7,151 research outputs found
No Spurious Local Minima in Nonconvex Low Rank Problems: A Unified Geometric Analysis
In this paper we develop a new framework that captures the common landscape
underlying the common non-convex low-rank matrix problems including matrix
sensing, matrix completion and robust PCA. In particular, we show for all above
problems (including asymmetric cases): 1) all local minima are also globally
optimal; 2) no high-order saddle points exists. These results explain why
simple algorithms such as stochastic gradient descent have global converge, and
efficiently optimize these non-convex objective functions in practice. Our
framework connects and simplifies the existing analyses on optimization
landscapes for matrix sensing and symmetric matrix completion. The framework
naturally leads to new results for asymmetric matrix completion and robust PCA
Some generalizations of the DDVV-type inequalities
In this paper we generalize the known DDVV-type inequalities for real
(skew-)symmetric and complex (skew-)Hermitian matrices into arbitrary real,
complex and quaternionic matrices. Inspired by the Erd\H{o}s-Mordell
inequality, we establish the DDVV-type inequalities for matrices in the
subspaces spanned by a Clifford system or a Clifford algebra. We also
generalize the B\"{o}ttcher-Wenzel inequality to quaternionic matrices.Comment: 21 page
Parallel Data Augmentation for Formality Style Transfer
The main barrier to progress in the task of Formality Style Transfer is the
inadequacy of training data. In this paper, we study how to augment parallel
data and propose novel and simple data augmentation methods for this task to
obtain useful sentence pairs with easily accessible models and systems.
Experiments demonstrate that our augmented parallel data largely helps improve
formality style transfer when it is used to pre-train the model, leading to the
state-of-the-art results in the GYAFC benchmark dataset.Comment: Accepted by ACL 2020. arXiv admin note: text overlap with
arXiv:1909.0600
How Much of Wireless Rate Can Smartphones Support in 5G Networks?
Due to the higher wireless transmission rates in the fifth generation (5G)
cellular networks, higher computation overhead is incurred in smartphones,
which can cause the wireless transmission rates to be limited by the
computation capability of wireless terminals. In this case, is there a maximum
receiving rate for smartphones to maintain stable wireless communications in 5G
cellular networks? The main objective of this article is to investigate the
maximum receiving rate of smartphones and its influence on 5G cellular
networks. Based on Landauer's principle and the safe temperature bound on the
smartphone surface, a maximum receiving rate of the smartphone is proposed for
5G cellular networks. Moreover, the impact of the maximum receiving rate of
smartphones on the link adaptive transmission schemes has been investigated.
Numerical analyses imply that the maximum receiving rate of smartphones cannot
always catch up with the downlink rates of future 5G cellular networks.
Therefore, the link adaptive transmission scheme for future 5G cellular
networks has to take the maximum receiving rate of smartphones into account
A theoretical prediction on huge hole and electron mobilities of 6,6,18-graphdiyne nanoribbons
Two-dimensional 6,6,18-graphdiyne and the corresponding one-dimensional
nanoribbons are investigated using crystal orbital method. Based on HSE06
functional, the one-dimensional confinement increases the band gaps. With band
gaps larger than 0.4 eV, thirty-three 6,6,18-graphdiyne nanoribbons have larger
majority carrier mobilities at room temperature than the highest value of
armchair graphene nanoribbons. Unlike {\gamma}-graphdiyne, 6,6,18-graphdiyne
nanoribbons have both huge hole and electron mobilities, depending on whether
they are armchair or zigzag type. The huge mobilities are explained by crystal
orbital analysis. The superior capabilities of 6,6,18-graphdiyne nanoribbons
make them possible candidates for high speed electronic devices in
complementary circuits
Shear Viscosity to Entropy Density Ratio in Higher Derivative Gravity with Momentum Dissipation
We investigate in linear scalar fields modified Gauss-Bonnet theory
that breaks translation invariance. We first calculate both
analytically and numerically and show its relationship with temperature in
log-log plot. Our results show that at low temperatures. The
causality is also considered in this work. We then find that causality
violation still happens in the presence of the linear scalar field and we
suggest there is a Gauss-Bonnet coupling dependent lower limit for the
effective mass of the graviton. If the effective mass of the graviton is big
enough, then there will be no causality violation and hence no constraints for
the Gauss-Bonnet coupling.Comment: 21 pages, 5 figures, revised version, references added, to appear in
PR
On a conjecture of Stanley depth of squarefree Veronese ideals
In this paper, we partially confirm a conjecture, proposed by Cimpoea\c{s},
Keller, Shen, Streib and Young, on the Stanley depth of squarefree Veronese
ideals . This conjecture suggests that, for positive integers , \sdepth (I_{n,d})= \lfloor \binom{n}{d+1}/\binom{n}{d} \rfloor+d.
Herzog, Vladoiu and Zheng established a connection between the Stanley depths
of quotients of monomial ideals and interval partitions of certain associated
posets. Based on this connection, Keller, Shen, Streib and Young recently
developed a useful combinatorial tool to analyze the interval partitions of the
posets associated with the squarefree Veronese ideals. We modify their ideas
and prove that if , then \sdepth (I_{n,d})= \lfloor
\binom{n}{d+1}/\binom{n}{d} \rfloor+d. We also obtain \lfloor
\frac{d+\sqrt{d^2+4(n+1)}}{2} \rfloor \le \sdepth(I_{n,d}) \le \lfloor
\binom{n}{d+1}/\binom{n}{d} \rfloor+d for . As a byproduct of our construction, We give
an alternative proof of Theorem in without graph theory.Comment: 11 pages; Theorem 1.2 has been changed due to a gap in the previous
versio
Base Station Switch-off with Mutual Repulsion in 5G Massive MIMO Networks
When small cells are densely deployed in the fifth generation (5G) cellular
networks, switching off a part of base stations (BSs) is a practical approach
for saving energy consumption considering the variation of traffic load. The
small cell network with the massive multi-input multi-output (massive MIMO)
system is analyzed in this paper due to the dense deployment and low power
consumption. Based on the BS switch-off strategy with distance constraints, the
energy and coverage efficiency are investigated to illustrate the performance
of the BS switch-off strategy. Simulation results indicate that the energy
efficiency and coverage efficiency of the proposed strategy are better than the
random strategy. The energy efficiency increases with the BS intensity and the
minimal distance, and a maximum coverage efficiency can be achieved with the
increase of the BS intensity and the minimum distance. In this case, the
optimal BS switch-off strategy can be designed under this work in the actual
scene.Comment: arXiv admin note: text overlap with arXiv:1612.0445
Low-Dose CT via Deep CNN with Skip Connection and Network in Network
A major challenge in computed tomography (CT) is how to minimize patient
radiation exposure without compromising image quality and diagnostic
performance. The use of deep convolutional (Conv) neural networks for noise
reduction in Low-Dose CT (LDCT) images has recently shown a great potential in
this important application. In this paper, we present a highly efficient and
effective neural network model for LDCT image noise reduction. Specifically, to
capture local anatomical features we integrate Deep Convolutional Neural
Networks (CNNs) and Skip connection layers for feature extraction. Also, we
introduce parallelized CNN, called Network in Network, to lower the
dimensionality of the output from the previous layer, achieving faster
computational speed at less feature loss. To optimize the performance of the
network, we adopt a Wasserstein generative adversarial network (WGAN)
framework. Quantitative and qualitative comparisons demonstrate that our
proposed network model can produce images with lower noise and more structural
details than state-of-the-art noise-reduction methods
An Accurate and Efficient Method to Calculate the Error Statistics of Block-based Approximate Adders
Adders are key building blocks of many error-tolerant applications.
Leveraging the application-level error tolerance, a number of approximate
adders were proposed recently. Many of them belong to the category of
block-based approximate adders. For approximate circuits, besides normal
metrics such as area and delay, another important metric is the error
measurement. Given the popularity of block-based approximate adders, in this
work, we propose an accurate and efficient method to obtain the error
statistics of these adders. We first show how to calculate the error rates.
Then, we demonstrate an approach to get the exact error distribution, which can
be used to calculate other error characteristics, such as mean error distance
and mean square error.Comment: 14 page
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