4,101 research outputs found
The conical K\"ahler-Ricci flow on Fano manifolds
In this paper, we study the long-term behavior of the conical K\"ahler-Ricci
flow on Fano manifold . First, based on our work of locally uniform
regularity for the twisted K\"ahler-Ricci flows, we obtain a long-time solution
to the conical K\"ahler-Ricci flow by limiting a sequence of these twisted
flows. Second, we study the uniform Perelman's estimates of the twisted
K\"ahler-Ricci flows. After that, we prove that the conical K\"ahler-Ricci flow
must converge to a conical K\"ahler-Einstein metric if there exists one.Comment: 46 page
LATTE: Application Oriented Social Network Embedding
In recent years, many research works propose to embed the network structured
data into a low-dimensional feature space, where each node is represented as a
feature vector. However, due to the detachment of embedding process with
external tasks, the learned embedding results by most existing embedding models
can be ineffective for application tasks with specific objectives, e.g.,
community detection or information diffusion. In this paper, we propose study
the application oriented heterogeneous social network embedding problem.
Significantly different from the existing works, besides the network structure
preservation, the problem should also incorporate the objectives of external
applications in the objective function. To resolve the problem, in this paper,
we propose a novel network embedding framework, namely the "appLicAtion
orienTed neTwork Embedding" (Latte) model. In Latte, the heterogeneous network
structure can be applied to compute the node "diffusive proximity" scores,
which capture both local and global network structures. Based on these computed
scores, Latte learns the network representation feature vectors by extending
the autoencoder model model to the heterogeneous network scenario, which can
also effectively unite the objectives of network embedding and external
application tasks. Extensive experiments have been done on real-world
heterogeneous social network datasets, and the experimental results have
demonstrated the outstanding performance of Latte in learning the
representation vectors for specific application tasks.Comment: 11 Pages, 12 Figures, 1 Tabl
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