3,514 research outputs found
Adaptive cyclically dominating game on co-evolving networks: Numerical and analytic results
A co-evolving and adaptive Rock (R)-Paper (P)-Scissors (S) game (ARPS) in
which an agent uses one of three cyclically dominating strategies is proposed
and studied numerically and analytically. An agent takes adaptive actions to
achieve a neighborhood to his advantage by rewiring a dissatisfying link with a
probability or switching strategy with a probability . Numerical
results revealed two phases in the steady state. An active phase for
has one connected network of agents using different
strategies who are continually interacting and taking adaptive actions. A
frozen phase for has three separate clusters of agents using
only R, P, and S, respectively with terminated adaptive actions. A mean-field
theory of link densities in co-evolving network is formulated in a general way
that can be readily modified to other co-evolving network problems of multiple
strategies. The analytic results agree with simulation results on ARPS well. We
point out the different probabilities of winning, losing, and drawing a game
among the agents as the origin of the small discrepancy between analytic and
simulation results. As a result of the adaptive actions, agents of higher
degrees are often those being taken advantage of. Agents with a smaller
(larger) degree than the mean degree have a higher (smaller) probability of
winning than losing. The results are useful in future attempts on formulating
more accurate theories.Comment: 17 pages, 4 figure
Role of quark-interchange processes in evolution of mesonic matter
We divide the cross section for a meson-meson reaction into three parts. The
first part is for the quark-interchange process, the second for quark-antiquark
annihilation processes and the third for resonant processes. Master rate
equations are established to yield time dependence of fugacities of pions,
rhos, kaons and vetor kaons. The equations include cross sections for inelastic
scattering of pions, rhos, kaons and vector kaons. Cross sections for
quark-interchange-induced reactions, that were obtained in a potential model,
are parametrized for convenient use. The number densities of pion and rho (kaon
and vector kaon) are altered by quark-interchange processes in equal magnitudes
but opposite signs. The master rate equations combined with the hydrodynamic
equations for longitudinal and transverse expansion are solved with many sets
of initial meson fugacities. Quark-interchange processes are shown to be
important in the contribution of the inelastic meson-meson scattering to
evolution of mesonic matter.Comment: 28 pages, 1 figure, 8 table
Atypical viral dynamics from transport through popular places
The flux of visitors through popular places undoubtedly influences viral
spreading -- from H1N1 and Zika viruses spreading through physical spaces such
as airports, to rumors and ideas spreading though online spaces such as
chatrooms and social media. However there is a lack of understanding of the
types of viral dynamics that can result. Here we present a minimal dynamical
model which focuses on the time-dependent interplay between the {\em mobility
through} and the {\em occupancy of} such spaces. Our generic model permits
analytic analysis while producing a rich diversity of infection profiles in
terms of their shapes, durations, and intensities. The general features of
these theoretical profiles compare well to real-world data of recent social
contagion phenomena.Comment: 14 pages, 16 figure
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