195,788 research outputs found
Phase transition in the two star Exponential Random Graph Model
This paper gives a way to simulate from the two star probability distribution
on the space of simple graphs via auxiliary variables. Using this simulation
scheme, the model is explored for various domains of the parameter values, and
the phase transition boundaries are identified, and shown to be similar as that
of the Curie-Weiss model of statistical physics. Concentration results are
obtained for all the degrees, which further validate the phase transition
predictions.Comment: 21 pages, 7 figure
edge2vec: Representation learning using edge semantics for biomedical knowledge discovery
Representation learning provides new and powerful graph analytical approaches
and tools for the highly valued data science challenge of mining knowledge
graphs. Since previous graph analytical methods have mostly focused on
homogeneous graphs, an important current challenge is extending this
methodology for richly heterogeneous graphs and knowledge domains. The
biomedical sciences are such a domain, reflecting the complexity of biology,
with entities such as genes, proteins, drugs, diseases, and phenotypes, and
relationships such as gene co-expression, biochemical regulation, and
biomolecular inhibition or activation. Therefore, the semantics of edges and
nodes are critical for representation learning and knowledge discovery in real
world biomedical problems. In this paper, we propose the edge2vec model, which
represents graphs considering edge semantics. An edge-type transition matrix is
trained by an Expectation-Maximization approach, and a stochastic gradient
descent model is employed to learn node embedding on a heterogeneous graph via
the trained transition matrix. edge2vec is validated on three biomedical domain
tasks: biomedical entity classification, compound-gene bioactivity prediction,
and biomedical information retrieval. Results show that by considering
edge-types into node embedding learning in heterogeneous graphs,
\textbf{edge2vec}\ significantly outperforms state-of-the-art models on all
three tasks. We propose this method for its added value relative to existing
graph analytical methodology, and in the real world context of biomedical
knowledge discovery applicability.Comment: 10 page
Dynamically generated cyclic dominance in spatial prisoner's dilemma games
We have studied the impact of time-dependent learning capacities of players
in the framework of spatial prisoner's dilemma game. In our model, this
capacity of players may decrease or increase in time after strategy adoption
according to a step-like function. We investigated both possibilities
separately and observed significantly different mechanisms that form the
stationary pattern of the system. The time decreasing learning activity helps
cooperator domains to recover the possible intrude of defectors hence supports
cooperation. In the other case the temporary restrained learning activity
generates a cyclic dominance between defector and cooperator strategies, which
helps to maintain the diversity of strategies via propagating waves. The
results are robust and remain valid by changing payoff values, interaction
graphs or functions characterizing time-dependence of learning activity. Our
observations suggest that dynamically generated mechanisms may offer
alternative ways to keep cooperators alive even at very larger temptation to
defect.Comment: 7 pages, 6 figures, accepted for publication in Physical Review
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