278,713 research outputs found
Context-aware Path Ranking for Knowledge Base Completion
Knowledge base (KB) completion aims to infer missing facts from existing ones
in a KB. Among various approaches, path ranking (PR) algorithms have received
increasing attention in recent years. PR algorithms enumerate paths between
entity pairs in a KB and use those paths as features to train a model for
missing fact prediction. Due to their good performances and high model
interpretability, several methods have been proposed. However, most existing
methods suffer from scalability (high RAM consumption) and feature explosion
(trains on an exponentially large number of features) problems. This paper
proposes a Context-aware Path Ranking (C-PR) algorithm to solve these problems
by introducing a selective path exploration strategy. C-PR learns global
semantics of entities in the KB using word embedding and leverages the
knowledge of entity semantics to enumerate contextually relevant paths using
bidirectional random walk. Experimental results on three large KBs show that
the path features (fewer in number) discovered by C-PR not only improve
predictive performance but also are more interpretable than existing baselines
Loop Corrections in Non-Linear Cosmological Perturbation Theory II. Two-point Statistics and Self-Similarity
We calculate the lowest-order non-linear contributions to the power spectrum,
two-point correlation function, and smoothed variance of the density field, for
Gaussian initial conditions and scale-free initial power spectra, . These results extend and in some cases correct previous work in the
literature on cosmological perturbation theory. Comparing with the scaling
behavior observed in N-body simulations, we find that the validity of
non-linear perturbation theory depends strongly on the spectral index . For
, we find excellent agreement over scales where the variance \sigma^2(R)
\la 10; however, for , perturbation theory predicts deviations from
self-similar scaling (which increase with ) not seen in numerical
simulations. This anomalous scaling suggests that the principal assumption
underlying cosmological perturbation theory, that large-scale fields can be
described perturbatively even when fluctuations are highly non-linear on small
scales, breaks down beyond leading order for spectral indices . For
, the power spectrum, variance, and correlation function in the scaling
regime can be calculated using dimensional regularization.Comment: 48 pages, 19 figures, uses axodraw.sty; also available at
http://fnas08.fnal.gov
Navier-Stokes-alpha model: LES equations with nonlinear dispersion
We present a framework for discussing LES equations with nonlinear
dispersion. In this framework, we discuss the properties of the nonlinearly
dispersive Navier-Stokes-alpha model of incompressible fluid turbulence ---
also called the viscous Camassa-Holm equations and the LANS equations in the
literature --- in comparison with the corresponding properties of large eddy
simulation (LES) equations obtained via the approximate-inverse approach.
In this comparison, we identify the spatially filtered NS-alpha equations
with a class of generalized LES similarity models. Applying a certain
approximate inverse to this class of LES models restores the Kelvin circulation
theorem for the defiltered velocity and shows that the NS-alpha model describes
the dynamics of the defiltered velocity for this class of generalized LES
similarity models. We also show that the subgrid scale forces in the NS-alpha
model transform covariantly under Galilean transformations and under a change
to a uniformly rotating reference frame. Finally, we discuss in the spectral
formulation how the NS-alpha model retains the local interactions among the
large scales, retains the nonlocal sweeping effects of large scales on small
scales, yet attenuates the local interactions of the small scales amongst
themselves.Comment: 15 pages, no figures, Special LES volume of ERCOFTAC bulletin, to
appear in 200
Dark energy domination in the Virgocentric flow
The standard \LambdaCDM cosmological model implies that all celestial bodies
are embedded in a perfectly uniform dark energy background, represented by
Einstein's cosmological constant, and experience its repulsive antigravity
action. Can dark energy have strong dynamical effects on small cosmic scales as
well as globally? Continuing our efforts to clarify this question, we focus now
on the Virgo Cluster and the flow of expansion around it. We interpret the
Hubble diagram, from a new database of velocities and distances of galaxies in
the cluster and its environment, using a nonlinear analytical model which
incorporates the antigravity force in terms of Newtonian mechanics. The key
parameter is the zero-gravity radius, the distance at which gravity and
antigravity are in balance. Our conclusions are: 1. The interplay between the
gravity of the cluster and the antigravity of the dark energy background
determines the kinematical structure of the system and controls its evolution.
2. The gravity dominates the quasi-stationary bound cluster, while the
antigravity controls the Virgocentric flow, bringing order and regularity to
the flow, which reaches linearity and the global Hubble rate at distances \ga
15 Mpc. 3. The cluster and the flow form a system similar to the Local Group
and its outflow. In the velocity-distance diagram, the cluster-flow structure
reproduces the group-flow structure with a scaling factor of about 10; the
zero-gravity radius for the cluster system is also 10 times larger. The phase
and dynamical similarity of the systems on the scales of 1-30 Mpc suggests that
a two-component pattern may be universal for groups and clusters: a
quasi-stationary bound central component and an expanding outflow around it,
due to the nonlinear gravity-antigravity interplay with the dark energy
dominating in the flow component.Comment: 7 pages, 2 figures, Astronomy and Astrophysics (accepted
Spectral Action Models of Gravity on Packed Swiss Cheese Cosmology
We present a model of (modified) gravity on spacetimes with fractal structure
based on packing of spheres, which are (Euclidean) variants of the Packed Swiss
Cheese Cosmology models. As the action functional for gravity we consider the
spectral action of noncommutative geometry, and we compute its expansion on a
space obtained as an Apollonian packing of 3-dimensional spheres inside a
4-dimensional ball. Using information from the zeta function of the Dirac
operator of the spectral triple, we compute the leading terms in the asymptotic
expansion of the spectral action. They consist of a zeta regularization of a
divergent sum which involves the leading terms of the spectral actions of the
individual spheres in the packing. This accounts for the contribution of the
points 1 and 3 in the dimension spectrum (as in the case of a 3-sphere). There
is an additional term coming from the residue at the additional point in the
real dimension spectrum that corresponds to the packing constant, as well as a
series of fluctuations coming from log-periodic oscillations, created by the
points of the dimension spectrum that are off the real line. These terms detect
the fractality of the residue set of the sphere packing. We show that the
presence of fractality influences the shape of the slow-roll potential for
inflation, obtained from the spectral action. We also discuss the effect of
truncating the fractal structure at a certain scale related to the energy scale
in the spectral action.Comment: 38 pages LaTe
Structural Deep Embedding for Hyper-Networks
Network embedding has recently attracted lots of attentions in data mining.
Existing network embedding methods mainly focus on networks with pairwise
relationships. In real world, however, the relationships among data points
could go beyond pairwise, i.e., three or more objects are involved in each
relationship represented by a hyperedge, thus forming hyper-networks. These
hyper-networks pose great challenges to existing network embedding methods when
the hyperedges are indecomposable, that is to say, any subset of nodes in a
hyperedge cannot form another hyperedge. These indecomposable hyperedges are
especially common in heterogeneous networks. In this paper, we propose a novel
Deep Hyper-Network Embedding (DHNE) model to embed hyper-networks with
indecomposable hyperedges. More specifically, we theoretically prove that any
linear similarity metric in embedding space commonly used in existing methods
cannot maintain the indecomposibility property in hyper-networks, and thus
propose a new deep model to realize a non-linear tuplewise similarity function
while preserving both local and global proximities in the formed embedding
space. We conduct extensive experiments on four different types of
hyper-networks, including a GPS network, an online social network, a drug
network and a semantic network. The empirical results demonstrate that our
method can significantly and consistently outperform the state-of-the-art
algorithms.Comment: Accepted by AAAI 1
Similarity Renormalization Group Evolution of Chiral Effective Nucleon-Nucleon Potentials in the Subtracted Kernel Method Approach
Methods based on Wilson's renormalization group have been successfully
applied in the context of nuclear physics to analyze the scale dependence of
effective nucleon-nucleon () potentials, as well as to consistently
integrate out the high-momentum components of phenomenological high-precision
potentials in order to derive phase-shift equivalent softer forms, the so
called potentials. An alternative renormalization group approach
that has been applied in this context is the Similarity Renormalization Group
(SRG), which is based on a series of continuous unitary transformations that
evolve hamiltonians with a cutoff on energy differences. In this work we study
the SRG evolution of a leading order (LO) chiral effective potential in
the channel derived within the framework of the Subtracted Kernel
Method (SKM), a renormalization scheme based on a subtracted scattering
equation.Comment: Published versio
Higher-Order Momentum Distributions and Locally Affine LDDMM Registration
To achieve sparse parametrizations that allows intuitive analysis, we aim to
represent deformation with a basis containing interpretable elements, and we
wish to use elements that have the description capacity to represent the
deformation compactly. To accomplish this, we introduce in this paper
higher-order momentum distributions in the LDDMM registration framework. While
the zeroth order moments previously used in LDDMM only describe local
displacement, the first-order momenta that are proposed here represent a basis
that allows local description of affine transformations and subsequent compact
description of non-translational movement in a globally non-rigid deformation.
The resulting representation contains directly interpretable information from
both mathematical and modeling perspectives. We develop the mathematical
construction of the registration framework with higher-order momenta, we show
the implications for sparse image registration and deformation description, and
we provide examples of how the parametrization enables registration with a very
low number of parameters. The capacity and interpretability of the
parametrization using higher-order momenta lead to natural modeling of
articulated movement, and the method promises to be useful for quantifying
ventricle expansion and progressing atrophy during Alzheimer's disease
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