4,839 research outputs found
Context Aware Machine Learning
We propose a principle for exploring context in machine learning models.
Starting with a simple assumption that each observation may or may not depend
on its context, a conditional probability distribution is decomposed into two
parts: context-free and context-sensitive. Then by employing the log-linear
word production model for relating random variables to their embedding space
representation and making use of the convexity of natural exponential function,
we show that the embedding of an observation can also be decomposed into a
weighted sum of two vectors, representing its context-free and
context-sensitive parts, respectively. This simple treatment of context
provides a unified view of many existing deep learning models, leading to
revisions of these models able to achieve significant performance boost.
Specifically, our upgraded version of a recent sentence embedding model not
only outperforms the original one by a large margin, but also leads to a new,
principled approach for compositing the embeddings of bag-of-words features, as
well as a new architecture for modeling attention in deep neural networks. More
surprisingly, our new principle provides a novel understanding of the gates and
equations defined by the long short term memory model, which also leads to a
new model that is able to converge significantly faster and achieve much lower
prediction errors. Furthermore, our principle also inspires a new type of
generic neural network layer that better resembles real biological neurons than
the traditional linear mapping plus nonlinear activation based architecture.
Its multi-layer extension provides a new principle for deep neural networks
which subsumes residual network (ResNet) as its special case, and its extension
to convolutional neutral network model accounts for irrelevant input (e.g.,
background in an image) in addition to filtering
Hermitian representations of the extended affine Lie algebra \widetilde{\frak{gl}_{2}(\bc_q)}
We use the idea of free fields to obtain highest weight representations for
the extended affine Lie algebra \widetilde{\frak{gl}_{2}(\bc_q)}
coordinatized by the quantum torus \bc_q and go on to construct a
contravariant hermitian form. We further give a necessary and sufficient
condition such that the contravariant hermitian form is positive definite.Comment: 24 page
On the connection problem for the second Painlev\'e equation with large initial data
We consider two special cases of the connection problem for the second
Painlev\'e equation (PII) using the method of uniform asymptotics proposed by
Bassom et al.. We give a classification of the real solutions of PII on the
negative (positive) real axis with respect to their initial data. By product, a
rigorous proof of a property associate with the nonlinear eigenvalue problem of
PII on the real axis, recently revealed by Bender and Komijani, is given by
deriving the asymptotic behavior of the Stokes multipliers.Comment: 25 pages,4 figures. arXiv admin note: text overlap with
arXiv:1612.0135
Fine Residual Carrier Frequency and Sampling Frequency Estimation in Wireless OFDM Systems
This paper presents a novel algorithm for residual phase estimation in
wireless OFDM systems, including the carrier frequency offset (CFO) and the
sampling frequency offset (SFO). The subcarriers are partitioned into several
regions which exhibit pairwise correlations. The phase increment between
successive OFDM blocks is exploited which can be estimated by two estimators
with different computational loads. Numerical results of estimation variance
are presented. Simulations indicate performance improvement of the proposed
technique over several conventional schemes in a multipath channel.Comment: Submitted to ICC 2013, Budapes
Application of uniform asymptotics to the connection formulas of the fifth Painlev\'{e} equation
We apply the uniform asymptotics method proposed by Bassom, Clarkson, Law and
McLeod to a special Painlev\'{e} V equation, and we provide a simpler and more
rigorous proof of the connection formulas for a special solution of the
equation, which have been established earlier by McCoy and Tang via the
isomonodromy and WKB methods.Comment: 18 page
B-spline one-center method for molecular Hartree-Fock calculations
We introduce one-center method in spherical coordinates to carry out
Hartree-Fock calculations. Both the radial wave function and the angular wave
function are expanded by B-splines, and the radial knots and angular knots are
adjusted to deal with cusps properly, resulting in the significant improvement
of convergence for several typical closed-shell diatomic molecules. B-splines
could represent both the bound state and continuum state wave function
properly, and the present approach has been applied to investigating ionization
dynamics for H in the intense laser field adopting single-active-electron
model
Effect of phantom dark energy on the holographic thermalization
Gravitational collapse of a shell of charged dust surrounded by the phantom
dark energy is probed by the minimal area surface, which is dual to probe the
thermalization in the boundary quantum field by expectation values of Wilson
loop in the framework of the AdS/CFT correspondence. We investigated mainly the
effect of the phantom dark energy parameter and chemical potential on the
thermalization. The result shows that the smaller the phantom dark energy
parameter is, the easier the plasma thermalizes as the chemical potential is
fixed, and the larger the chemical potential is, the harder the plasma
thermalizes as the dark energy parameter is fixed. We get the fitting function
of the thermalization curve and with it, the thermalization velocity and
thermalization acceleration are discussed.Comment: arXiv admin note: text overlap with arXiv:1412.3878, arXiv:1405.5745
by other author
A note on the connection problem of some special Painlev\'e V functions
As a new application of the method of "uniform asymptotics" proposed by
Bassom, Clarkson, Law and McLeod, we provide a simpler and more rigorous proof
of the connection formulas of some special solutions of the fifth Painlev\'e
equation, which have been established earlier by Andreev and Kitaev
Weak cosmic censorship conjecture with pressure and volume in the Gauss-Bonnet AdS black hole
With the Hamilton-Jacobi equation, we obtain the energy-momentum relation of
a charged particle as it is absorbed by the Gauss-Bonnet AdS black hole. On the
basis of the energy-momentum relation at the event horizon, we investigate the
first law, second law, and weak cosmic censorship conjecture in both the normal
phase space and extended phase space. Our results show that the first law,
second law as well as the weak cosmic censorship conjecture are valid in the
normal phase space for all the initial states are black holes. However, in the
extended phase space, the second law is violated for the extremal and
near-extremal black holes, and the weak cosmic censorship conjecture is
violable for the near-extremal black hole, though the first law is still valid.
In addition, in both the the normal and extended phase spaces, we find the
absorbed particle changes the configuration of the near-extremal black hole,
while don't change that of the extremal black hole.Comment: typos have been fixe
Fitting the trajectories of particles in the equatorial plane of a magnetic dipole with epicycloids
In this paper we discuss epicycloid approximation of the trajectories of
charged particles in axisymmetric magnetic fields. Epicycloid trajectories are
natural in the Guiding Center approximation and we study in detail the errors
arising in this approach. We also discuss how using exact results for particle
motion in the equatorial plane of a magnetic dipole the accuracy of this
approximation can be significantly extended. We also show that the epicycloids
approximate the trajectory of a charged particle more accurately than the
position of the particle along the trajectory.Comment: 8 pages, 10 figure
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