arXiv subjects

Xuan Zhou

Publications and source records attributed to Xuan Zhou.

62 records · Page 4Linked to original sources

arXiv2015

GAIL---Guaranteed Automatic Integration Library in MATLAB: Documentation for Version 2.1

Automatic and adaptive approximation, optimization, or integration of functions in a cone with guarantee of accuracy is a relatively new paradigm. Our purpose is to create an open-source MATLAB package, Guaranteed Automatic Integration Library (GAIL), following the philosophy of reproducible research and sustainable practices of robust scientific software development. For our conviction that true scholarship in computational sciences are characterized by reliable reproducibility, we employ the best practices in mathematical research and software engineering known to us and available in MATLAB. This document describes the key features of functions in GAIL, which includes one-dimensional function approximation and minimization using linear splines, one-dimensional numerical integration using trapezoidal rule, and last but not least, mean estimation and multidimensional integration by Monte Carlo methods or Quasi Monte Carlo methods.

cs.MS↗

arXiv2015

Transmutation Theory and Quantization Approach for Quantum Groupoids

Let $H$ and $L$ be quantum groupoids. If $H$ has a quasitriangular structure, then we show that $L$ induces a Hopf algebra $C_{L}(L_s)$ in the category $_{H}\mathcal{M}$, which generalizes the transmutation theory introduced by Majid. Furthermore, if $H$ is commutative, we can construct a Hopf algebra $C_H(H_s)_F$ in the category $_H\mathcal{M}_F$ for a weak invertible unit 2-cocycle $F$, which generalizes the results in \cite{D83}. Finally, we consider the relation between two Hopf algebras: $C_H(H_s)_F$ and $C_{\widetilde H}(\widetilde{H}_s)$, and obtain that they are isomorphic as objects in the category $_{\widetilde H}\mathcal{M}$, where $(\widetilde H, \widetilde{\mathcal{R}})$ is a new quasitriangular quantum groupoid induced by $(H, \mathcal{R})$.

math.RA↗

arXiv2014

Large-scale Spatial Distribution Identification of Base Stations in Cellular Networks

The performance of cellular system significantly depends on its network topology, where the spatial deployment of base stations (BSs) plays a key role in the downlink scenario. Moreover, cellular networks are undergoing a heterogeneous evolution, which introduces unplanned deployment of smaller BSs, thus complicating the performance evaluation even further. In this paper, based on large amount of real BS locations data, we present a comprehensive analysis on the spatial modeling of cellular network structure. Unlike the related works, we divide the BSs into different subsets according to geographical factor (e.g. urban or rural) and functional type (e.g. macrocells or microcells), and perform detailed spatial analysis to each subset. After examining the accuracy of Poisson point process (PPP) in BS locations modeling, we take into account the Gibbs point processes as well as Neyman-Scott point processes and compare their accuracy in view of large-scale modeling test. Finally, we declare the inaccuracy of the PPP model, and reveal the general clustering nature of BSs deployment, which distinctly violates the traditional assumption. This paper carries out a first large-scale identification regarding available literatures, and provides more realistic and more general results to contribute to the performance analysis for the forthcoming heterogeneous cellular networks.

cs.NI↗

arXiv2014

Tractability of the function approximation problem in terms of the kernel's shape and scale parameters

This article studies the problem of approximating functions belonging to a Hilbert space $\mathcal H_d$ with a reproducing kernel of the form $$\tilde K_d(\boldsymbol x,\boldsymbol t):=\prod_{\ell=1}^d \left(1-α_\ell^2+α_\ell^2K_{γ_\ell}(x_\ell,t_\ell)\right)\ \ \ \mbox{for all} \ \ \ \boldsymbol x,\boldsymbol t\in\mathbb R^d.$$ The $α_\ell\in[0,1]$ are scale parameters, and the $γ_\ell>0$ are sometimes called shape parameters. The reproducing kernel $K_γ$ corresponds to some Hilbert space of functions defined on $\mathbb R$. The kernel $\tilde K_d$ generalizes the anisotropic Gaussian reproducing kernel, whose tractability properties have been established in the literature. We present sufficient conditions on $\{α_\ell γ_\ell\}_{\ell=1}^{\infty}$ under which polynomial tractability holds for function approximation problems on $\mathcal H_d$. The exponent of strong polynomial tractability arises from bounds on the eigenvalues of a positive definite linear operator.

math.NA↗

arXiv2014

Recommendation Scheme Based on Converging Properties for Contents Broadcasting

Popular videos are often clicked by a mount of users in a short period. With content recommendation, the popular contents could be broadcast to the potential users in wireless network, to save huge transmitting resource. In this paper, the contents propagation model is analyzed due to users' historical behavior, location, and the converging properties in wireless data transmission, with the users' communication log in the Chinese commercial cellular network. And a recommendation scheme is proposed to achieve high energy efficiency.

cs.MM↗

arXiv2014

Two-tier Spatial Modeling of Base Stations in Cellular Networks

Poisson Point Process (PPP) has been widely adopted as an efficient model for the spatial distribution of base stations (BSs) in cellular networks. However, real BSs deployment are rarely completely random, due to environmental impact on actual site planning. Particularly, for multi-tier heterogeneous cellular networks, operators have to place different BSs according to local coverage and capacity requirement, and the diversity of BSs' functions may result in different spatial patterns on each networking tier. In this paper, we consider a two-tier scenario that consists of macrocell and microcell BSs in cellular networks. By analyzing these two tiers separately and applying both classical statistics and network performance as evaluation metrics, we obtain accurate spatial model of BSs deployment for each tier. Basically, we verify the inaccuracy of using PPP in BS locations modeling for either macrocells or microcells. Specifically, we find that the first tier with macrocell BSs is dispersed and can be precisely modelled by Strauss point process, while Matern cluster process captures the second tier's aggregation nature very well. These statistical models coincide with the inherent properties of macrocell and microcell BSs respectively, thus providing a new perspective in understanding the relationship between spatial structure and operational functions of BSs.

cs.NI↗

arXiv2014

Characterizing Spatial Patterns of Base Stations in Cellular Networks

The topology of base stations (BSs) in cellular networks, serving as a basis of networking performance analysis, is considered to be obviously distinctive with the traditional hexagonal grid or square lattice model, thus stimulating a fundamental rethinking. Recently, stochastic geometry based models, especially the Poisson point process (PPP), attracts an ever-increasing popularity in modeling BS deployment of cellular networks due to its merits of tractability and capability for capturing nonuniformity. In this study, a detailed comparison between common stochastic models and real BS locations is performed. Results indicate that the PPP fails to precisely characterize either urban or rural BS deployment. Furthermore, the topology of real data in both regions are examined and distinguished by statistical methods according to the point interaction trends they exhibit. By comparing the corresponding real data with aggregative point process models as well as repulsive point process models, we verify that the capacity-centric deployment in urban areas can be modeled by typical aggregative processes such as the Matern cluster process, while the coverage-centric deployment in rural areas can be modeled by representative

cs.NI↗

arXiv2013

Generalized Yetter-Drinfel'd module categories for regular multiplier Hopf algebras

For a regular multiplier Hopf algebra $A$, the Yetter-Drinfel'd module category ${}_{A}\mathcal{YD}^{A}$ is equivalent to the centre $Z({}_{A}\mathcal{M})$ of the unital left $A$-module category ${}_{A}\mathcal{M}$. Then we introduce the generalized $(α, β)$-Yetter-Drinfel'd module categories ${}_{A}\mathcal{GYD}^{A}(α, β)$, which are treated as components of a braided $T$-category. Especially when $A$ is a coFrobenius Hopf algebra, ${}_{A}\mathcal{YD}^{A}(α, β)$ is isomorphic to the unital $\hat{A} \bowtie A(α, β)$-module category ${}_{\hat{A} \bowtie A(α, β)}\mathcal{M}$. Finally for a Yetter-Drinfel'd $A$-module algebra $H$, we introduce Yetter-Drinfel'd $(H, A)$-module category, which is a monoidal.

math.RA↗