1,321 research outputs found
Stable and unstable attractors in Boolean networks
Boolean networks at the critical point have been a matter of debate for many
years as, e.g., scaling of number of attractor with system size. Recently it
was found that this number scales superpolynomially with system size, contrary
to a common earlier expectation of sublinear scaling. We here point to the fact
that these results are obtained using deterministic parallel update, where a
large fraction of attractors in fact are an artifact of the updating scheme.
This limits the significance of these results for biological systems where
noise is omnipresent. We here take a fresh look at attractors in Boolean
networks with the original motivation of simplified models for biological
systems in mind. We test stability of attractors w.r.t. infinitesimal
deviations from synchronous update and find that most attractors found under
parallel update are artifacts arising from the synchronous clocking mode. The
remaining fraction of attractors are stable against fluctuating response
delays. For this subset of stable attractors we observe sublinear scaling of
the number of attractors with system size.Comment: extended version, additional figur
Critical Kauffman networks under deterministic asynchronous update
We investigate the influence of a deterministic but non-synchronous update on
Random Boolean Networks, with a focus on critical networks. Knowing that
``relevant components'' determine the number and length of attractors, we focus
on such relevant components and calculate how the length and number of
attractors on these components are modified by delays at one or more nodes. The
main findings are that attractors decrease in number when there are more
delays, and that periods may become very long when delays are not integer
multiples of the basic update step.Comment: 8 pages, 3 figures, submitted to a journa
Global culture: A noise induced transition in finite systems
We analyze the effect of cultural drift, modeled as noise, in Axelrod's model
for the dissemination of culture. The disordered multicultural configurations
are found to be metastable. This general result is proven rigorously in d=1,
where the dynamics is described in terms of a Lyapunov potential. In d=2, the
dynamics is governed by the average relaxation time T of perturbations. Noise
at a rate r 1/T sustains
disorder. In the thermodynamic limit, the relaxation time diverges and global
polarization persists in spite of a dynamics of local convergence.Comment: 4 pages, 5 figures. For related material visit
http://www.imedea.uib.es/physdept
Tensor Product and Permutation Branes on the Torus
We consider B-type D-branes in the Gepner model consisting of two minimal
models at k=2. This Gepner model is mirror to a torus theory. We establish the
dictionary identifying the B-type D-branes of the Gepner model with A-type
Neumann and Dirichlet branes on the torus.Comment: 26 page
Superconductivity of Quasi-One and Quasi-Two Dimensional Tight-Binding Electrons in Magnetic Field
The upper critical field of the tight-binding electrons in the
three-dimensional lattice is investigated.
The electrons make Cooper pairs between the eigenstates with the same energy
in the strong magnetic field. The transition lines in the quasi-one dimensional
case are shown to deviate from the previously obtained results where the
hopping matrix elements along the magnetic field are neglected. In the absence
of the Pauli pair breaking the transition temperature of the quasi-two
dimensional electrons is obtained to oscillationally increase as the magnetic
field becomes large and reaches to in the strong field as in the
quasi-one dimensional case.Comment: 4pages,4figures,to be published in J.Phys.Soc.Jp
Quivers via anomaly chains
We study quivers in the context of matrix models. We introduce chains of
generalized Konishi anomalies to write the quadratic and cubic equations that
constrain the resolvents of general affine and non-affine quiver gauge
theories, and give a procedure to calculate all higher-order relations. For
these theories we also evaluate, as functions of the resolvents, VEV's of
chiral operators with two and four bifundamental insertions. As an example of
the general procedure we explicitly consider the two simplest quivers A2 and
A1(affine), obtaining in the first case a cubic algebraic curve, and for the
affine theory the same equation as that of U(N) theories with adjoint matter,
successfully reproducing the RG cascade result.Comment: 32 pages, latex; typos corrected, published versio
Non-ohmic critical fluctuation conductivity of layered superconductors in magnetic field
Thermal fluctuation conductivity for a layered superconductor in
perpendicular magnetic field is treated in the frame of the self-consistent
Hartree approximation for an arbitrarily strong in-plane electric field. The
simultaneous application of the two fields results in a slightly stronger
suppression of the superconducting fluctuations, compared to the case when the
fields are applied individually.Comment: 4 pages, 1 figure, to be published in Phys. Rev.
Gravitational F-terms of N=1 Supersymmetric Gauge Theories
We consider four-dimensional N=1 supersymmetric gauge theories in a
supergravity background. We use generalized Konishi anomaly equations and
R-symmetry anomaly to compute the exact perturbative and non-perturbative
gravitational F-terms. We study two types of theories: The first model breaks
supersymmetry dynamically, and the second is based on a gauge group. The
results are compared with the corresponding vector models. We discuss the
diagrammatic expansion of the theory.Comment: LaTeX2e, 23 pages, 2 figures. Added a reference and converted into
JHEP styl
Superpotentials from flux compactifications of M-theory
In flux compactifications of M-theory a superpotential is generated whose
explicit form depends on the structure group of the 7-dimensional internal
manifold. In this note, we discuss superpotentials for the structure groups:
G_2, SU(3) or SU(2). For the G_2 case all internal fluxes have to vanish. For
SU(3) structures, the non-zero flux components entering the superpotential
describe an effective 1-dimensional model and a Chern-Simons model if there are
SU(2) structures.Comment: 10 page
Exact scaling properties of a hierarchical network model
We report on exact results for the degree , the diameter , the
clustering coefficient , and the betweenness centrality of a
hierarchical network model with a replication factor . Such quantities are
calculated exactly with the help of recursion relations. Using the results, we
show that (i) the degree distribution follows a power law with , (ii) the diameter grows
logarithmically as with the number of nodes , (iii) the
clustering coefficient of each node is inversely proportional to its degree, , and the average clustering coefficient is nonzero in the infinite
limit, and (iv) the betweenness centrality distribution follows a power law
. We discuss a classification scheme of scale-free networks
into the universality class with the clustering property and the betweenness
centrality distribution.Comment: 4 page
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