arXiv subjects
Publications and source records attributed to Ning Zhang.
In this paper, we construct two convex bodies $K$ and $L$ in $\mathbb{R}^n$, $n\geq 3$, such that their projections $K|H$, $L|H$ onto every subspace $H$ are congruent, but nevertheless, $K$ and $L$ do not coincide up to a translation or a reflection in the origin. This gives a negative answer to an old conjecture posed by Nakajima and Süss.
In this paper, we consider the initial-boundary value problem of the Kundu-Eckhaus equation on the half-line by using of the Fokas unified transform method. Assuming that the solution $u(x,t)$ exists, we show that it can be expressed in terms of the unique solution of a matrix Riemann-Hilbert problem formulated in the plane of the complex spectral parameter $λ$. Moreover, we also get there exist spectral functions are not independent and they are satisfying the so-called global relation.
In this paper, combining the $p$-capacity for $p\in (1, n)$ with the Orlicz addition of convex domains, we develop the $p$-capacitary Orlicz-Brunn-Minkowski theory. In particular, the Orlicz $L_ϕ$ mixed $p$-capacity of two convex domains is introduced and its geometric interpretation is obtained by the $p$-capacitary Orlicz-Hadamard variational formula. The $p$-capacitary Orlicz-Brunn-Minkowski and Orlicz-Minkowski inequalities are established, and the equivalence of these two inequalities are discussed as well. The $p$-capacitary Orlicz-Minkowski problem is proposed and solved under some mild conditions on the involving functions and measures. In particular, we provide the solutions for the normalized $p$-capacitary $L_q$ Minkowski problems with $q>1$ for both discrete and general measures.
We show \begin{align*} \frac{ \int_{E \cap θ^+} f(x) dx }{ \int_E f(x) dx } \geq \left(\frac{k γ+1}{(n+1) γ+1}\right)^{\frac{k γ+1}γ} \end{align*} for all $k$-dimensional subspaces $E\subset\mathbb{R}^n$, $θ\in E\cap S^{n-1}$, and all $γ$-concave functions $f:\mathbb{R}^n\rightarrow [0,\infty)$ with $γ>0$, $0< \int_{\mathbb{R}^n} f(x)\, dx <\infty$, and $\int_{\mathbb{R}^n} x f(x)\, dx$ at the origin $o\in\mathbb{R}^n$. Here, $θ^+ := \lbrace x\, : \, \langle x,θ\rangle \geq 0 \rbrace$. As a consequence of this result, we get the following generalization of Grünbaum's inequality: \begin{align*} \frac{ \mbox{vol}_k(K\cap E\capθ^+) }{ \mbox{vol}_k(K\cap E) } \geq \left( \frac{k}{n+1} \right)^k \end{align*} for all convex bodies $K\subset\mathbb{R}^n$ with centroid at the origin, $k$-dimensional subspaces $E\subset\mathbb{R}^n$, and $θ\in E\cap S^{n-1}$. The lower bounds in both of our inequalities are the best possible, and we discuss the equality conditions.
The linearization of a power flow (PF) model is an important approach for simplifying and accelerating the calculation of a power system's control, operation, and optimization. Traditional model-based methods derive linearized PF models by making approximations in the analytical PF model according to the physical characteristics of the power system. Today, more measurements of the power system are available and thus facilitate data-driven approaches beyond model-driven approaches. This work studies a linearized PF model through a data-driven approach. Both a forward regression model ((P, Q) as a function of (theta, V)) and an inverse regression model ((theta, V) as a function of (P, Q)) are proposed. Partial least square (PLS)- and Bayesian linear regression (BLR)-based algorithms are designed to address data collinearity and avoid overfitting. The proposed approach is tested on a series of IEEE standard cases, which include both meshed transmission grids and radial distribution grids, with both Monte Carlo simulated data and public testing data. The results show that the proposed approach can realize a higher calculation accuracy than model-based approaches can. The results also demonstrate that the obtained regression parameter matrices of data-driven models reflect power system physics by demonstrating similar patterns with some power system matrices (e.g., the admittance matrix).
In this paper, on the sublinear expectation space, we establish a comparison theorem between independent and convolutionary random vectors, which states that the partial sums of those two sequences of random vectors are identically distributed. Under the sublinear framework, through the comparison theorem, several fundamental limit theorems for convolutionary random vectors are obtained, including the law of large numbers, the central limit theorem and the law of iterated logarithm.
Mobile edge caching enables content delivery directly within the radio access network, which effectively alleviates the backhaul burden and reduces round-trip latency. To fully exploit the edge resources, the most popular contents should be identified and cached. Observing that content popularity varies greatly at different locations, to maximize local hit rate, this paper proposes an online learning algorithm that dynamically predicts content hit rate, and makes location-differentiated caching decisions. Specifically, a linear model is used to estimate the future hit rate. Considering the variations in user demand, a perturbation is added to the estimation to account for uncertainty. The proposed learning algorithm requires no training phase, and hence is adaptive to the time-varying content popularity profile. Theoretical analysis indicates that the proposed algorithm asymptotically approaches the optimal policy in the long term. Extensive simulations based on real world traces show that, the proposed algorithm achieves higher hit rate and better adaptiveness to content popularity fluctuation, compared with other schemes.
In this paper, we investigate multi-message authentication to combat adversaries with infinite computational capacity. An authentication framework over a wiretap channel $(W_1,W_2)$ is proposed to achieve information-theoretic security with the same key. The proposed framework bridges the two research areas in physical (PHY) layer security: secure transmission and message authentication. Specifically, the sender Alice first transmits message $M$ to the receiver Bob over $(W_1,W_2)$ with an error correction code; then Alice employs a hash function (i.e., $\varepsilon$-AWU$_2$ hash functions) to generate a message tag $S$ of message $M$ using key $K$, and encodes $S$ to a codeword $X^n$ by leveraging an existing strongly secure channel coding with exponentially small (in code length $n$) average probability of error; finally, Alice sends $X^n$ over $(W_1,W_2)$ to Bob who authenticates the received messages. We develop a theorem regarding the requirements/conditions for the authentication framework to be information-theoretic secure for authenticating a polynomial number of messages in terms of $n$. Based on this theorem, we propose an authentication protocol that can guarantee the security requirements, and prove its authentication rate can approach infinity when $n$ goes to infinity. Furthermore, we design and implement an efficient and feasible authentication protocol over binary symmetric wiretap channel (BSWC) by using \emph{Linear Feedback Shifting Register} based (LFSR-based) hash functions and strong secure polar code. Through extensive experiments, it is demonstrated that the proposed protocol can achieve low time cost, high authentication rate, and low authentication error rate.
This paper investigates one of the fundamental issues in cache-enabled heterogeneous networks (HetNets): how many cache instances should be deployed at different base stations, in order to provide guaranteed service in a cost-effective manner. Specifically, we consider two-tier HetNets with hierarchical caching, where the most popular files are cached at small cell base stations (SBSs) while the less popular ones are cached at macro base stations (MBSs). For a given network cache deployment budget, the cache sizes for MBSs and SBSs are optimized to maximize network capacity while satisfying the file transmission rate requirements. As cache sizes of MBSs and SBSs affect the traffic load distribution, inter-tier traffic steering is also employed for load balancing. Based on stochastic geometry analysis, the optimal cache sizes for MBSs and SBSs are obtained, which are threshold-based with respect to cache budget in the networks constrained by SBS backhauls. Simulation results are provided to evaluate the proposed schemes and demonstrate the applications in cost-effective network deployment.
In this article, we investigate the cost-effective 5G-enabled vehicular networks to support emerging vehicular applications, such as autonomous driving, in-car infotainment and location-based road services. To this end, self-sustaining caching stations (SCSs) are introduced to liberate on-road base stations from the constraints of power lines and wired backhauls. Specifically, the cache-enabled SCSs are powered by renewable energy and connected to core networks through wireless backhauls, which can realize "drop-and-play" deployment, green operation, and low-latency services. With SCSs integrated, a 5G-enabled heterogeneous vehicular networking architecture is further proposed, where SCSs are deployed along roadside for traffic offloading while conventional macro base stations (MBSs) provide ubiquitous coverage to vehicles. In addition, a hierarchical network management framework is designed to deal with high dynamics in vehicular traffic and renewable energy, where content caching, energy management and traffic steering are jointly investigated to optimize the service capability of SCSs with balanced power demand and supply in different time scales. Case studies are provided to illustrate SCS deployment and operation designs, and some open research issues are also discussed.
In this paper, based on the initiation of the notion of negatively associated random variables under nonlinear probability, a strong limit theorem for weighted sums of random variables within the same frame is achieved without assumptions of independence and identical distribution, from which the Marcinkiewich-Zygmund type and Kolmogorov type strong laws of large numbers are derived. In addition, as applications of our results, Stranssen type invariance principles of negatively associated random variables and vertically independent random variables are proposed respectively.
Renewable energy harvesting (EH) technology is expected to be pervasively utilized in the next generation (5G) mobile networks to support sustainable network developments and operations. However, the renewable energy supply is inherently random and intermittent, which could lead to energy outage, energy overflow, quality of service (QoS) degradation, etc. Accordingly, how to enhance renewable energy sustainability is a critical issue for green networking. To this end, an energy-sustainable traffic steering framework is proposed in this article, where the traffic load is dynamically adjusted to match with energy distributions in both spatial and temporal domains by means of inter- and intra-tier steering, caching and pushing. Case studies are carried out, which demonstrate the proposed framework can reduce on-grid energy demand while satisfying QoS requirements. Research topics and challenges of energy-sustainable traffic steering are also discussed.
This article proposes a software defined space-air-ground integrated network architecture for supporting diverse vehicular services in a seamless, efficient, and cost-effective manner. Firstly, the motivations and challenges for integration of space-air-ground networks are reviewed. Secondly, a software defined network architecture with a layered structure is presented. To protect the legacy services in satellite, aerial, and territorial segments, resources in each segment are sliced through network slicing to achieve service isolation. Then, available resources are put into a common and dynamic space-air-ground resource pool, which is managed by hierarchical controllers to accommodate vehicular services. Finally, a case study is carried out, followed by discussion on some open research topics.
We consider the nonlinear Schrödinger equation $-Δu+(λa(x)+1)u=|u|^{p-1}u$ on a locally finite graph $G=(V,E)$. We prove via the Nehari method that if $a(x)$ satisfies certain assumptions, for any $λ>1$, the equation admits a ground state solution $u_λ$. Moreover, as $λ\rightarrow \infty$, the solution $u_λ$ converges to a solution of the Dirichlet problem $-Δu+u=|u|^{p-1}u$ which is defined on the potential well $Ω$. We also provide a numerical experiment which solves the equation on a finite graph to illustrate our results.
Image captioning is a challenging problem owing to the complexity in understanding the image content and diverse ways of describing it in natural language. Recent advances in deep neural networks have substantially improved the performance of this task. Most state-of-the-art approaches follow an encoder-decoder framework, which generates captions using a sequential recurrent prediction model. However, in this paper, we introduce a novel decision-making framework for image captioning. We utilize a "policy network" and a "value network" to collaboratively generate captions. The policy network serves as a local guidance by providing the confidence of predicting the next word according to the current state. Additionally, the value network serves as a global and lookahead guidance by evaluating all possible extensions of the current state. In essence, it adjusts the goal of predicting the correct words towards the goal of generating captions similar to the ground truth captions. We train both networks using an actor-critic reinforcement learning model, with a novel reward defined by visual-semantic embedding. Extensive experiments and analyses on the Microsoft COCO dataset show that the proposed framework outperforms state-of-the-art approaches across different evaluation metrics.
In this paper, we use the Fokas method to analyze the complex Sharma-Tasso-Olver(cSTO) equation on the half line. We show that it can be represented in terms of the solution of a matrix RHP formulated in the plane of the complex spectral parameter λ.
Next generation (5G) wireless networks are expected to support the massive data and accommodate a wide range of services/use cases with distinct requirements in a cost-effective, flexible, and agile manner. As a promising solution, wireless network virtualization (WNV), or network slicing, enables multiple virtual networks to share the common infrastructure on demand, and to be customized for different services/use cases. This article focuses on network-wide resource allocation for realizing WNV. Specifically, the motivations, the enabling platforms, and the benefits of WNV, are first reviewed. Then, resource allocation for WNV along with the technical challenges is discussed. Afterwards, a software defined networking (SDN) enabled resource allocation framework is proposed to facilitate WNV, including the key procedures and the corresponding modeling approaches. Furthermore, a case study is provided as an example of resource allocation in WNV. Finally, some open research topics essential to WNV are discussed.
This paper analyzes birth cohort effects and develops an approach which is based on differential geometry to identify and measure cohort effects in mortality data sets. The measurement is quantitative and provides a potential method to compare cohort effects among different countries or groups. Data sets of four countries (e.g. U.k., U.S., Canada and Japan) are taken as examples to explain our approach and applications of the measurement to a modified Lee-Carter model are analyzed. In fact, this paper is an upgrade version of our paper arXiv:1504.00327. There is a new section which gives applications of our approach based on the Lee-Carter and APC models.