arXiv subjects

Li Wang

Publications and source records attributed to Li Wang.

At least 415 records · Page 23Linked to original sources

arXiv2021

Data-driven peakon and periodic peakon travelling wave solutions of some nonlinear dispersive equations via deep learning

In the field of mathematical physics, there exist many physically interesting nonlinear dispersive equations with peakon solutions, which are solitary waves with discontinuous first-order derivative at the wave peak. In this paper, we apply the multi-layer physics-informed neural networks (PINNs) deep learning to successfully study the data-driven peakon and periodic peakon solutions of some well-known nonlinear dispersion equations with initial-boundary value conditions such as the Camassa-Holm (CH) equation, Degasperis-Procesi equation, modified CH equation with cubic nonlinearity, Novikov equation with cubic nonlinearity, mCH-Novikov equation, b-family equation with quartic nonlinearity, generalized modified CH equation with quintic nonlinearity, and etc. These results will be useful to further study the peakon solutions and corresponding experimental design of nonlinear dispersive equations.

nlin.PS↗

arXiv2020

Blockchain-Based Approach for Securing Spectrum Trading in Multibeam Satellite Systems

This paper presents a blockchain-based approach for securing spectrum sharing in multi-beam satellite systems. Satellite spectrum is a scarce resource that requires highly efficient management schemes for optimized sharing by network users. However, spectrum sharing is vulnerable to attacks by malicious protocol participants. In order to ensure efficient spectrum management in the face of dishonest satellite users or cyber attackers, it is important for spectrum sharing mechanism to provide transparency and traceability of the trading process so as to enable the system to detect, and hence eliminate, unauthorized access by malicious users. We address these requirements by proposing the use of blockchain which, apart from its ability to provide transparency and traceability, ensures an immutable means for keeping track of user trading reputation. Besides, in order to address the practical constraints of heterogeneous user nodes, we also propose the use of edge computing to support users with limited computing power. In this paper, we propose a blockchain-based spectrum trading framework and, based on which, a multibeam satellite spectrum sharing algorithm for interference pricing and heterogeneous spectrum demands is devised to improve the efficiency of satellite spectrum. By leveraging on the system characteristics of blockchain, a dynamic spectrum sharing mechanism with traceability, openness and transparency for whole trading process is presented. Numerical results are also provided to evaluate the system benefits and spectrum pricing of the proposed mechanism.

cs.CR↗

arXiv2020

Rogue wave formation and interactions in the defocusing nonlinear Schrödinger equation with external potentials

The defocusing nonlinear Schrödinger (NLS) equation has no the modulational instability, and was not found to possess the rogue wave (RW) phenomenon up to now. In this paper, we firstly investigate some novel nonlinear wave structures in the defocusing NLS equation with real-valued time-dependent and time-independent potentials such that the stable new RWs and W-shaped solitons are found, respectively. Moreover, the interactions of two or three RWs are explored such that the RWs with higher amplitudes are generated in the defocusing NLS equation with real-valued time-dependent potentials. Finally, we study the defocusing NLS equation with complex PT -symmetric potentials such that some RWs and W-shaped solitons are also found. These novel results will be useful to design the related physical experiments to generate the RW phenomena and W-shaped solitons in the case of defocusing nonlinear interactions, and to apply them in the related fields of nonlinear or even linear sciences.

nlin.PS↗

arXiv2020

Data-driven rogue waves and parameter discovery in the defocusing NLS equation with a potential using the PINN deep learning

The physics-informed neural networks (PINNs) can be used to deep learn the nonlinear partial differential equations and other types of physical models. In this paper, we use the multi-layer PINN deep learning method to study the data-driven rogue wave solutions of the defocusing nonlinear Schrödinger (NLS) equation with the time-dependent potential by considering several initial conditions such as the rogue wave, Jacobi elliptic cosine function, two-Gaussian function, or three-hyperbolic-secant function, and periodic boundary conditions. Moreover, the multi-layer PINN algorithm can also be used to learn the parameter in the defocusing NLS equation with the time-dependent potential under the sense of the rogue wave solution. These results will be useful to further discuss the rogue wave solutions of the defocusing NLS equation with a potential in the study of deep learning neural networks.

nlin.PS↗

arXiv2020

Computer Stereo Vision for Autonomous Driving

As an important component of autonomous systems, autonomous car perception has had a big leap with recent advances in parallel computing architectures. With the use of tiny but full-feature embedded supercomputers, computer stereo vision has been prevalently applied in autonomous cars for depth perception. The two key aspects of computer stereo vision are speed and accuracy. They are both desirable but conflicting properties, as the algorithms with better disparity accuracy usually have higher computational complexity. Therefore, the main aim of developing a computer stereo vision algorithm for resource-limited hardware is to improve the trade-off between speed and accuracy. In this chapter, we introduce both the hardware and software aspects of computer stereo vision for autonomous car systems. Then, we discuss four autonomous car perception tasks, including 1) visual feature detection, description and matching, 2) 3D information acquisition, 3) object detection/recognition and 4) semantic image segmentation. The principles of computer stereo vision and parallel computing on multi-threading CPU and GPU architectures are then detailed.

cs.CV↗

arXiv2020

Spatiotemporal Dynamics, Nowcasting and Forecasting of COVID-19 in the United States

Epidemic modeling is an essential tool to understand the spread of the novel coronavirus and ultimately assist in disease prevention, policymaking, and resource allocation. In this article, we establish a state of the art interface between classic mathematical and statistical models and propose a novel space-time epidemic modeling framework to study the spatial-temporal pattern in the spread of infectious disease. We propose a quasi-likelihood approach via the penalized spline approximation and alternatively reweighted least-squares technique to estimate the model. Furthermore, we provide a short-term and long-term county-level prediction of the infected/death count for the U.S. by accounting for the control measures, health service resources, and other local features. Utilizing spatiotemporal analysis, our proposed model enhances the dynamics of the epidemiological mechanism and dissects the spatiotemporal structure of the spreading disease. To assess the uncertainty associated with the prediction, we develop a projection band based on the envelope of the bootstrap forecast paths. The performance of the proposed method is evaluated by a simulation study. We apply the proposed method to model and forecast the spread of COVID-19 at both county and state levels in the United States.

stat.AP↗

arXiv2020

Variational Asymptotic Preserving Scheme for the Vlasov-Poisson-Fokker-Planck System

We design a variational asymptotic preserving scheme for the Vlasov-Poisson-Fokker-Planck system with the high field scaling, which describes the Brownian motion of a large system of particles in a surrounding bath. Our scheme builds on an implicit-explicit framework, wherein the stiff terms coming from the collision and field effects are solved implicitly while the convection terms are solved explicitly. To treat the implicit part, we propose a variational approach by viewing it as a Wasserstein gradient flow of the relative entropy, and solve it via a proximal quasi-Newton method. In so doing we get positivity and asymptotic preservation for free. The method is also massively parallelizable and thus suitable for high dimensional problems. We further show that the convergence of our implicit solver is uniform across different scales. A suite of numerical examples are presented at the end to validate the performance of the proposed scheme.

math.NA↗

arXiv2020

Complex Relation Extraction: Challenges and Opportunities

Relation extraction aims to identify the target relations of entities in texts. Relation extraction is very important for knowledge base construction and text understanding. Traditional binary relation extraction, including supervised, semi-supervised and distant supervised ones, has been extensively studied and significant results are achieved. In recent years, many complex relation extraction tasks, i.e., the variants of simple binary relation extraction, are proposed to meet the complex applications in practice. However, there is no literature to fully investigate and summarize these complex relation extraction works so far. In this paper, we first report the recent progress in traditional simple binary relation extraction. Then we summarize the existing complex relation extraction tasks and present the definition, recent progress, challenges and opportunities for each task.

cs.CL↗

arXiv2020

Recollements of extriangulated categories

We give a simultaneous generalization of recollements of abelian categories and triangulated categories, which we call recollements of extriangulated categories. For a recollement $(\mathcal{A}$, $\mathcal{B}$, $\mathcal{C})$ of extriangulated categories, we show that cotorsion pairs in $\mathcal{A}$ and $\mathcal{C}$ induce cotorsion pairs in $\mathcal{B}$ under certain conditions. As an application, our main result recovers a result given by Chen for recollements of triangulated categories, and it also shows a new phenomena when it is applied to abelian categories.

math.RT↗

arXiv2020

A relaxation accelerated two-sweep modulus-based matrix splitting iteration method for solving linear complementarity problems

For a linear complementarity problem, we present a relaxaiton accelerated two-sweep matrix splitting iteration method. The convergence analysis illustrates that the proposed method converges to the exact solution of the linear complementarity problem when the system matrix is an $H_+$-matrix and the convergence conditions are given. Numerical experiments show that the proposed method is more efficient than the existing ones.

math.OC↗

arXiv2020

Comparing and Integrating US COVID-19 Data from Multiple Sources with Anomaly Detection and Repairing

Over the past few months, the outbreak of Coronavirus disease (COVID-19) has been expanding over the world. A reliable and accurate dataset of the cases is vital for scientists to conduct related research and for policy-makers to make better decisions. We collect the United States COVID-19 daily reported data from four open sources: the New York Times, the COVID-19 Data Repository by Johns Hopkins University, the COVID Tracking Project at the Atlantic, and the USAFacts, then compare the similarities and differences among them. To obtain reliable data for further analysis, we first examine the cyclical pattern and the following anomalies, which frequently occur in the reported cases: (1) the order dependencies violation, (2) the point or period anomalies, and (3) the issue of reporting delay. To address these detected issues, we propose the corresponding repairing methods and procedures if corrections are necessary. In addition, we integrate the COVID-19 reported cases with the county-level auxiliary information of the local features from official sources, such as health infrastructure, demographic, socioeconomic, and environmental information, which are also essential for understanding the spread of the virus.

stat.AP↗

arXiv2020

Improving Federated Relational Data Modeling via Basis Alignment and Weight Penalty

Federated learning (FL) has attracted increasing attention in recent years. As a privacy-preserving collaborative learning paradigm, it enables a broader range of applications, especially for computer vision and natural language processing tasks. However, to date, there is limited research of federated learning on relational data, namely Knowledge Graph (KG). In this work, we present a modified version of the graph neural network algorithm that performs federated modeling over KGs across different participants. Specifically, to tackle the inherent data heterogeneity issue and inefficiency in algorithm convergence, we propose a novel optimization algorithm, named FedAlign, with 1) optimal transportation (OT) for on-client personalization and 2) weight constraint to speed up the convergence. Extensive experiments have been conducted on several widely used datasets. Empirical results show that our proposed method outperforms the state-of-the-art FL methods, such as FedAVG and FedProx, with better convergence.

cs.LG↗

arXiv2020

Uncorrelated Semi-paired Subspace Learning

Multi-view datasets are increasingly collected in many real-world applications, and we have seen better learning performance by existing multi-view learning methods than by conventional single-view learning methods applied to each view individually. But, most of these multi-view learning methods are built on the assumption that at each instance no view is missing and all data points from all views must be perfectly paired. Hence they cannot handle unpaired data but ignore them completely from their learning process. However, unpaired data can be more abundant in reality than paired ones and simply ignoring all unpaired data incur tremendous waste in resources. In this paper, we focus on learning uncorrelated features by semi-paired subspace learning, motivated by many existing works that show great successes of learning uncorrelated features. Specifically, we propose a generalized uncorrelated multi-view subspace learning framework, which can naturally integrate many proven learning criteria on the semi-paired data. To showcase the flexibility of the framework, we instantiate five new semi-paired models for both unsupervised and semi-supervised learning. We also design a successive alternating approximation (SAA) method to solve the resulting optimization problem and the method can be combined with the powerful Krylov subspace projection technique if needed. Extensive experimental results on multi-view feature extraction and multi-modality classification show that our proposed models perform competitively to or better than the baselines.

cs.LG↗

arXiv2020

Survey and Open Problems in Privacy Preserving Knowledge Graph: Merging, Query, Representation, Completion and Applications

Knowledge Graph (KG) has attracted more and more companies' attention for its ability to connect different types of data in meaningful ways and support rich data services. However, the data isolation problem limits the performance of KG and prevents its further development. That is, multiple parties have their own KGs but they cannot share with each other due to regulation or competition reasons. Therefore, how to conduct privacy preserving KG becomes an important research question to answer. That is, multiple parties conduct KG related tasks collaboratively on the basis of protecting the privacy of multiple KGs. To date, there is few work on solving the above KG isolation problem. In this paper, to fill this gap, we summarize the open problems for privacy preserving KG in data isolation setting and propose possible solutions for them. Specifically, we summarize the open problems in privacy preserving KG from four aspects, i.e., merging, query, representation, and completion. We present these problems in details and propose possible technical solutions for them. Moreover, we present three privacy preserving KG-aware applications and simply describe how can our proposed techniques be applied into these applications.

cs.DB↗

arXiv2020

Highway freight transportation diversity of cities based on radiation models

Using a unique data set containing about 15.06 million truck transportation records in five months, we investigate the highway freight transportation diversity of 338 Chinese cities based on the truck transportation probability $p_{ij}$ from one city to the other. The transportation probabilities are calculated from the radiation model based on the geographic distance and its cost-based version based on the driving distance as the proxy of cost. For each model, we consider both the population and the gross domestic product, and find quantitatively very similar results. We find that the transportation probabilities have nice power-law tails with the tail exponents close to 0.5 for all the models. The two transportation probabilities in each model fall around the diagonal $p_{ij}=p_{ji}$ but are often not the same. In addition, the corresponding transportation probabilities calculated from the raw radiation model and the cost-based radiation model also fluctuate around the diagonal $p_{ij}^{\rm{geo}}=p_{ij}^{\rm{cost}}$. We calculate four sets of highway truck transportation diversity according to the four sets of transportation probabilities that are found to be close to each other for each city pair. Further, it is found that the population, the gross domestic product, the in-flux, and the out-flux scale as power laws with respect to the transportation diversity in the raw and cost-based radiation models. It implies that a more developed city usually has higher diversity in highway truck transportation, which reflects the fact that a more developed city usually has a more diverse economic structure.

physics.soc-ph↗

arXiv2020

Quantum dynamics on a lossy non-Hermitian lattice

We investigate quantum dynamics of a quantum walker on a finite bipartite non-Hermitian lattice, in which the particle can leak out with certain rate whenever it visits one of the two sublattices. Quantum walker initially located on one of the non-leaky sites will finally totally disappear after a length of evolution time and the distribution of decay probability on each unit cell is obtained. In one regime, the resultant distribution shows an expected decreasing behavior as the distance from the initial site increases. However, in the other regime, we find that the resultant distribution of local decay probability is very counterintuitive, in which a relatively high population of decay probability appears on the edge unit cell which is the farthest from the starting point of the quantum walker. We then analyze the energy spectrum of the non-Hermitian lattice with pure loss, and find that the intriguing behavior of the resultant decay probability distribution is intimately related to the existence and specific property of edge states, which are topologically protected and can be well predicted by the non-Bloch winding number. The exotic dynamics may be observed experimentally with arrays of coupled resonator optical waveguides.

quant-ph↗

arXiv2020

A Theoretical Perspective on Differentially Private Federated Multi-task Learning

In the era of big data, the need to expand the amount of data through data sharing to improve model performance has become increasingly compelling. As a result, effective collaborative learning models need to be developed with respect to both privacy and utility concerns. In this work, we propose a new federated multi-task learning method for effective parameter transfer with differential privacy to protect gradients at the client level. Specifically, the lower layers of the networks are shared across all clients to capture transferable feature representation, while top layers of the network are task-specific for on-client personalization. Our proposed algorithm naturally resolves the statistical heterogeneity problem in federated networks. We are, to the best of knowledge, the first to provide both privacy and utility guarantees for such a proposed federated algorithm. The convergences are proved for the cases with Lipschitz smooth objective functions under the non-convex, convex, and strongly convex settings. Empirical experiment results on different datasets have been conducted to demonstrate the effectiveness of the proposed algorithm and verify the implications of the theoretical findings.

cs.LG↗

arXiv2020

Exploiting Reconfigurable Intelligent Surfaces in Edge Caching: Joint Hybrid Beamforming and Content Placement Optimization

Edge caching can effectively reduce backhaul burden at core network and increase quality-ofservice at wireless edge nodes. However, the beneficial role of edge caching cannot be fully realized when the offloading link is in deep fade. Fortunately, the impairments induced by wireless propagation environments could be renovated by a reconfigurable intelligent surface (RIS). In this paper, a new RIS-aided edge caching system is proposed, where a network cost minimization problem is formulated to optimize content placement at cache units, active beamforming at base station and passive phase shifting at RIS. After decoupling the content placement subproblem with hybrid beamforming design, we propose an alternating optimization algorithm to tackle the active beamforming and passive phase shifting. For active beamforming, we transform the problem into a semidefinite programming (SDP) and prove that the optimal solution of SDP is always rank-1. For passive phase shifting, we introduce block coordinate descent method to alternately optimize the auxiliary variables and the RIS phase shifts. Further, a conjugate gradient algorithm based on manifold optimization is proposed to deal with the non-convex unit-modulus constraints. Numerical results show that our RIS-aided edge caching design can effectively decrease the network cost in terms of backhaul capacity and power consumption.

cs.IT↗