1,787 research outputs found
Canalization in the Critical States of Highly Connected Networks of Competing Boolean Nodes
Canalization is a classic concept in Developmental Biology that is thought to
be an important feature of evolving systems. In a Boolean network it is a form
of network robustness in which a subset of the input signals control the
behavior of a node regardless of the remaining input. It has been shown that
Boolean networks can become canalized if they evolve through a frustrated
competition between nodes. This was demonstrated for large networks in which
each node had K=3 inputs. Those networks evolve to a critical steady-state at
the boarder of two phases of dynamical behavior. Moreover, the evolution of
these networks was shown to be associated with the symmetry of the evolutionary
dynamics. We extend these results to the more highly connected K>3 cases and
show that similar canalized critical steady states emerge with the same
associated dynamical symmetry, but only if the evolutionary dynamics is biased
toward homogeneous Boolean functions.Comment: 8 pages, 5 figure
Nonlinear evolution of surface morphology in InAs/AlAs superlattices via surface diffusion
Continuum simulations of self-organized lateral compositional modulation
growth in InAs/AlAs short-period superlattices on InP substrate are presented.
Results of the simulations correspond quantitatively to the results of
synchrotron x-ray diffraction experiments. The time evolution of the
compositional modulation during epitaxial growth can be explained only
including a nonlinear dependence of the elastic energy of the growing epitaxial
layer on its thickness. From the fit of the experimental data to the growth
simulations we have determined the parameters of this nonlinear dependence. It
was found that the modulation amplitude don't depend on the values of the
surface diffusion constants of particular elements.Comment: 4 pages, 3 figures, published in Phys. Rev. Lett.
http://link.aps.org/abstract/PRL/v96/e13610
Competition in Social Networks: Emergence of a Scale-free Leadership Structure and Collective Efficiency
Using the minority game as a model for competition dynamics, we investigate
the effects of inter-agent communications on the global evolution of the
dynamics of a society characterized by competition for limited resources. The
agents communicate across a social network with small-world character that
forms the static substrate of a second network, the influence network, which is
dynamically coupled to the evolution of the game. The influence network is a
directed network, defined by the inter-agent communication links on the
substrate along which communicated information is acted upon. We show that the
influence network spontaneously develops hubs with a broad distribution of
in-degrees, defining a robust leadership structure that is scale-free.
Furthermore, in realistic parameter ranges, facilitated by information exchange
on the network, agents can generate a high degree of cooperation making the
collective almost maximally efficient.Comment: 4 pages, 2 postscript figures include
Optimal transport on wireless networks
We present a study of the application of a variant of a recently introduced
heuristic algorithm for the optimization of transport routes on complex
networks to the problem of finding the optimal routes of communication between
nodes on wireless networks. Our algorithm iteratively balances network traffic
by minimizing the maximum node betweenness on the network. The variant we
consider specifically accounts for the broadcast restrictions imposed by
wireless communication by using a different betweenness measure. We compare the
performance of our algorithm to two other known algorithms and find that our
algorithm achieves the highest transport capacity both for minimum node degree
geometric networks, which are directed geometric networks that model wireless
communication networks, and for configuration model networks that are
uncorrelated scale-free networks.Comment: 5 pages, 4 figure
Mean-Field Analysis and Monte Carlo Study of an Interacting Two-Species Catalytic Surface Reaction Model
We study the phase diagram and critical behavior of an interacting one
dimensional two species monomer-monomer catalytic surface reaction model with a
reactive phase as well as two equivalent adsorbing phase where one of the
species saturates the system. A mean field analysis including correlations up
to triplets of sites fails to reproduce the phase diagram found by Monte Carlo
simulations. The three phases coexist at a bicritical point whose critical
behavior is described by the even branching annihilating random walk
universality class. This work confirms the hypothesis that the conservation
modulo 2 of the domain walls under the dynamics at the bicritical point is the
essential feature in producing critical behavior different from directed
percolation. The interfacial fluctuations show the same universal behavior seen
at the bicritical point in a three-species model, supporting the conjecture
that these fluctuations are a new universal characteristic of the model.Comment: 11 pages using RevTeX, plus 4 Postscript figures. Uses psfig.st
An Upsilon Point in a Spin Model
We present analytic evidence for the occurrence of an upsilon point, an
infinite checkerboard structure of modulated phases, in the ground state of a
spin model. The structure of the upsilon point is studied by calculating
interface--interface interactions using an expansion in inverse spin
anisotropy.Comment: 18 pages ReVTeX file, including 6 figures encoded with uufile
Interacting Monomer-Dimer Model with Infinitely Many Absorbing States
We study a modified version of the interacting monomer-dimer (IMD) model that
has infinitely many absorbing (IMA) states. Unlike all other previously studied
models with IMA states, the absorbing states can be divided into two equivalent
groups which are dynamically separated infinitely far apart. Monte Carlo
simulations show that this model belongs to the directed Ising universality
class like the ordinary IMD model with two equivalent absorbing states. This
model is the first model with IMA states which does not belong to the directed
percolation (DP) universality class. The DP universality class can be restored
in two ways, i.e., by connecting the two equivalent groups dynamically or by
introducing a symmetry-breaking field between the two groups.Comment: 5 pages, 5 figure
Nature of phase transitions in a probabilistic cellular automaton with two absorbing states
We present a probabilistic cellular automaton with two absorbing states,
which can be considered a natural extension of the Domany-Kinzel model. Despite
its simplicity, it shows a very rich phase diagram, with two second-order and
one first-order transition lines that meet at a tricritical point. We study the
phase transitions and the critical behavior of the model using mean field
approximations, direct numerical simulations and field theory. A closed form
for the dynamics of the kinks between the two absorbing phases near the
tricritical point is obtained, providing an exact correspondence between the
presence of conserved quantities and the symmetry of absorbing states. The
second-order critical curves and the kink critical dynamics are found to be in
the directed percolation and parity conservation universality classes,
respectively. The first order phase transition is put in evidence by examining
the hysteresis cycle. We also study the "chaotic" phase, in which two replicas
evolving with the same noise diverge, using mean field and numerical
techniques. Finally, we show how the shape of the potential of the
field-theoretic formulation of the problem can be obtained by direct numerical
simulations.Comment: 19 pages with 7 figure
Directed avalanche processes with underlying interface dynamics
We describe a directed avalanche model; a slowly unloading sandbox driven by
lowering a retaining wall. The directness of the dynamics allows us to
interpret the stable sand surfaces as world sheets of fluctuating interfaces in
one lower dimension. In our specific case, the interface growth dynamics
belongs to the Kardar-Parisi-Zhang (KPZ) universality class. We formulate
relations between the critical exponents of the various avalanche distributions
and those of the roughness of the growing interface. The nonlinear nature of
the underlying KPZ dynamics provides a nontrivial test of such generic exponent
relations. The numerical values of the avalanche exponents are close to the
conventional KPZ values, but differ sufficiently to warrant a detailed study of
whether avalanche correlated Monte Carlo sampling changes the scaling exponents
of KPZ interfaces. We demonstrate that the exponents remain unchanged, but that
the traces left on the surface by previous avalanches give rise to unusually
strong finite-size corrections to scaling. This type of slow convergence seems
intrinsic to avalanche dynamics.Comment: 13 pages, 13 figure
Lifting of Multiphase Degeneracy by Quantum Fluctuations
We study the effect of quantum fluctuations on the multiphase point of the
Heisenberg model with first- and second-neighbor competing interactions and
strong uniaxial spin anisotropy . By studying the structure of perturbation
theory we show that the multiphase degeneracy which exists for
(i.e., for the ANNNI model) is lifted and that the effect of quantum
fluctuations is to stabilize a sequence of phases of wavelength 4,6,8,...~.
This sequence is probably an infinite one. We also show that quantum
fluctuations can mediate an infinite sequence of layering transitions through
which an interface can unbind from a wall.Comment: 55 pages ReVTeX (encoded with uufiles) + 17 uuencoded figure
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