1,455 research outputs found
Complex Network Analysis of State Spaces for Random Boolean Networks
We apply complex network analysis to the state spaces of random Boolean
networks (RBNs). An RBN contains Boolean elements each with inputs. A
directed state space network (SSN) is constructed by linking each dynamical
state, represented as a node, to its temporal successor. We study the
heterogeneity of an SSN at both local and global scales, as well as
sample-to-sample fluctuations within an ensemble of SSNs. We use in-degrees of
nodes as a local topological measure, and the path diversity [Phys. Rev. Lett.
98, 198701 (2007)] of an SSN as a global topological measure. RBNs with exhibit non-trivial fluctuations at both local and global scales,
while K=2 exhibits the largest sample-to-sample, possibly non-self-averaging,
fluctuations. We interpret the observed ``multi scale'' fluctuations in the
SSNs as indicative of the criticality and complexity of K=2 RBNs. ``Garden of
Eden'' (GoE) states are nodes on an SSN that have in-degree zero. While
in-degrees of non-GoE nodes for SSNs can assume any integer value between
0 and , for K=1 all the non-GoE nodes in an SSN have the same in-degree
which is always a power of two
Dry and wet interfaces: Influence of solvent particles on molecular recognition
We present a coarse-grained lattice model to study the influence of water on
the recognition process of two rigid proteins. The basic model is formulated in
terms of the hydrophobic effect. We then investigate several modifications of
our basic model showing that the selectivity of the recognition process can be
enhanced by considering the explicit influence of single solvent particles.
When the number of cavities at the interface of a protein-protein complex is
fixed as an intrinsic geometric constraint, there typically exists a
characteristic fraction that should be filled with water molecules such that
the selectivity exhibits a maximum. In addition the optimum fraction depends on
the hydrophobicity of the interface so that one has to distinguish between dry
and wet interfaces.Comment: 11 pages, 7 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
. 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
New Universality Classes for Two-Dimensional -Models
We argue that the two-dimensional -invariant lattice -model
with mixed isovector/isotensor action has a one-parameter family of nontrivial
continuum limits, only one of which is the continuum -model constructed
by conventional perturbation theory. We test the proposed scenario with a
high-precision Monte Carlo simulation for on lattices up to , using a Wolff-type embedding algorithm. [CPU time 7 years IBM
RS-6000/320H] The finite-size-scaling data confirm the existence of the
predicted new family of continuum limits. In particular, the and
-vector models do not lie in the same universality class.Comment: 10 pages (includes 2 figures), 211176 bytes Postscript,
NYU-TH-93/07/03, IFUP-TH 34/9
Random sampling vs. exact enumeration of attractors in random Boolean networks
We clarify the effect different sampling methods and weighting schemes have
on the statistics of attractors in ensembles of random Boolean networks (RBNs).
We directly measure cycle lengths of attractors and sizes of basins of
attraction in RBNs using exact enumeration of the state space. In general, the
distribution of attractor lengths differs markedly from that obtained by
randomly choosing an initial state and following the dynamics to reach an
attractor. Our results indicate that the former distribution decays as a
power-law with exponent 1 for all connectivities in the infinite system
size limit. In contrast, the latter distribution decays as a power law only for
K=2. This is because the mean basin size grows linearly with the attractor
cycle length for , and is statistically independent of the cycle length
for K=2. We also find that the histograms of basin sizes are strongly peaked at
integer multiples of powers of two for
Temperature Chaos in Two-Dimensional Ising Spin Glasses with Binary Couplings: a Further Case for Universality
We study temperature chaos in a two-dimensional Ising spin glass with random
quenched bimodal couplings, by an exact computation of the partition functions
on large systems. We study two temperature correlators from the total free
energy and from the domain wall free energy: in the second case we detect a
chaotic behavior. We determine and discuss the chaos exponent and the fractal
dimension of the domain walls.Comment: 5 pages, 6 postscript figures; added reference
Topological correlations in soap froths
Correlation in two-dimensional soap froth is analysed with an effective
potential for the first time. Cells with equal number of sides repel (with
linear correlation) while cells with different number of sides attract (with
NON-bilinear) for nearest neighbours, which cannot be explained by the maximum
entropy argument. Also, the analysis indicates that froth is correlated up to
the third shell neighbours at least, contradicting the conventional ideas that
froth is not strongly correlated.Comment: 10 Pages LaTeX, 6 Postscript figure
Zero-temperature behavior of the random-anisotropy model in the strong-anisotropy limit
We consider the random-anisotropy model on the square and on the cubic
lattice in the strong-anisotropy limit. We compute exact ground-state
configurations, and we use them to determine the stiffness exponent at zero
temperature; we find and respectively
in two and three dimensions. These results show that the low-temperature phase
of the model is the same as that of the usual Ising spin-glass model. We also
show that no magnetic order occurs in two dimensions, since the expectation
value of the magnetization is zero and spatial correlation functions decay
exponentially. In three dimensions our data strongly support the absence of
spontaneous magnetization in the infinite-volume limit
Simple model of self-organized biological evolution as completely integrable dissipative system
The Bak-Sneppen model of self-organized biological evolution of an infinite
ecosystem of randomly interacting species is represented in terms of an
infinite set of variables which can be considered as an analog to the set of
integrals of motion of completely integrable system. Each of this variables
remains to be constant but its influence on the evolution process is restricted
in time and after definite moment its value is excluded from description of the
system dynamics.Comment: LaTeX, 7 page
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