arXiv subjects

Hao Zhu

Publications and source records attributed to Hao Zhu.

At least 289 records · Page 16Linked to original sources

arXiv2018

Linear inviscid damping for the $β$-plane equation

In this paper, we study the linear inviscid damping for the linearized $β$-plane equation around shear flows. We develop a new method to give the explicit decay rate of the velocity for a class of monotone shear flows. This method is based on the space-time estimate and the vector field method in sprit of the wave equation. For general shear flows including the Sinus flow, we also prove the linear damping by establishing the limiting absorption principle, which is based on the compactness method introduced by Wei-Zhang-Zhao in \cite{WZZ2}. The main difficulty is that the Rayleigh-Kuo equation has more singular points due to the Coriolis effects so that the compactness argument becomes more involved and delicate.

math.AP↗

arXiv2018

Dense Light Field Reconstruction From Sparse Sampling Using Residual Network

A light field records numerous light rays from a real-world scene. However, capturing a dense light field by existing devices is a time-consuming process. Besides, reconstructing a large amount of light rays equivalent to multiple light fields using sparse sampling arises a severe challenge for existing methods. In this paper, we present a learning based method to reconstruct multiple novel light fields between two mutually independent light fields. We indicate that light rays distributed in different light fields have the same consistent constraints under a certain condition. The most significant constraint is a depth related correlation between angular and spatial dimensions. Our method avoids working out the error-sensitive constraint by employing a deep neural network. We solve residual values of pixels on epipolar plane image (EPI) to reconstruct novel light fields. Our method is able to reconstruct 2 to 4 novel light fields between two mutually independent input light fields. We also compare our results with those yielded by a number of alternatives elsewhere in the literature, which shows our reconstructed light fields have better structure similarity and occlusion relationship.

cs.CV↗

arXiv2018

A note on eigenvalues of a class of singular continuous and discrete linear Hamiltonian systems

In this paper, we show that the analytic and geometric multiplicities of an eigenvalue of a class of singular linear Hamiltonian systems are equal, where both endpoints are in the limit circle cases. The proof is fundamental and is given for both continuous and discrete Hamiltonian systems. The method used in this paper also works for both endpoints are regular, or one endpoint is regular and the other is in the limit circle case.

math.SP↗

arXiv2018

Incorporating Chinese Characters of Words for Lexical Sememe Prediction

Sememes are minimum semantic units of concepts in human languages, such that each word sense is composed of one or multiple sememes. Words are usually manually annotated with their sememes by linguists, and form linguistic common-sense knowledge bases widely used in various NLP tasks. Recently, the lexical sememe prediction task has been introduced. It consists of automatically recommending sememes for words, which is expected to improve annotation efficiency and consistency. However, existing methods of lexical sememe prediction typically rely on the external context of words to represent the meaning, which usually fails to deal with low-frequency and out-of-vocabulary words. To address this issue for Chinese, we propose a novel framework to take advantage of both internal character information and external context information of words. We experiment on HowNet, a Chinese sememe knowledge base, and demonstrate that our framework outperforms state-of-the-art baselines by a large margin, and maintains a robust performance even for low-frequency words.

cs.CL↗

arXiv2018

Singularity of the $n$-th eigenvalue of high dimensional Sturm-Liouville problems

It is natural to consider continuous dependence of the $n$-th eigenvalue on $d$-dimensional ($d\geq2$) Sturm-Liouville problems after the results on $1$-dimensional case by Kong, Wu and Zettl [14]. In this paper, we find all the boundary conditions such that the $n$-th eigenvalue is not continuous, and give complete characterization of asymptotic behavior of the $n$-th eigenvalue. This renders a precise description of the jump phenomena of the $n$-th eigenvalue near such a boundary condition. Furthermore, we divide the space of boundary conditions into $2d+1$ layers and show that the $n$-th eigenvalue is continuously dependent on Sturm-Liouville equations and on boundary conditions when restricted into each layer. In addition, we prove that the analytic and geometric multiplicities of an eigenvalue are equal. Finally, we obtain derivative formula and positive direction of eigenvalues with respect to boundary conditions.

math.SP↗

arXiv2018

View Extrapolation of Human Body from a Single Image

We study how to synthesize novel views of human body from a single image. Though recent deep learning based methods work well for rigid objects, they often fail on objects with large articulation, like human bodies. The core step of existing methods is to fit a map from the observable views to novel views by CNNs; however, the rich articulation modes of human body make it rather challenging for CNNs to memorize and interpolate the data well. To address the problem, we propose a novel deep learning based pipeline that explicitly estimates and leverages the geometry of the underlying human body. Our new pipeline is a composition of a shape estimation network and an image generation network, and at the interface a perspective transformation is applied to generate a forward flow for pixel value transportation. Our design is able to factor out the space of data variation and makes learning at each step much easier. Empirically, we show that the performance for pose-varying objects can be improved dramatically. Our method can also be applied on real data captured by 3D sensors, and the flow generated by our methods can be used for generating high quality results in higher resolution.

cs.CV↗

arXiv2018

Distributed Equilibrium-Learning for Power Network Voltage Control With a Locally Connected Communication Network

In current power distribution systems, one of the most challenging operation tasks is to coordinate the network- wide distributed energy resources (DERs) to maintain the stability of voltage magnitude of the system. This voltage control task has been investigated actively under either distributed optimization-based or local feedback control-based characterizations. The former architecture requires a strongly-connected communication network among all DERs for implementing the optimization algorithms, a scenario not yet realistic in most of the existing distribution systems with under-deployed communication infrastructure. The latter one, on the other hand, has been proven to suffer from loss of network-wide op- erational optimality. In this paper, we propose a game-theoretic characterization for semi-local voltage control with only a locally connected communication network. We analyze the existence and uniqueness of the generalized Nash equilibrium (GNE) for this characterization and develop a fully distributed equilibrium-learning algorithm that relies on only neighbor-to-neighbor information exchange. Provable convergence results are provided along with numerical tests which corroborate the robust convergence property of the proposed algorithm.

eess.SY↗

arXiv2018

Dynamic Power Distribution System Management With a Locally Connected Communication Network

Coordinated optimization and control of distribution-level assets can enable a reliable and optimal integration of massive amount of distributed energy resources (DERs) and facilitate distribution system management (DSM). Accordingly, the objective is to coordinate the power injection at the DERs to maintain certain quantities across the network, e.g., voltage magnitude, line flows, or line losses, to be close to a desired profile. By and large, the performance of the DSM algorithms has been challenged by two factors: i) the possibly non strongly connected communication network over DERs that hinders the coordination; ii) the dynamics of the real system caused by the DERs with heterogeneous capabilities, time-varying operating conditions, and real-time measurement mismatches. In this paper, we investigate the modeling and algorithm design and analysis with the consideration of these two factors. In particular, a game-theoretic characterization is first proposed to account for a locally connected communication network over DERs, along with the analysis of the existence and uniqueness of the Nash equilibrium (NE) therein. To achieve the equilibrium in a distributed fashion, a projected-gradient-based asynchronous DSM algorithm is then advocated. The algorithm performance, including the convergence speed and the tracking error, is analytically guaranteed under the dynamic setting. Extensive numerical tests on both synthetic and realistic cases corroborate the analytical results derived.

eess.SY↗

arXiv2018

On distributional chaos in non-autonomous discrete systems

This paper studies distributional chaos in non-autonomous discrete systems generated by given sequences of maps in metric spaces. In the case that the metric space is compact, it is shown that a system is Li-Yorkeδ-chaotic if and only if it is distributionallyδ'-chaotic in a sequence; and three criteria of distributional δ-chaos are established, which are caused by topologically weak mixing, asymptotic average shadowing property, and some expanding condition, respectively, where δ and δ' are positive constants. In a general case, a criterion of distributional chaos in a sequence induced by a Xiong chaotic set is established.

math.DS↗

arXiv2017

Light Field Segmentation From Super-pixel Graph Representation

Efficient and accurate segmentation of light field is an important task in computer vision and graphics. The large volume of input data and the redundancy of light field make it an open challenge. In the paper, we propose a novel graph representation for interactive light field segmentation based on light field super-pixel (LFSP). The LFSP not only maintains light field redundancy, but also greatly reduces the graph size. These advantages make LFSP useful to improve segmentation efficiency. Based on LFSP graph structure, we present an efficient light field segmentation algorithm using graph-cuts. Experimental results on both synthetic and real dataset demonstrate that our method is superior to previous light field segmentation algorithms with respect to accuracy and efficiency.

cs.CV↗

arXiv2017

PSSE Redux: Convex Relaxation, Decentralized, Robust, and Dynamic Approaches

This chapter aspires to glean some of the recent advances in power system state estimation (PSSE), though our collection is not exhaustive by any means. The Cram{é}r-Rao bound, a lower bound on the (co)variance of any unbiased estimator, is first derived for the PSSE setup. After reviewing the classical Gauss-Newton iterations, contemporary PSSE solvers leveraging relaxations to convex programs and successive convex approximations are explored. A disciplined paradigm for distributed and decentralized schemes is subsequently exemplified under linear(ized) and exact grid models. Novel bad data processing models and fresh perspectives linking critical measurements to cyber-attacks on the state estimator are presented. Finally, spurred by advances in online convex optimization, model-free and model-based state trackers are reviewed.

eess.SY↗

arXiv2017

Hybrid Voltage Control in Distribution Networks Under Limited Communication Rates

Voltage regulation in distribution networks is challenged by increasing penetration of distributed energy resources (DERs). Thanks to advancement in power electronics, these DERs can be leveraged to regulate the grid voltage by quickly changing the reactive power outputs. This paper develops a hybrid voltage control (HVC) strategy that can seamlessly integrate both local and distributed designs to coordinate the network-wide reactive power resources from DERs. \ws{By minimizing a special voltage mismatch objective, we achieve the proposed HVC architecture using partial primal-dual (PPD) gradient updates that allow for a distributed and online implementation}. The proposed HVC design improves over existing distributed approaches by integrating with local voltage feedback. As a result, it can dynamically adapt to varying system operating conditions while being fully cognizant to the instantaneous availability of communication links. Under the worst-case scenario of a total link outage, the proposed design naturally boils down to a surrogate local control implementation. Numerical tests on realistic feeder cases have been to corroborate our analytical results and demonstrate the algorithmic performance.

math.OC↗

arXiv2016

Strain effect engineered in α-Al2O3/monolayer MoS2 interface by first principle calculations

With the advances in low dimensional transition metal dichalcolgenides (TMDCs) based metal oxide semiconductor field effect transistor (MOSFET), the interface between semiconductors and dielectrics has received considerable attention due to its dramatic effects on the morphology and charge transport of semiconductors. In this study, first principle calculations were utilized to investigate the strain effect induced by the interface between Al2O3 (0001) and monolayer MoS2. The results indicate that Al2O3 in 1.3nm thickness can apply the strain of 0.3% on MoS2 monolayer. The strain effect monotonically increases with the larger thickness of the dielectric layer. Also, the study on temperature effect indicates the monotonic lattice expansion induced by the higher temperature. Our study proposes that the dielectric engineering can be an effective tool for strain effect in the nanotechnology.

physics.comp-ph↗

arXiv2016

Dirac Fermions induced in strained zigzag phosphorus nanotubes and the applications in field effect transistors

In this work, Dirac fermions have been obtained and engineered in one-dimensional (1D) zigzag phosphorus nanotubes (ZPNTs). We have performed a comprehensive first-principle computational study of the electronic properties of ZPNTs with various diameters. The results indicate that as the lattice parameter (Lc) along axial direction increases, ZPNTs undergo transitions from metal to semimetal and semimetal to semiconductor, whereas Dirac fermions appear at Lc ranging from 3.90Å to 4.10Å. In particular, a field effect transistor (FET) based on a 12-ZPNT (with 12 unit cells in transverse direction) exhibits semiconductor behaviors with efficient gate-effect modulation at Lc= 4.60Å. However, only weak gate modulation is demonstrated when the nanotube becomes semimetal at Lc= 4.10Å. This study indicates that ZPNTs are profoundly appealing in applications in the strain sensors. Our findings pave the way for development of high-performance strain-engineered electronics based on Dirac Fermions in 1D materials.

cond-mat.mes-hall↗

arXiv2016

Occlusion-Model Guided Anti-Occlusion Depth Estimation in Light Field

Occlusion is one of the most challenging problems in depth estimation. Previous work has modeled the single-occluder occlusion in light field and get good results, however it is still difficult to obtain accurate depth for multi-occluder occlusion. In this paper, we explore the multi-occluder occlusion model in light field, and derive the occluder-consistency between the spatial and angular space which is used as a guidance to select the un-occluded views for each candidate occlusion point. Then an anti-occlusion energy function is built to regularize depth map. The experimental results on public light field datasets have demonstrated the advantages of the proposed algorithm compared with other state-of-the-art light field depth estimation algorithms, especially in multi-occluder areas.

cs.CV↗

arXiv2016

Decentralized Dynamic Optimization for Power Network Voltage Control

Voltage control in power distribution networks has been greatly challenged by the increasing penetration of volatile and intermittent devices. These devices can also provide limited reactive power resources that can be used to regulate the network-wide voltage. A decentralized voltage control strategy can be designed by minimizing a quadratic voltage mismatch error objective using gradient-projection (GP) updates. Coupled with the power network flow, the local voltage can provide the instantaneous gradient information. This paper aims to analyze the performance of this decentralized GP-based voltage control design under two dynamic scenarios: i) the nodes perform the decentralized update in an asynchronous fashion, and ii) the network operating condition is time-varying. For the asynchronous voltage control, we improve the existing convergence condition by recognizing that the voltage based gradient is always up-to-date. By modeling the network dynamics using an autoregressive process and considering time-varying resource constraints, we provide an error bound in tracking the instantaneous optimal solution to the quadratic error objective. This result can be extended to more general \textit{constrained dynamic optimization} problems with smooth strongly convex objective functions under stochastic processes that have bounded iterative changes. Extensive numerical tests have been performed to demonstrate and validate our analytical results for realistic power networks.

eess.SY↗

arXiv2016

Weakly mixing, topologically weakly mixing, and sensitivity for non-autonomous discrete systems

This paper is concerned with relationships of weakly mixing, topologically weakly mixing, and sensitivity for non-autonomous discrete systems. It is shown that weakly mixing implies topologically weakly mixing and sensitivity for measurable systems with a fully supported measure; and topological weakly mixing implies sensitivity for general dynamical systems. However, the inverse conclusions are not true and some counterexamples are given. The related existing results for autonomous discrete systems are generalized to non-autonomous discrete systems and their conditions are weaken.

math.DS↗

arXiv2016

Lyapunov exponents, sensitivity, and stability for non-autonomous discrete systems

This paper is concerned with relationships of Lyapunov exponents with sensitivity and stability for non-autonomous discrete systems. Some new concepts are introduced for non-autonomous discrete systems, including Lyapunov exponents, strong sensitivity at a point and in a set, Lyapunov stability, and exponential asymptotical stability. It is shown that the positive Lyapunov exponent at a point implies strong sensitivity for a class of non-autonomous discrete systems. Furthermore, the uniformly positive Lyapunov exponents in a totally invariant set imply strong sensitivity in this set under certain conditions. It is also shown that the negative Lyapunov exponent at a point implies exponential asymptotical stability for a class of non-autonomous discrete systems. The related existing results for autonomous discrete systems are generalized to non-autonomous discrete systems and their conditions are weaken. One example is provided for illustration.

math.DS↗