315 research outputs found

### Critical Boolean networks with scale-free in-degree distribution

We investigate analytically and numerically the dynamical properties of
critical Boolean networks with power-law in-degree distributions. When the
exponent of the in-degree distribution is larger than 3, we obtain results
equivalent to those obtained for networks with fixed in-degree, e.g., the
number of the non-frozen nodes scales as $N^{2/3}$ with the system size $N$.
When the exponent of the distribution is between 2 and 3, the number of the
non-frozen nodes increases as $N^x$, with $x$ being between 0 and 2/3 and
depending on the exponent and on the cutoff of the in-degree distribution.
These and ensuing results explain various findings obtained earlier by computer
simulations.Comment: 5 pages, 1 graph, 1 sketch, submitte

### Formation of Space-Time Structure in a Forest-Fire Model

We present a general stochastic forest-fire model which shows a variety of
different structures depending on the parameter values. The model contains
three possible states per site (tree, burning tree, empty site) and three
parameters (tree growth probability $p$, lightning probability $f$, and
immunity $g$). We review analytic and computer simulation results for a
quasideterministic state with spiral-shaped fire fronts, for a percolation-like
phase transition and a self-organized critical state. Possible applications to
excitable systems are discussed.Comment: 20 pages REVTEX, 9 figures upon reques

### Relevant components in critical random Boolean networks

Random Boolean networks were introduced in 1969 by Kauffman as a model for
gene regulation. By combining analytical arguments and efficient numerical
simulations, we evaluate the properties of relevant components of critical
random Boolean networks independently of update scheme. As known from previous
work, the number of relevant components grows logarithmically with network
size. We find that in most networks all relevant nodes with more than one
relevant input sit in the same component, while all other relevant components
are simple loops. As the proportion of nonfrozen nodes with two relevant inputs
increases, the number of relevant components decreases and the size and
complexity of the largest complex component grows. We evaluate the probability
distribution of different types of complex components in an ensemble of
networks and confirm that it becomes independent of network size in the limit
of large network size. In this limit, we determine analytically the frequencies
of occurence of complex components with different topologies.Comment: 9 pages, 6 figure

### Modelling Food Webs

We review theoretical approaches to the understanding of food webs. After an
overview of the available food web data, we discuss three different classes of
models. The first class comprise static models, which assign links between
species according to some simple rule. The second class are dynamical models,
which include the population dynamics of several interacting species. We focus
on the question of the stability of such webs. The third class are species
assembly models and evolutionary models, which build webs starting from a few
species by adding new species through a process of "invasion" (assembly models)
or "speciation" (evolutionary models). Evolutionary models are found to be
capable of building large stable webs.Comment: 34 pages, 2 figures. To be published in "Handbook of graphs and
networks" S. Bornholdt and H. G. Schuster (eds) (Wiley-VCH, Berlin

### Crossover from Percolation to Self-Organized Criticality

We include immunity against fire as a new parameter into the self-organized
critical forest-fire model. When the immunity assumes a critical value,
clusters of burnt trees are identical to percolation clusters of random bond
percolation. As long as the immunity is below its critical value, the
asymptotic critical exponents are those of the original self-organized critical
model, i.e. the system performs a crossover from percolation to self-organized
criticality. We present a scaling theory and computer simulation results.Comment: 4 pages Revtex, two figures included, to be published in PR

### On the influence of the intermolecular potential on the wetting properties of water on silica surfaces

We study the wetting properties of water on silica surfaces using molecular
dynamics (MD) simulations. To describe the intermolecular interaction between
water and silica atoms, two types of interaction potential models are used: the
standard Br\'odka and Zerda (BZ) model, and the Gulmen and Thompson (GT) model.
We perform an in-depth analysis of the influence of the choice of the potential
on the arrangement of the water molecules in partially filled pores and on top
of silica slabs. We find that at moderate pore filling ratios, the GT silica
surface is completely wetted by water molecules, which agrees well with
experimental findings, while the commonly used BZ surface is less hydrophilic
and is only partially wetted. We interpret our simulation results using an
analytical calculation of the phase diagram of water in partially filled pores.
Moreover, an evaluation of the contact angle of the water droplet on top of the
silica slab reveals that the interaction becomes more hydrophilic with
increasing slab thickness and saturates around 2.5-3 nm, in agreement with the
experimentally found value. Our analysis also shows that the hydroaffinity of
the surface is mainly determined by the electrostatic interaction, but that the
van der Waals interaction nevertheless is strong enough that it can turn a
hydrophobic surface into a hydrophilic surface.Comment: Article: 9 pages, 7 Figures. There is also a supplementary
information file: 2 pages, 3 Figure

### The phase diagram of random threshold networks

Threshold networks are used as models for neural or gene regulatory networks.
They show a rich dynamical behaviour with a transition between a frozen and a
chaotic phase. We investigate the phase diagram of randomly connected threshold
networks with real-valued thresholds h and a fixed number of inputs per node.
The nodes are updated according to the same rules as in a model of the
cell-cycle network of Saccharomyces cereviseae [PNAS 101, 4781 (2004)]. Using
the annealed approximation, we derive expressions for the time evolution of the
proportion of nodes in the "on" and "off" state, and for the sensitivity
$\lambda$. The results are compared with simulations of quenched networks. We
find that for integer values of h the simulations show marked deviations from
the annealed approximation even for large networks. This can be attributed to
the particular choice of the updating rule.Comment: 8 pages, 6 figure

### Scaling laws and simulation results for the self--organized critical forest--fire model

We discuss the properties of a self--organized critical forest--fire model
which has been introduced recently. We derive scaling laws and define critical
exponents. The values of these critical exponents are determined by computer
simulations in 1 to 8 dimensions. The simulations suggest a critical dimension
$d_c=6$ above which the critical exponents assume their mean--field values.
Changing the lattice symmetry and allowing trees to be immune against fire, we
show that the critical exponents are universal.Comment: 12 pages, postscript uuencoded, figures included, to appear in Phys.
Rev.

### Boolean networks with reliable dynamics

We investigated the properties of Boolean networks that follow a given
reliable trajectory in state space. A reliable trajectory is defined as a
sequence of states which is independent of the order in which the nodes are
updated. We explored numerically the topology, the update functions, and the
state space structure of these networks, which we constructed using a minimum
number of links and the simplest update functions. We found that the clustering
coefficient is larger than in random networks, and that the probability
distribution of three-node motifs is similar to that found in gene regulation
networks. Among the update functions, only a subset of all possible functions
occur, and they can be classified according to their probability. More
homogeneous functions occur more often, leading to a dominance of canalyzing
functions. Finally, we studied the entire state space of the networks. We
observed that with increasing systems size, fixed points become more dominant,
moving the networks close to the frozen phase.Comment: 11 Pages, 15 figure

### Forest fires and other examples of self-organized criticality

We review the properties of the self-organized critical (SOC) forest-fire
model. The paradigm of self-organized criticality refers to the tendency of
certain large dissipative systems to drive themselves into a critical state
independent of the initial conditions and without fine-tuning of the
parameters. After an introduction, we define the rules of the model and discuss
various large-scale structures which may appear in this system. The origin of
the critical behavior is explained, critical exponents are introduced, and
scaling relations between the exponents are derived. Results of computer
simulations and analytical calculations are summarized. The existence of an
upper critical dimension and the universality of the critical behavior under
changes of lattice symmetry or the introduction of immunity are discussed. A
survey of interesting modifications of the forest-fire model is given. Finally,
several other important SOC models are briefly described.Comment: 37 pages RevTeX, 13 PostScript figures (Figs 1, 4, 13 are of reduced
quality to keep download times small

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