Dilemma game in
scale-free networks have demonstrated that the heterogeneity of the network
interconnections enhances the evolutionary success of cooperation. In this
paper we address the issue of how the characterization of the asymptotic states
of the evolutionary dynamics depends on the initial concentration of
cooperators. We find that the measure and the connectedness properties of the
set of nodes where cooperation reaches fixation is largely independent of
initial conditions, in contrast with the behavior of both the set of nodes
where defection is fixed, and the fluctuating nodes. We also check for the
robustness of these results when varying the degree heterogeneity along a
one-parametric family of networks interpolating between the class of
Erdos-Renyi graphs and the Barabasi-Albert networks.Comment: 18 pages, 6 figures, revised version accepted for publication in New
Journal of Physics (2007
Phase transitions in social sciences: two-populations mean field theory
A new mean field statistical mechanics model of two interacting groups of
spins is introduced and the phase transition studied in terms of their relative
size. A jump of the average magnetization is found for large values of the
mutual interaction when the relative percentage of the two populations crosses
a critical threshold. It is shown how the critical percentage depends on
internal interactions and on the initial magnetizations. The model is
interpreted as a prototype of resident-immigrant cultural interaction and
conclusions from the social sciences perspectives are drawn
Chaos and unpredictability in evolutionary dynamics in discrete time
A discrete-time version of the replicator equation for two-strategy games is
studied. The stationary properties differ from that of continuous time for
sufficiently large values of the parameters, where periodic and chaotic
behavior replace the usual fixed-point population solutions. We observe the
familiar period-doubling and chaotic-band-splitting attractor cascades of
unimodal maps but in some cases more elaborate variations appear due to
bimodality. Also unphysical stationary solutions have unusual physical
implications, such as uncertainty of final population caused by sensitivity to
initial conditions and fractality of attractor preimage manifolds.Comment: 4 pages, 4 figure
Competitive market for multiple firms and economic crisis
The origin of economic crises is a key problem for economics. We present a
model of long-run competitive markets to show that the multiplicity of
behaviors in an economic system, over a long time scale, emerge as statistical
regularities (perfectly competitive markets obey Bose-Einstein statistics and
purely monopolistic-competitive markets obey Boltzmann statistics) and that how
interaction among firms influences the evolutionary of competitive markets. It
has been widely accepted that perfect competition is most efficient. Our study
shows that the perfectly competitive system, as an extreme case of competitive
markets, is most efficient but not stable, and gives rise to economic crises as
society reaches full employment. In the economic crisis revealed by our model,
many firms condense (collapse) into the lowest supply level (zero supply,
namely bankruptcy status), in analogy to Bose-Einstein condensation. This
curious phenomenon arises because perfect competition (homogeneous
competitions) equals symmetric (indistinguishable) investment direction, a fact
abhorred by nature. Therefore, we urge the promotion of monopolistic
competition (heterogeneous competitions) rather than perfect competition. To
provide early warning of economic crises, we introduce a resolving index of
investment, which approaches zero in the run-up to an economic crisis. On the
other hand, our model discloses, as a profound conclusion, that the
technological level for a long-run social or economic system is proportional to
the freedom (disorder) of this system; in other words, technology equals the
entropy of system. As an application of this new concept, we give a possible
answer to the Needham question: "Why was it that despite the immense
achievements of traditional China it had been in Europe and not in China that
the scientific and industrial revolutions occurred?"Comment: 17 pages; 3 figure
Hawks and Doves on Small-World Networks
We explore the Hawk-Dove game on networks with topologies ranging from
regular lattices to random graphs with small-world networks in between. This is
done by means of computer simulations using several update rules for the
population evolutionary dynamics. We find the overall result that cooperation
is sometimes inhibited and sometimes enhanced in those network structures, with
respect to the mixing population case. The differences are due to different
update rules and depend on the gain-to-cost ratio. We analyse and qualitatively
explain this behavior by using local topological arguments.Comment: 12 pages, 8 figure
- …