8,164 research outputs found

### Shadows of the SIS immortality transition in small networks

Much of the research on the behavior of the SIS model on networks has
concerned the infinite size limit; in particular the phase transition between a
state where outbreaks can reach a finite fraction of the population, and a
state where only a finite number would be infected. For finite networks, there
is also a dynamic transition---the immortality transition---when the
per-contact transmission probability $\lambda$ reaches one. If $\lambda < 1$,
the probability that an outbreak will survive by an observation time $t$ tends
to zero as $t \rightarrow \infty$; if $\lambda = 1$, this probability is one.
We show that treating $\lambda = 1$ as a critical point predicts the
$\lambda$-dependence of the survival probability also for more moderate
$\lambda$-values. The exponent, however, depends on the underlying network.
This fact could, by measuring how a vertex' deletion changes the exponent, be
used to evaluate the role of a vertex in the outbreak. Our work also confirms
an extremely clear separation between the early die-off (from the outbreak
failing to take hold in the population) and the later extinctions
(corresponding to rare stochastic events of several consecutive transmission
events failing to occur).Comment: Bug fixes from the first versio

### Model validation of simple-graph representations of metabolism

The large-scale properties of chemical reaction systems, such as the
metabolism, can be studied with graph-based methods. To do this, one needs to
reduce the information -- lists of chemical reactions -- available in
databases. Even for the simplest type of graph representation, this reduction
can be done in several ways. We investigate different simple network
representations by testing how well they encode information about one
biologically important network structure -- network modularity (the propensity
for edges to be cluster into dense groups that are sparsely connected between
each other). To reach this goal, we design a model of reaction-systems where
network modularity can be controlled and measure how well the reduction to
simple graphs capture the modular structure of the model reaction system. We
find that the network types that best capture the modular structure of the
reaction system are substrate-product networks (where substrates are linked to
products of a reaction) and substance networks (with edges between all
substances participating in a reaction). Furthermore, we argue that the
proposed model for reaction systems with tunable clustering is a general
framework for studies of how reaction-systems are affected by modularity. To
this end, we investigate statistical properties of the model and find, among
other things, that it recreate correlations between degree and mass of the
molecules.Comment: to appear in J. Roy. Soc. Intefac

### Threshold model of cascades in temporal networks

Threshold models try to explain the consequences of social influence like the
spread of fads and opinions. Along with models of epidemics, they constitute a
major theoretical framework of social spreading processes. In threshold models
on static networks, an individual changes her state if a certain fraction of
her neighbors has done the same. When there are strong correlations in the
temporal aspects of contact patterns, it is useful to represent the system as a
temporal network. In such a system, not only contacts but also the time of the
contacts are represented explicitly. There is a consensus that bursty temporal
patterns slow down disease spreading. However, as we will see, this is not a
universal truth for threshold models. In this work, we propose an extension of
Watts' classic threshold model to temporal networks. We do this by assuming
that an agent is influenced by contacts which lie a certain time into the past.
I.e., the individuals are affected by contacts within a time window. In
addition to thresholds as the fraction of contacts, we also investigate the
number of contacts within the time window as a basis for influence. To
elucidate the model's behavior, we run the model on real and randomized
empirical contact datasets.Comment: 7 pages, 5 figures, 2 table

### Attractiveness and activity in Internet communities

Datasets of online communication often take the form of contact sequences --
ordered lists contacts (where a contact is defined as a triple of a sender, a
recipient and a time). We propose measures of attractiveness and activity for
such data sets and analyze these quantities for anonymized contact sequences
from an Internet dating community. For this data set the attractiveness and
activity measures show broad power-law like distributions. Our attractiveness
and activity measures are more strongly correlated in the real-world data than
in our reference model. Effects that indirectly can make active users more
attractive are discussed

### A Zero-Temperature Study of Vortex Mobility in Two-Dimensional Vortex Glass Models

Three different vortex glass models are studied by examining the energy
barrier against vortex motion across the system. In the two-dimensional gauge
glass this energy barrier is found to increase logarithmically with system size
which is interpreted as evidence for a low-temperature phase with zero
resistivity. Associated with the large energy barriers is a breaking of
ergodicity which explains why the well established results from equilibrium
studies could fail. The behavior of the more realistic random pinning model is
however different with decreasing energy barriers a no finite critical
temperature

- â€¦