arXiv subjects
Publications and source records attributed to Xiao Wang.
We classify rooted trees which have strictly unimodal q-polynomials (plucking polynomial). We also give criteria for a trapezoidal shape of a plucking polynomial. We generalize results of Pak and Panova on strict unimodality of q-binomial coefficients. We discuss which polynomials can be realized as plucking polynomials and whether or not different rooted trees can have the same plucking polynomial.
In spite of the recent interest and advances in linear controllability of complex networks, controlling nonlinear network dynamics remains to be an outstanding problem. We develop an experimentally feasible control framework for nonlinear dynamical networks that exhibit multistability (multiple coexisting final states or attractors), which are representative of, e.g., gene regulatory networks (GRNs). The control objective is to apply parameter perturbation to drive the system from one attractor to another, assuming that the former is undesired and the latter is desired. To make our framework practically useful, we consider RESTRICTED parameter perturbation by imposing the following two constraints: (a) it must be experimentally realizable and (b) it is applied only temporarily. We introduce the concept of ATTRACTOR NETWORK, in which the nodes are the distinct attractors of the system, and there is a directional link from one attractor to another if the system can be driven from the former to the latter using restricted control perturbation. Introduction of the attractor network allows us to formulate a controllability framework for nonlinear dynamical networks: a network is more controllable if the underlying attractor network is more strongly connected, which can be quantified. We demonstrate our control framework using examples from various models of experimental GRNs. A finding is that, due to nonlinearity, noise can counter-intuitively facilitate control of the network dynamics.
In this paper we study stochastic quasi-Newton methods for nonconvex stochastic optimization, where we assume that only stochastic information of the gradients of the objective function is available via a stochastic first-order oracle (SFO). Firstly, we propose a general framework of stochastic quasi-Newton methods for solving nonconvex stochastic optimization. The proposed framework extends the classic quasi-Newton methods working in deterministic settings to stochastic settings, and we prove its almost sure convergence to stationary points. Secondly, we propose a general framework for a class of randomized stochastic quasi-Newton methods, in which the number of iterations conducted by the algorithm is a random variable. The worst-case SFO-calls complexities of this class of methods are analyzed. Thirdly, we present two specific methods that fall into this framework, namely stochastic damped-BFGS method and stochastic cyclic Barzilai-Borwein method. Finally, we report numerical results to demonstrate the efficiency of the proposed methods.
Using combined theoretical and experimental approaches, we studied the structural and electronic origin of the magnetic structure in hexagonal LuFeO$_3$. Besides showing the strong exchange coupling that is consistent with the high magnetic ordering temperature, the previously observed spin reorientation transition is explained by the theoretically calculated magnetic phase diagram. The structural origin of this spin reorientation that is responsible for the appearance of spontaneous magnetization, is identified by theory and verified by x-ray diffraction and absorption experiments.
In this paper, we study a few theoretical issues in the discretized Kohn-Sham (KS) density functional theory (DFT). The equivalence between either a local or global minimizer of the KS total energy minimization problem and the solution to the KS equation is established under certain assumptions. The nonzero charge densities of a strong local minimizer are shown to be bounded below by a positive constant uniformly. We analyze the self-consistent field (SCF) iteration by formulating the KS equation as a fixed point map with respect to the potential. The Jacobian of these fixed point maps is derived explicitly. Both global and local convergence of the simple mixing scheme can be established if the gap between the occupied states and unoccupied states is sufficiently large. This assumption can be relaxed if the charge density is computed using the Fermi-Dirac distribution and it is not required if there is no exchange correlation functional in the total energy functional. Although our assumption on the gap is very stringent and is almost never satisfied in reality, our analysis is still valuable for a better understanding of the KS minimization problem, the KS equation and the SCF iteration.
Inspired by recent observation of charged charmoniumlike structure $Z_c(4025)$, we explore the $Y(4260)\to (D^*\bar{D}^*)^- π^+$ decay through the initial-single-pion-emission mechanism, where the $D^*\bar{D}^*\to D^*\bar{D}^*$ interaction is studied by the ladder approximation including a non-interacting case. Our calculation of the differential decay width for $Y(4260)\to (D^*\bar{D}^*)^- π^+$ indicates that a charged enhancement structure around $D^*\bar{D}^*$ appears in the $D^*\bar{D}^*$ invariant mass spectrum for this process, which can correspond to newly observed $Z_c(4025)$ structure.
It is well known that the self-consistent field (SCF) iteration for solving the Kohn-Sham (KS) equation often fails to converge, yet there is no clear explanation. In this paper, we investigate the SCF iteration from the perspective of minimizing the corresponding KS total energy functional. By analyzing the second-order Taylor expansion of the KS total energy functional and estimating the relationship between the Hamiltonian and the part of the Hessian which is not used in the SCF iteration, we are able to prove global convergence from an arbitrary initial point and local linear convergence from an initial point sufficiently close to the solution of the KS equation under assumptions that the gap between the occupied states and unoccupied states is sufficiently large and the second-order derivatives of the exchange correlation functional are uniformly bounded from above. Although these conditions are very stringent and are almost never satisfied in reality, our analysis is interesting in the sense that it provides a qualitative prediction of the behavior of the SCF iteration.
In this work, we systematically study the two-body strong decay of the $ρ/ρ_3$ states, which are observed and grouped into the $ρ/ρ_3$ meson family. By performing the phenomenological analysis, the underlying properties of these states are obtained and tested. What is more important is that abundant information of their two-body strong decays is predicted, which will be helpful to further and experimentally study these states.
Estimation of convex functions finds broad applications in engineering and science, while convex shape constraint gives rise to numerous challenges in asymptotic performance analysis. This paper is devoted to minimax optimal estimation of univariate convex functions from the Hölder class in the framework of shape constrained nonparametric estimation. Particularly, the paper establishes the optimal rate of convergence in two steps for the minimax sup-norm risk of convex functions with the Hölder order between one and two. In the first step, by applying information theoretical results on probability measure distance, we establish the minimax lower bound under the supreme norm by constructing a novel family of piecewise quadratic convex functions in the Hölder class. In the second step, we develop a penalized convex spline estimator and establish the minimax upper bound under the supreme norm. Due to the convex shape constraint, the optimality conditions of penalized convex splines are characterized by nonsmooth complementarity conditions. By exploiting complementarity methods, a critical uniform Lipschitz property of optimal spline coefficients in the infinity norm is established. This property, along with asymptotic estimation techniques, leads to uniform bounds for bias and stochastic errors on the entire interval of interest. This further yields the optimal rate of convergence by choosing the suitable number of knots and penalty value. The present paper provides the first rigorous justification of the optimal minimax risk for convex estimation under the supreme norm.
This paper considers the development of spatially adaptive smoothing splines for the estimation of a regression function with non-homogeneous smoothness across the domain. Two challenging issues that arise in this context are the evaluation of the equivalent kernel and the determination of a local penalty. The roughness penalty is a function of the design points in order to accommodate local behavior of the regression function. It is shown that the spatially adaptive smoothing spline estimator is approximately a kernel estimator. The resulting equivalent kernel is spatially dependent. The equivalent kernels for traditional smoothing splines are a special case of this general solution. With the aid of the Green's function for a two-point boundary value problem, the explicit forms of the asymptotic mean and variance are obtained for any interior point. Thus, the optimal roughness penalty function is obtained by approximately minimizing the asymptotic integrated mean square error. Simulation results and an application illustrate the performance of the proposed estimator.
The functional generalized additive model (FGAM) provides a more flexible nonlinear functional regression model than the well-studied functional linear regression model. This paper restricts attention to the FGAM with identity link and additive errors, which we will call the additive functional model, a generalization of the functional linear model. This paper studies the minimax rate of convergence of predictions from the additive functional model in the framework of reproducing kernel Hilbert space. It is shown that the optimal rate is determined by the decay rate of the eigenvalues of a specific kernel function, which in turn is determined by the reproducing kernel and the joint distribution of any two points in the random predictor function. For the special case of the functional linear model, this kernel function is jointly determined by the covariance function of the predictor function and the reproducing kernel. The easily implementable roughness-regularized predictor is shown to achieve the optimal rate of convergence. Numerical studies are carried out to illustrate the merits of the predictor. Our simulations and real data examples demonstrate a competitive performance against the existing approach.
As popular tools for spreading spam and malware, Sybils (or fake accounts) pose a serious threat to online communities such as Online Social Networks (OSNs). Today, sophisticated attackers are creating realistic Sybils that effectively befriend legitimate users, rendering most automated Sybil detection techniques ineffective. In this paper, we explore the feasibility of a crowdsourced Sybil detection system for OSNs. We conduct a large user study on the ability of humans to detect today's Sybil accounts, using a large corpus of ground-truth Sybil accounts from the Facebook and Renren networks. We analyze detection accuracy by both "experts" and "turkers" under a variety of conditions, and find that while turkers vary significantly in their effectiveness, experts consistently produce near-optimal results. We use these results to drive the design of a multi-tier crowdsourcing Sybil detection system. Using our user study data, we show that this system is scalable, and can be highly effective either as a standalone system or as a complementary technique to current tools.
In this work, we present a systematic study of the observed isoscalar tensor $f_2$ states. With the detailed analysis of the mass spectrum and calculation of the $f_2$ two-body strong decays, we extract information of their underly structures, and try to categorize them into the conventional tensor meson family ($n^{3}P_{2}$ $(n=1,2,3,4)$ and $m^{3}F_{2}$ ($m=1,2$)). We also give predictions for other decay modes of these tensor mesons, which are useful for further experimental investigations.
The optical conductivity ($σ_{1}$) of SrTiO$_{3}$ for various vacancies has been systematically studied using a combination of ultraviolet - vacuum ultraviolet (UV-VUV) reflectivity and spectroscopic ellipsometry. For cation (Ti) vacancies, $σ_{1}$ shows large spectral weight transfer over a wide range of energy from as high as 35 eV to as low as 0.5 eV and the presence of mid-gap states, suggesting that strong correlations play an important role. While for anion (O) vacancies $σ_{1}$ shows changes from 7.4 eV up to 35 eV. These unexpected results can be explained in terms of orbital reconstruction.
The high level of dynamics in today's online social networks (OSNs) creates new challenges for their infrastructures and providers. In particular, dynamics involving edge creation has direct implications on strategies for resource allocation, data partitioning and replication. Understanding network dynamics in the context of physical time is a critical first step towards a predictive approach towards infrastructure management in OSNs. Despite increasing efforts to study social network dynamics, current analyses mainly focus on change over time of static metrics computed on snapshots of social graphs. The limited prior work models network dynamics with respect to a logical clock. In this paper, we present results of analyzing a large timestamped dataset describing the initial growth and evolution of Renren, the leading social network in China. We analyze and model the burstiness of link creation process, using the second derivative, i.e. the acceleration of the degree. This allows us to detect bursts, and to characterize the social activity of a OSN user as one of four phases: acceleration at the beginning of an activity burst, where link creation rate is increasing; deceleration when burst is ending and link creation process is slowing; cruising, when node activity is in a steady state, and complete inactivity.
Data confidentiality policies at major social network providers have severely limited researchers' access to large-scale datasets. The biggest impact has been on the study of network dynamics, where researchers have studied citation graphs and content-sharing networks, but few have analyzed detailed dynamics in the massive social networks that dominate the web today. In this paper, we present results of analyzing detailed dynamics in the Renren social network, covering a period of 2 years when the network grew from 1 user to 19 million users and 199 million edges. Rather than validate a single model of network dynamics, we analyze dynamics at different granularities (user-, community- and network- wide) to determine how much, if any, users are influenced by dynamics processes at different scales. We observe in- dependent predictable processes at each level, and find that while the growth of communities has moderate and sustained impact on users, significant events such as network merge events have a strong but short-lived impact that is quickly dominated by the continuous arrival of new users.
This paper addresses the problem of estimating a convex regression function under both the sup-norm risk and the pointwise risk using B-splines. The presence of the convex constraint complicates various issues in asymptotic analysis, particularly uniform convergence analysis. To overcome this difficulty, we establish the uniform Lipschitz property of optimal spline coefficients in the $\ell_\infty$-norm by exploiting piecewise linear and polyhedral theory. Based upon this property, it is shown that this estimator attains optimal rates of convergence on the entire interval of interest over the Hölder class under both the risks. In addition, adaptive estimates are constructed under both the sup-norm risk and the pointwise risk when the exponent of the Hölder class is between one and two. These estimates achieve a maximal risk within a constant factor of the minimax risk over the Hölder class.
Inspired by the observed Y(2175) state, we predict its non-strange partner Y(1915), which has a resonance structure with mass around 1915 MeV and width about $317\sim 354$ MeV. Experimental search for Y(1915) is proposed by analyzing the $ωf_0(980)$ or $ωππ$ invariant mass spectrum of the $e^+e^-\to ωf_0(980), ωππ$ and $J/ψ\to ηωf_0(980)$ processes, which are accessible at Belle, BaBar, BESIII and forthcoming BelleII. Considering similarity between two families, the comparison of the mass spectra of $ω$ and $ϕ$ families can provide important information on the 1D state of $ϕ$ family, $ϕ(1910)$, which has a very broad resonance structure with mass around 1910 MeV regarded as the strangeonium partner of $ω(1650)$. This also answers the question why the 1D state $ϕ(1910)$ is still missing in experiment. This is supported by our former study on the properties of Y(2175), which explains Y(2175) as the 2D strangeonium because our theoretical total width is comparable with the Belle data.