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 $\eta/s$ in linear scalar fields modified Gauss-Bonnet theory that breaks translation invariance. We first calculate $\eta/s$ both analytically and numerically and show its relationship with temperature in log-log plot. Our results show that $\eta/s\sim T^2$ 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 $I_{n,d}$. This conjecture suggests that, for positive integers $1 \le d \le n$, \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 $1 \le d \le n \le (d+1) \lfloor \frac{1+\sqrt{5+4d}}{2}\rfloor+2d$, 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 $n > (d+1) \lfloor \frac{1+\sqrt{5+4d}}{2}\rfloor+2d$. As a byproduct of our construction, We give an alternative proof of Theorem $1.1$ in $[13]$ 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 $1\times 1$ 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