210 research outputs found
Stability of the Kauffman Model
Random Boolean networks, the Kauffman model, are revisited by means of a
novel decimation algorithm, which reduces the networks to their dynamical
cores. The average size of the removed part, the stable core, grows
approximately linearly with N, the number of nodes in the original networks. We
show that this can be understood as the percolation of the stability signal in
the network. The stability of the dynamical core is investigated and it is
shown that this core lacks the well known stability observed in full Kauffman
networks. We conclude that, somewhat counter-intuitive, the remarkable
stability of Kauffman networks is generated by the dynamics of the stable core.
The decimation method is also used to simulate large critical Kauffman
networks. For networks up to N=32 we perform full enumeration studies. Strong
evidence is provided for that the number of limit cycles grows linearly with N.
This result is in sharp contrast to the often cited behavior.Comment: 12 pages, 4 figure
The Strong-Coupling Expansion in Simplicial Quantum Gravity
We construct the strong-coupling series in 4d simplicial quantum gravity up
to volume 38. It is used to calculate estimates for the string susceptibility
exponent gamma for various modifications of the theory. It provides a very
efficient way to get a first view of the phase structure of the models.Comment: LATTICE98(surfaces), 3 pages, 4 eps figure
Probabilistic estimation of microarray data reliability and underlying gene expression
Background: The availability of high throughput methods for measurement of
mRNA concentrations makes the reliability of conclusions drawn from the data
and global quality control of samples and hybridization important issues. We
address these issues by an information theoretic approach, applied to
discretized expression values in replicated gene expression data.
Results: Our approach yields a quantitative measure of two important
parameter classes: First, the probability that a gene is in the
biological state in a certain variety, given its observed expression
in the samples of that variety. Second, sample specific error probabilities
which serve as consistency indicators of the measured samples of each variety.
The method and its limitations are tested on gene expression data for
developing murine B-cells and a -test is used as reference. On a set of
known genes it performs better than the -test despite the crude
discretization into only two expression levels. The consistency indicators,
i.e. the error probabilities, correlate well with variations in the biological
material and thus prove efficient.
Conclusions: The proposed method is effective in determining differential
gene expression and sample reliability in replicated microarray data. Already
at two discrete expression levels in each sample, it gives a good explanation
of the data and is comparable to standard techniques.Comment: 11 pages, 4 figure
Phase Transition of 4D Simplicial Quantum Gravity with U(1) Gauge Field
The phase transition of 4D simplicial quantum gravity coupled to U(1) gauge
fields is studied using Monte-Carlo simulations. The phase transition of the
dynamical triangulation model with vector field () is smooth as
compared with the pure gravity(). The node susceptibility () is
studied in the finite size scaling method. At the critical point, the node
distribution has a sharp peak in contrast to the double peak in the pure
gravity. From the numerical results, we expect that 4D simplicial quantum
gravity with U(1) vector fields has higher order phase transition than 1st
order, which means the possibility to take the continuum limit at the critical
point.Comment: 3 pages, latex, 3 eps figures, uses espcrc2.sty. Talk presented at
LATTICE99(gravity
On the number of attractors in random Boolean networks
The evaluation of the number of attractors in Kauffman networks by Samuelsson
and Troein is generalized to critical networks with one input per node and to
networks with two inputs per node and different probability distributions for
update functions. A connection is made between the terms occurring in the
calculation and between the more graphic concepts of frozen, nonfrozen and
relevant nodes, and relevant components. Based on this understanding, a
phenomenological argument is given that reproduces the dependence of the
attractor numbers on system size.Comment: 6 page
Universality of hypercubic random surfaces
We study universality properties of the Weingarten hyper-cubic random
surfaces. Since a long time ago the model with a local restriction forbidding
surface self-bendings has been thought to be in a different universality class
from the unrestricted model defined on the full set of surfaces. We show that
both models in fact belong to the same universality class with the entropy
exponent gamma = 1/2 and differ by finite size effects which are much more
pronounced in the restricted model.Comment: 8 pages, 3 figure
Phase transition and topology in 4d simplicial gravity
We present data indicating that the recent evidence for the phase transition
being of first order does not result from a breakdown of the ergodicity of the
algorithm. We also present data showing that the thermodynamical limit of the
model is independent of topology.Comment: 3 latex pages + 4 ps fig. + espcrc2.sty. Talk presented at
LATTICE(gravity
Simulating Four-Dimensional Simplicial Gravity using Degenerate Triangulations
We extend a model of four-dimensional simplicial quantum gravity to include
degenerate triangulations in addition to combinatorial triangulations
traditionally used. Relaxing the constraint that every 4-simplex is uniquely
defined by a set of five distinct vertexes, we allow triangulations containing
multiply connected simplexes and distinct simplexes defined by the same set of
vertexes. We demonstrate numerically that including degenerated triangulations
substantially reduces the finite-size effects in the model. In particular, we
provide a strong numerical evidence for an exponential bound on the entropic
growth of the ensemble of degenerate triangulations, and show that a
discontinuous crumpling transition is already observed on triangulations of
volume N_4 ~= 4000.Comment: Latex, 8 pages, 4 eps-figure
4d Simplicial Quantum Gravity Interacting with Gauge Matter Fields
The effect of coupling non-compact gauge fields to four dimensional
simplicial quantum gravity is studied using strong coupling expansions and
Monte Carlo simulations. For one gauge field the back-reaction of the matter on
the geometry is weak. This changes, however, as more matter fields are
introduced. For more than two gauge fields the degeneracy of random manifolds
into branched polymers does not occur, and the branched polymer phase seems to
be replaced by a new phase with a negative string susceptibility exponent
and fractal dimension .Comment: latex2e, 10 pages incorporating 2 tables and 3 figures (using epsf
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