25,256 research outputs found
Mining Frequent Neighborhood Patterns in Large Labeled Graphs
Over the years, frequent subgraphs have been an important sort of targeted
patterns in the pattern mining literatures, where most works deal with
databases holding a number of graph transactions, e.g., chemical structures of
compounds. These methods rely heavily on the downward-closure property (DCP) of
the support measure to ensure an efficient pruning of the candidate patterns.
When switching to the emerging scenario of single-graph databases such as
Google Knowledge Graph and Facebook social graph, the traditional support
measure turns out to be trivial (either 0 or 1). However, to the best of our
knowledge, all attempts to redefine a single-graph support resulted in measures
that either lose DCP, or are no longer semantically intuitive.
This paper targets mining patterns in the single-graph setting. We resolve
the "DCP-intuitiveness" dilemma by shifting the mining target from frequent
subgraphs to frequent neighborhoods. A neighborhood is a specific topological
pattern where a vertex is embedded, and the pattern is frequent if it is shared
by a large portion (above a given threshold) of vertices. We show that the new
patterns not only maintain DCP, but also have equally significant semantics as
subgraph patterns. Experiments on real-life datasets display the feasibility of
our algorithms on relatively large graphs, as well as the capability of mining
interesting knowledge that is not discovered in prior works.Comment: 9 page
Holographic Van der Waals phase transition for a hairy black hole
The Van der Waals(VdW) phase transition in a hairy black hole is investigated
by analogizing its charge, temperature, and entropy as the temperature,
pressure, and volume in the fluid respectively. The two point correlation
function(TCF), which is dual to the geodesic length, is employed to probe this
phase transition. We find the phase structure in the temperaturegeodesic
length plane resembles as that in the temperaturethermal entropy plane
besides the scale of the horizontal coordinate. In addition, we find the equal
area law(EAL) for the first order phase transition and critical exponent of the
heat capacity for the second order phase transition in the
temperaturegeodesic length plane are consistent with that in
temperaturethermal entropy plane, which implies that the TCF is a good probe
to probe the phase structure of the back hole.Comment: Accepted by Advances in High Energy Physics(The special issue:
Applications of the Holographic Duality to Strongly Coupled Quantum Systems
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