29,817 research outputs found
Inequalities of Dirichlet eigenvalues for degenerate elliptic partial differential operators
Let be vector fields satisfying
H\"{o}rmander's condition and . In this paper, we establish some inequalities of Dirichlet
eigenvalues for degenerate elliptic partial differential operator
and . These inequalities extend Yang's inequalities for Dirichlet
eigenvalues of Laplacian to the settings here and the forms of inequalities are
more general than Yang's inequalities. To obtain them, we give a generalization
of the inequality by Chebyshev
Near Optimal Jointly Private Packing Algorithms via Dual Multiplicative Weight Update
We present an improved -jointly differentially private
algorithm for packing problems. Our algorithm gives a feasible output that is
approximately optimal up to an additive factor as long as the supply
of each resource is at least , where
is the number of resources. This improves the previous result by Hsu et
al.~(SODA '16), which requires the total supply to be at least , and only guarantees approximate feasibility in terms of
total violation. Further, we complement our algorithm with an almost matching
hardness result, showing that supply is necessary for any -jointly
differentially private algorithm to compute an approximately optimal packing
solution. Finally, we introduce an alternative approach that runs in linear
time, is exactly truthful, can be implemented online, and can be
-jointly differentially private, but requires a larger supply of each
resource.Comment: 18 pages, ACM-SIAM Symposium on Discrete Algorithms (SODA 2018
Orbital angular momentum induced by nonabsorbing optical elements through space-variant polarization-state manipulations
To manipulate orbital angular momentum (OAM) carried by light beams, there is
a great interest in designing various optical elements from the
deep-ultraviolet to the microwave. Normally, the OAM variation introduced by
optical elements can be attributed to two terms, namely the dynamic and
geometric phases. Up till now, the dynamic contribution induced by optical
elements has been clearly recognized. However, the contribution of geometric
phase still seems obscure, especially considering the vector vortex beams. In
this work, an analytical formula is derived to fully describe the OAM variation
introduced by the nonabsorbing optical elements, which perform space-variant
polarization-state manipulations. It is found that the geometric contribution
can be further divided into two parts: one is directly related to optical
elements and the other one explicitly relies solely on the vortices before and
after the transformations. Based on this result, the same OAM variation can be
achieved with different combinations of the dynamic and/or geometric
contributions. With numerical simulations, it is shown that transformation of
the optical vortices can be fully and flexibly designed with a family of
optical elements. We believe that these results are helpful to understand the
effect of optical elements and offer a new perspective to design the optical
elements for manipulating the OAM carried by light beams.Comment: 13 pages, 8 figure
Towards Instance-level Image-to-Image Translation
Unpaired Image-to-image Translation is a new rising and challenging vision
problem that aims to learn a mapping between unaligned image pairs in diverse
domains. Recent advances in this field like MUNIT and DRIT mainly focus on
disentangling content and style/attribute from a given image first, then
directly adopting the global style to guide the model to synthesize new domain
images. However, this kind of approaches severely incurs contradiction if the
target domain images are content-rich with multiple discrepant objects. In this
paper, we present a simple yet effective instance-aware image-to-image
translation approach (INIT), which employs the fine-grained local (instance)
and global styles to the target image spatially. The proposed INIT exhibits
three import advantages: (1) the instance-level objective loss can help learn a
more accurate reconstruction and incorporate diverse attributes of objects; (2)
the styles used for target domain of local/global areas are from corresponding
spatial regions in source domain, which intuitively is a more reasonable
mapping; (3) the joint training process can benefit both fine and coarse
granularity and incorporates instance information to improve the quality of
global translation. We also collect a large-scale benchmark for the new
instance-level translation task. We observe that our synthetic images can even
benefit real-world vision tasks like generic object detection.Comment: Accepted to CVPR 2019. Project page:
http://zhiqiangshen.com/projects/INIT/index.htm
Fermi Bubbles under Dark Matter Scrutiny Part II: Particle Physics Analysis
The analysis of the gamma-ray photons collected by the Fermi Large Area
Telescope reveals, after removal of astrophysical background, the existence of
an excess towards the Galactic center. This excess peaks around few GeV, and
its origin is compatible with the gamma-ray flux originating from Dark Matter
annihilation. In this work we take a closer look on this interpretation; we
investigate which kind of Dark Matter, and which type of interactions with the
Standard Model fields are able to reproduce the observed signal. The structure
of the paper is twofold. In the first part, we follow an effective field theory
approach considering both fermionic and scalar Dark Matter. The computation of
the relic density, the constraint imposed from the null result of direct
searches, and the reliability of the effective field theory description allow
us to single out only two viable dim-6 operators in the case of fermionic Dark
Matter. In the second part, we analyze some concrete models. In particular, we
find that the scalar Higgs portal can provide a simple, concrete and realistic
scenario able to explain the GeV excess under scrutiny.Comment: 39 pages, 9 figures; note and refs. added; version accepted by JCA
Fermi Bubbles under Dark Matter Scrutiny. Part I: Astrophysical Analysis
The quest for Dark Matter signals in the gamma-ray sky is one of the most
intriguing and exciting challenges in astrophysics. In this paper we perform
the analysis of the energy spectrum of the \textit{Fermi bubbles} at different
latitudes, making use of the gamma-ray data collected by the Fermi Large Area
Telescope. By exploring various setups for the full-sky analysis we achieve
stable results in all the analyzed latitudes. At high latitude,
, the \textit{Fermi bubbles} energy spectrum can be
reproduced by gamma-ray photons generated by inverse Compton scattering
processes, assuming the existence of a population of high-energy electrons. At
low latitude, , the presence of a bump at
GeV, reveals the existence of an extra component
compatible with Dark Matter annihilation. Our best-fit candidate corresponds to
annihilation into with mass GeV and
cross section
cms. In addition, using the energy spectrum of the \textit{Fermi
bubbles}, we derive new conservative but stringent upper limits on the Dark
Matter annihilation cross section.Comment: 23 pages + 2 appendices, 19 figures; v2: minor changes, various
comments added in all the section
On-Demand Video Dispatch Networks: A Scalable End-to-End Learning Approach
We design a dispatch system to improve the peak service quality of video on
demand (VOD). Our system predicts the hot videos during the peak hours of the
next day based on the historical requests, and dispatches to the content
delivery networks (CDNs) at the previous off-peak time. In order to scale to
billions of videos, we build the system with two neural networks, one for video
clustering and the other for dispatch policy developing. The clustering network
employs autoencoder layers and reduces the video number to a fixed value. The
policy network employs fully connected layers and ranks the clustered videos
with dispatch probabilities. The two networks are coupled with weight-sharing
temporal layers, which analyze the video request sequences with convolutional
and recurrent modules. Therefore, the clustering and dispatch tasks are trained
in an end-to-end mechanism. The real-world results show that our approach
achieves an average prediction accuracy of 17%, compared with 3% from the
present baseline method, for the same amount of dispatches.Comment: 12 pages, 11 figure
A Distributional Representation Model For Collaborative Filtering
In this paper, we propose a very concise deep learning approach for
collaborative filtering that jointly models distributional representation for
users and items. The proposed framework obtains better performance when
compared against current state-of-art algorithms and that made the
distributional representation model a promising direction for further research
in the collaborative filtering
Exceptionally Regular Tensors and Tensor Complementarity Problems
Recently, many structured tensors are defined and their properties are
discussed in the literature. In this paper, we introduce a new class of
structured tensors, called exceptionally regular tensor, which is relevant to
the tensor complementarity problem. We show that this class of tensors is a
wide class of tensors which includes many important structured tensors as its
special cases. By constructing two examples, we demonstrate that an
exceptionally regular tensor can be, but not always, an -tensor. We also
show that within the class of the semi-positive tensors, the class of
exceptionally regular tensors coincides with the class of -tensors. In
addition, we consider the tensor complementarity problem with an exceptionally
regular tensor or an -tensor or a -tensor, and show that the
solution sets of these classes of tensor complementarity problems are nonempty
and compact
Insight into High-order Harmonic Generation from Solids: The Contributions of the Bloch Wave-packets Moving on the Group and Phase Velocities
We study numerically the Bloch electron wavepacket dynamics in periodic
potentials to simulate laser-solid interactions. We introduce a new perspective
in the coordinate space combined with the motion of the Bloch electron
wavepackets moving at group and phase velocities under the laser fields. This
model interprets the origins of the two contributions (intra- and interband
transitions) of the high-order harmonic generation (HHG) by investigating the
local and global behavior of the wavepackets. It also elucidates the underlying
physical picture of the HHG intensity enhancement by means of carrier-envelope
phase (CEP), chirp and inhomogeneous fields. It provides a deep insight into
the emission of high-order harmonics from solids. This model is instructive for
experimental measurements and provides a new avenue to distinguish mechanisms
of the HHG from solids in diffrent laser fields
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