336 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

### 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

### Exploring Temporal Networks with Greedy Walks

Temporal networks come with a wide variety of heterogeneities, from
burstiness of event sequences to correlations between timings of node and link
activations. In this paper, we set to explore the latter by using greedy walks
as probes of temporal network structure. Given a temporal network (a sequence
of contacts), greedy walks proceed from node to node by always following the
first available contact. Because of this, their structure is particularly
sensitive to temporal-topological patterns involving repeated contacts between
sets of nodes. This becomes evident in their small coverage per step as
compared to a temporal reference model -- in empirical temporal networks,
greedy walks often get stuck within small sets of nodes because of correlated
contact patterns. While this may also happen in static networks that have
pronounced community structure, the use of the temporal reference model takes
the underlying static network structure out of the equation and indicates that
there is a purely temporal reason for the observations. Further analysis of the
structure of greedy walks indicates that burst trains, sequences of repeated
contacts between node pairs, are the dominant factor. However, there are larger
patterns too, as shown with non-backtracking greedy walks. We proceed further
to study the entropy rates of greedy walks, and show that the sequences of
visited nodes are more structured and predictable in original data as compared
to temporally uncorrelated references. Taken together, these results indicate a
richness of correlated temporal-topological patterns in temporal networks

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