23,652 research outputs found
Planar growth generates scale free networks
In this paper we introduce a model of spatial network growth in which nodes
are placed at randomly selected locations on a unit square in ,
forming new connections to old nodes subject to the constraint that edges do
not cross. The resulting network has a power law degree distribution, high
clustering and the small world property. We argue that these characteristics
are a consequence of the two defining features of the network formation
procedure; growth and planarity conservation. We demonstrate that the model can
be understood as a variant of random Apollonian growth and further propose a
one parameter family of models with the Random Apollonian Network and the
Deterministic Apollonian Network as extreme cases and our model as a midpoint
between them. We then relax the planarity constraint by allowing edge crossings
with some probability and find a smooth crossover from power law to exponential
degree distributions when this probability is increased.Comment: 27 pages, 9 figure
Maximal planar networks with large clustering coefficient and power-law degree distribution
In this article, we propose a simple rule that generates scale-free networks
with very large clustering coefficient and very small average distance. These
networks are called {\bf Random Apollonian Networks}(RAN) as they can be
considered as a variation of Apollonian networks. We obtain the analytic
results of power-law exponent and clustering coefficient
, which agree very well with the
simulation results. We prove that the increasing tendency of average distance
of RAN is a little slower than the logarithm of the number of nodes in RAN.
Since most real-life networks are both scale-free and small-world networks, RAN
may perform well in mimicking the reality. The RAN possess hierarchical
structure as that in accord with the observations of many
real-life networks. In addition, we prove that RAN are maximal planar networks,
which are of particular practicability for layout of printed circuits and so
on. The percolation and epidemic spreading process are also studies and the
comparison between RAN and Barab\'{a}si-Albert(BA) as well as Newman-Watts(NW)
networks are shown. We find that, when the network order (the total number
of nodes) is relatively small(as ), the performance of RAN under
intentional attack is not sensitive to , while that of BA networks is much
affected by . And the diseases spread slower in RAN than BA networks during
the outbreaks, indicating that the large clustering coefficient may slower the
spreading velocity especially in the outbreaks.Comment: 13 pages, 10 figure
Heterogeneity for IGF-II production maintained by public goods dynamics in neuroendocrine pancreatic cancer
The extensive intratumor heterogeneity revealed by sequencing cancer genomes is an essential determinant of tumor progression, diagnosis, and treatment. What maintains heterogeneity remains an open question because competition within a tumor leads to a strong selection for the fittest subclone. Cancer cells also cooperate by sharing molecules with paracrine effects, such as growth factors, and heterogeneity can be maintained if subclones depend on each other for survival. Without strict interdependence between subclones, however, nonproducer cells can free-ride on the growth factors produced by neighboring producer cells, a collective action problem known in game theory as the “tragedy of the commons,” which has been observed in microbial cell populations. Here, we report that similar dynamics occur in cancer cell populations. Neuroendocrine pancreatic cancer (insulinoma) cells that do not produce insulin-like growth factor II (IGF-II) grow slowly in pure cultures but have a proliferation advantage in mixed cultures, where they can use the IGF-II provided by producer cells. We show that, as predicted by evolutionary game theory, producer cells do not go extinct because IGF-II acts as a nonlinear public good, creating negative frequency-dependent selection that leads to a stable coexistence of the two cell types. Intratumor cell heterogeneity can therefore be maintained even without strict interdependence between cell subclones. Reducing the amount of growth factors available within a tumor may lead to a reduction in growth followed by a new equilibrium, which may explain relapse in therapies that target growth factors
A deterministic small-world network created by edge iterations
Small-world networks are ubiquitous in real-life systems. Most previous
models of small-world networks are stochastic. The randomness makes it more
difficult to gain a visual understanding on how do different nodes of networks
interact with each other and is not appropriate for communication networks that
have fixed interconnections. Here we present a model that generates a
small-world network in a simple deterministic way. Our model has a discrete
exponential degree distribution. We solve the main characteristics of the
model.Comment: 9 pages, 1 figure. to appear in Physica
- …