arXiv subjects

Cheng Wang

Publications and source records attributed to Cheng Wang.

514 records · Page 29Linked to original sources

arXiv2013

On Identity Tests for High Dimensional Data Using RMT

In this work, we redefined two important statistics, the CLRT test (Bai et.al., Ann. Stat. 37 (2009) 3822-3840) and the LW test (Ledoit and Wolf, Ann. Stat. 30 (2002) 1081-1102) on identity tests for high dimensional data using random matrix theories. Compared with existing CLRT and LW tests, the new tests can accommodate data which has unknown means and non-Gaussian distributions. Simulations demonstrate that the new tests have good properties in terms of size and power. What is more, even for Gaussian data, our new tests perform favorably in comparison to existing tests. Finally, we find the CLRT is more sensitive to eigenvalues less than 1 while the LW test has more advantages in relation to detecting eigenvalues larger than 1.

stat.ME↗

arXiv2013

Asymptotic power of likelihood ratio tests for high dimensional data

This paper considers the asymptotic power of likelihood ratio test (LRT) for the identity test when the dimension p is large compared to the sample size n. The asymptotic distribution of LRT under alternatives is given and an explicit expression of the power is derived. A simulation study is carried out to compare LRT with other tests. All these studies show that LRT is a powerful test to detect eigenvalues around zero. Key words and phrases: Covariance matrix, High dimensional data, Identity test, Likelihood ratio test, Power

math.ST↗

arXiv2013

Algorithms for Generating Large-scale Clustered Random Graphs

Real social networks are often compared to random graphs in order to assess whether their typological structure could be the result of random processes. However, an Erdős-Rényi random graph in large scale is often lack of local structure beyond the dyadic level and as a result we need to generate the clustered random graph instead of the simple random graph to compare the local structure at the triadic level. In this paper a generalized version of Gleeson's algorithm is advanced to generate a clustered random graph in large-scale which persists the number of nodes |V|, the number of edges |E|, and the global clustering coefficient CΔ as in the real network. And it also has advantages in randomness evaluation and computation time when comparing with the existing algorithms.

physics.soc-ph↗

arXiv2012

Faster Approximation of Max Flow for Directed Graphs

I extend the methods in "Electrical Flows, Laplacian Systems, and Faster Approximation of Maximum Flow in Undirected Graphs, with Paul Christiano, Jonathan Kelner, Daniel Spielman, and Shang-Hua Teng" to directed graphs with a variation of the framework in the paper, which lead to an algorithm that approximately solves the directed max flow problem in nearly-linear time.

cs.DM↗

arXiv2012

AMBER: Automatic Supervision for Multi-Attribute Extraction

The extraction of multi-attribute objects from the deep web is the bridge between the unstructured web and structured data. Existing approaches either induce wrappers from a set of human-annotated pages or leverage repeated structures on the page without supervision. What the former lack in automation, the latter lack in accuracy. Thus accurate, automatic multi-attribute object extraction has remained an open challenge. AMBER overcomes both limitations through mutual supervision between the repeated structure and automatically produced annotations. Previous approaches based on automatic annotations have suffered from low quality due to the inherent noise in the annotations and have attempted to compensate by exploring multiple candidate wrappers. In contrast, AMBER compensates for this noise by integrating repeated structure analysis with annotation-based induction: The repeated structure limits the search space for wrapper induction, and conversely, annotations allow the repeated structure analysis to distinguish noise from relevant data. Both, low recall and low precision in the annotations are mitigated to achieve almost human quality (more than 98 percent) multi-attribute object extraction. To achieve this accuracy, AMBER needs to be trained once for an entire domain. AMBER bootstraps its training from a small, possibly noisy set of attribute instances and a few unannotated sites of the domain.

cs.DB↗

arXiv2012

Energy Stable and Efficient Finite-Difference Nonlinear Multigrid Schemes for the Modified Phase Field Crystal Equation

In this paper we present two unconditionally energy stable finite difference schemes for the Modified Phase Field Crystal (MPFC) equation, a sixth-order nonlinear damped wave equation, of which the purely parabolic Phase Field Crystal (PFC) model can be viewed as a special case. The first is a convex splitting scheme based on an appropriate decomposition of the discrete energy and is first order accurate in time and second order accurate in space. The second is a new, fully second-order scheme that also respects the convex splitting of the energy. Both schemes are nonlinear but may be formulated from the gradients of strictly convex, coercive functionals. Thus, both are uniquely solvable regardless of the time and space step sizes. The schemes are solved by efficient nonlinear multigrid methods. Numerical results are presented demonstrating the accuracy, energy stability, efficiency, and practical utility of the schemes. In particular, we show that our multigrid solvers enjoy optimal, or nearly optimal complexity in the solution of the nonlinear schemes.

math.NA↗

arXiv2012

Convergence Analysis of a Second Order Convex Splitting Scheme for the Modified Phase Field Crystal Equation

In this paper we provide a detailed convergence analysis for an unconditionally energy stable, second-order accurate convex splitting scheme for the Modified Phase Field Crystal equation, a generalized damped wave equation for which the usual Phase Field Crystal equation is a special degenerate case. The fully discrete, fully second-order finite difference scheme in question was derived in a recent work [2]. An introduction of a new variable ψ, corresponding to the temporal derivative of the phase variable ϕ, could bring an accuracy reduction in the formal consistency estimate, because of the hyperbolic nature of the equation. A higher order consistency analysis by an asymptotic expansion is performed to overcome this difficulty. In turn, second order convergence in both time and space is established in a discrete L^\infty (0,T; H^3) norm.

math.NA↗

arXiv2011

Weighted reciprocity in human communication networks

In this paper we define a metric for reciprocity---the degree of balance in a social relationship---appropriate for weighted social networks in order to investigate the distribution of this dyadic feature in a large-scale system built from trace-logs of over a billion cell-phone communication events across millions of actors. We find that dyadic relations in this network are characterized by much larger degrees of imbalance than we would expect if persons kept only those relationships that exhibited close to full reciprocity. We point to two structural features of human communication behavior and relationship formation---the division of contacts into strong and weak ties and the tendency to form relationships with similar others---that either help or hinder the ability of persons to obtain communicative balance in their relationships. We examine the extent to which deviations from reciprocity in the observed network are partially traceable to these characteristics.

cs.SI↗

arXiv2011

Long time stability of a classical efficient scheme for two dimensional Navier-Stokes equations

We prove that a popular classical implicit-explicit scheme for the 2D incompressible Navier--Stokes equations that treats the viscous term implicitly while the nonlinear advection term explicitly is long time stable provided that the time step is sufficiently small in the case with periodic boundary conditions. The long time stability in the $L^2$ and $H^1$ norms further leads to the convergence of the global attractors and invariant measures of the scheme to those of the NSE itself at vanishing time step. Both semi-discrete in time and fully discrete schemes with either Galerkin Fourier spectral or collocation Fourier spectral methods are considered.

math.NA↗

arXiv2010

Trapping, focusing and sorting of microparticles through bubble streaming

Ultrasound-driven microbubbles rectify oscillatory motion into strong steady streaming flow [1, 2]. In this fluid dynamics video, we show size-dependent trapping, focusing and sorting of microparticles, utilizing the interaction between bubble streaming and the induced streaming around the mobile particles. This mechanism is purely passive and is selective for sizes and size differentials far smaller than any scale imposed by the device geometry.

physics.flu-dyn↗