833,060 research outputs found
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
Neural network setups for a precise detection of the many-body localization transition: finite-size scaling and limitations
Determining phase diagrams and phase transitions semi-automatically using
machine learning has received a lot of attention recently, with results in good
agreement with more conventional approaches in most cases. When it comes to
more quantitative predictions, such as the identification of universality class
or precise determination of critical points, the task is more challenging. As
an exacting test-bed, we study the Heisenberg spin-1/2 chain in a random
external field that is known to display a transition from a many-body localized
to a thermalizing regime, which nature is not entirely characterized. We
introduce different neural network structures and dataset setups to achieve a
finite-size scaling analysis with the least possible physical bias (no assumed
knowledge on the phase transition and directly inputing wave-function
coefficients), using state-of-the-art input data simulating chains of sizes up
to L=24. In particular, we use domain adversarial techniques to ensure that the
network learns scale-invariant features. We find a variability of the output
results with respect to network and training parameters, resulting in
relatively large uncertainties on final estimates of critical point and
correlation length exponent which tend to be larger than the values obtained
from conventional approaches. We put the emphasis on interpretability
throughout the paper and discuss what the network appears to learn for the
various used architectures. Our findings show that a it quantitative analysis
of phase transitions of unknown nature remains a difficult task with neural
networks when using the minimally engineered physical input.Comment: v2: published versio
Fair Evaluation of Global Network Aligners
Biological network alignment identifies topologically and functionally
conserved regions between networks of different species. It encompasses two
algorithmic steps: node cost function (NCF), which measures similarities
between nodes in different networks, and alignment strategy (AS), which uses
these similarities to rapidly identify high-scoring alignments. Different
methods use both different NCFs and different ASs. Thus, it is unclear whether
the superiority of a method comes from its NCF, its AS, or both. We already
showed on MI-GRAAL and IsoRankN that combining NCF of one method and AS of
another method can lead to a new superior method. Here, we evaluate MI-GRAAL
against newer GHOST to potentially further improve alignment quality. Also, we
approach several important questions that have not been asked systematically
thus far. First, we ask how much of the node similarity information in NCF
should come from sequence data compared to topology data. Existing methods
determine this more-less arbitrarily, which could affect the resulting
alignment(s). Second, when topology is used in NCF, we ask how large the size
of the neighborhoods of the compared nodes should be. Existing methods assume
that larger neighborhood sizes are better.
We find that MI-GRAAL's NCF is superior to GHOST's NCF, while the performance
of the methods' ASs is data-dependent. Thus, the combination of MI-GRAAL's NCF
and GHOST's AS could be a new superior method for certain data. Also, which
amount of sequence information is used within NCF does not affect alignment
quality, while the inclusion of topological information is crucial. Finally,
larger neighborhood sizes are preferred, but often, it is the second largest
size that is superior, and using this size would decrease computational
complexity.
Together, our results give several general recommendations for a fair
evaluation of network alignment methods.Comment: 19 pages. 10 figures. Presented at the 2014 ISMB Conference, July
13-15, Boston, M
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