41,275 research outputs found
Nonparametric Independence Screening via Favored Smoothing Bandwidth
We propose a flexible nonparametric regression method for
ultrahigh-dimensional data. As a first step, we propose a fast screening method
based on the favored smoothing bandwidth of the marginal local constant
regression. Then, an iterative procedure is developed to recover both the
important covariates and the regression function. Theoretically, we prove that
the favored smoothing bandwidth based screening possesses the model selection
consistency property. Simulation studies as well as real data analysis show the
competitive performance of the new procedure.Comment: 22 page
Numerical evaluation of a two loop diagram in the cutoff regularization
The sunset diagram of theory is evaluated numerically in
cutoff scheme and a nonzero finite term (in accordance with dimensional
regularization (DR) result) is found in contrast to published calculations.
This finding dramatically reduces the critical couplings for symmetry breaking
in the two loop effective potential discussed in our previous work.Comment: 6 pages, revtex, to appear in Comm. Theor. Phy
Representation Learning for Scale-free Networks
Network embedding aims to learn the low-dimensional representations of
vertexes in a network, while structure and inherent properties of the network
is preserved. Existing network embedding works primarily focus on preserving
the microscopic structure, such as the first- and second-order proximity of
vertexes, while the macroscopic scale-free property is largely ignored.
Scale-free property depicts the fact that vertex degrees follow a heavy-tailed
distribution (i.e., only a few vertexes have high degrees) and is a critical
property of real-world networks, such as social networks. In this paper, we
study the problem of learning representations for scale-free networks. We first
theoretically analyze the difficulty of embedding and reconstructing a
scale-free network in the Euclidean space, by converting our problem to the
sphere packing problem. Then, we propose the "degree penalty" principle for
designing scale-free property preserving network embedding algorithm: punishing
the proximity between high-degree vertexes. We introduce two implementations of
our principle by utilizing the spectral techniques and a skip-gram model
respectively. Extensive experiments on six datasets show that our algorithms
are able to not only reconstruct heavy-tailed distributed degree distribution,
but also outperform state-of-the-art embedding models in various network mining
tasks, such as vertex classification and link prediction.Comment: 8 figures; accepted by AAAI 201
The equation of state for scalar-tensor gravity
We show that the field equation of Brans-Dicke gravity and scalar-tensor
gravity can be derived as the equation of state of Rindler spacetime, where the
local thermodynamic equilibrium is maintained. Our derivation implies that the
effective energy can not feel the heat flow across the Rindler horizon.Comment: 6 pages, to be published in Prog. Theor. Phy
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