Inequalities of Dirichlet eigenvalues for degenerate elliptic partial differential operators

Let ${X_j},{Y_j}(j = 1, \cdot \cdot \cdot,n)$ be vector fields satisfying H\"{o}rmander's condition and ${\Delta_L} = \sum\limits_{j = 1}^n {(X_j^2 + Y_j^2)}$. In this paper, we establish some inequalities of Dirichlet eigenvalues for degenerate elliptic partial differential operator ${\Delta_L}$ and $\Delta_L^2$. 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 $(\epsilon, \delta)$-jointly differentially private algorithm for packing problems. Our algorithm gives a feasible output that is approximately optimal up to an $\alpha n$ additive factor as long as the supply of each resource is at least $\tilde{O}(\sqrt{m} / \alpha \epsilon)$, where $m$ 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 $\tilde{O}(m^2 / \alpha \epsilon)$, and only guarantees approximate feasibility in terms of total violation. Further, we complement our algorithm with an almost matching hardness result, showing that $\Omega(\sqrt{m \ln(1/\delta)} / \alpha \epsilon)$ supply is necessary for any $(\epsilon, \delta)$-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 $\epsilon$-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, $|b|=20^{\circ}-50^{\circ}$, 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, $|b|=10^{\circ}-20^{\circ}$, the presence of a bump at $E_{\gamma}\sim 1-4$ GeV, reveals the existence of an extra component compatible with Dark Matter annihilation. Our best-fit candidate corresponds to annihilation into $b\bar{b}$ with mass $M_{\rm DM}= 61.8^{+6.9}_{-4.9}$ GeV and cross section $= 3.30^{+0.69}_{-0.49}\times 10^{-26}$ cm$^{3}$s$^{-1}$. 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 $R$-tensor. We also show that within the class of the semi-positive tensors, the class of exceptionally regular tensors coincides with the class of $R$-tensors. In addition, we consider the tensor complementarity problem with an exceptionally regular tensor or an $R$-tensor or a $P_0+R_0$-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