arXiv subjects

Bing Li

Publications and source records attributed to Bing Li.

At least 505 records · Page 28Linked to original sources

arXiv2015

Intermediate β-shifts of finite type

An aim of this article is to highlight dynamical differences between the greedy, and hence the lazy, $β$-shift (transformation) and an intermediate $β$-shift (transformation), for a fixed $β\in (1, 2)$. Specifically, a classification in terms of the kneading invariants of the linear maps $T_{β,α} \colon x \mapsto βx + α\bmod 1$ for which the corresponding intermediate $β$-shift is of finite type is given. This characterisation is then employed to construct a class of pairs $(β,α)$ such that the intermediate $β$-shift associated with $T_{β, α}$ is a subshift of finite type. It is also proved that these maps $T_{β,α}$ are not transitive. This is in contrast to the situation for the corresponding greedy and lazy $β$-shifts and $β$-transformations, for which both of the two properties do not hold.

math.DS↗

arXiv2015

RF Transport Electromagnetic Properties of CVD Graphene from DC to 110 MHz

We report measurement of the radio-frequency (RF) transport electromagnetic properties of chemical vapour deposition (CVD) graphene over the DC to 110 MHz frequency range at room temperature. Graphene on Si/SiO2 substrate was mounted in a shielded four terminal-pair (4TP) adaptor which enabled direct connection to a calibrated precision impedance analyser for measurements. Good agreement is observed for the DC four-probe resistance and the 4TP resistance at 40 Hz, both yielding R ~ 104 Ω. In general the apparent graphene channel electromagnetic properties are found to be strongly influenced by the substrate parasitic capacitance and resistance, particularly for high-frequencies f > 1 MHz. A phenomenological lumped-parameter equivalent circuit model is presented which matches the frequency response of the graphene 4TP impedance device over approximately seven decades of the frequency range of the applied transport alternating current. Based on this model, it is shown for the first time, that the intrinsic graphene channel resistance of the 4TP device is frequency-independent (i.e. dissipationless) with RG ~ 105 Ω or sheet resistance of approximately 182 Ω / sq. The parasitic substrate impedance of the device is found shunt RG with RP ~ 2.2 Ω in series with CP ~ 600 pF. These results suggest that our new RF 4TP method is in good agreement with the conventional DC four-probe method for measuring the intrinsic sheet resistance of single-atom thick materials and could potentially open up new applications in RF electronics, AC quantum Hall effect metrology and sensors based on graphene 4TP devices operating over broad range of frequencies.

cond-mat.mtrl-sci↗

arXiv2014

An Empirical Study on Software Defect Prediction with a Simplified Metric Set

Software defect prediction plays a crucial role in estimating the most defect-prone components of software, and a large number of studies have pursued improving prediction accuracy within a project or across projects. However, the rules for making an appropriate decision between within- and cross-project defect prediction when available historical data are insufficient remain unclear. The objective of this work is to validate the feasibility of the predictor built with a simplified metric set for software defect prediction in different scenarios, and to investigate practical guidelines for the choice of training data, classifier and metric subset of a given project. First, based on six typical classifiers, we constructed three types of predictors using the size of software metric set in three scenarios. Then, we validated the acceptable performance of the predictor based on Top-k metrics in terms of statistical methods. Finally, we attempted to minimize the Top-k metric subset by removing redundant metrics, and we tested the stability of such a minimum metric subset with one-way ANOVA tests. The experimental results indicate that (1) the choice of training data should depend on the specific requirement of prediction accuracy; (2) the predictor built with a simplified metric set works well and is very useful in case limited resources are supplied; (3) simple classifiers (e.g., Naive Bayes) also tend to perform well when using a simplified metric set for defect prediction; and (4) in several cases, the minimum metric subset can be identified to facilitate the procedure of general defect prediction with acceptable loss of prediction precision in practice. The guideline for choosing a suitable simplified metric set in different scenarios is presented in Table 12.

cs.SE↗

arXiv2014

Towards Cross-Project Defect Prediction with Imbalanced Feature Sets

Cross-project defect prediction (CPDP) has been deemed as an emerging technology of software quality assurance, especially in new or inactive projects, and a few improved methods have been proposed to support better defect prediction. However, the regular CPDP always assumes that the features of training and test data are all identical. Hence, very little is known about whether the method for CPDP with imbalanced feature sets (CPDP-IFS) works well. Considering the diversity of defect data sets available on the Internet as well as the high cost of labeling data, to address the issue, in this paper we proposed a simple approach according to a distribution characteristic-based instance (object class) mapping, and demonstrated the validity of our method based on three public defect data sets (i.e., PROMISE, ReLink and AEEEM). Besides, the empirical results indicate that the hybrid model composed of CPDP and CPDP-IFS does improve the prediction performance of the regular CPDP to some extent.

cs.SE↗

arXiv2014

Simplification of Training Data for Cross-Project Defect Prediction

Cross-project defect prediction (CPDP) plays an important role in estimating the most likely defect-prone software components, especially for new or inactive projects. To the best of our knowledge, few prior studies provide explicit guidelines on how to select suitable training data of quality from a large number of public software repositories. In this paper, we have proposed a training data simplification method for practical CPDP in consideration of multiple levels of granularity and filtering strategies for data sets. In addition, we have also provided quantitative evidence on the selection of a suitable filter in terms of defect-proneness ratio. Based on an empirical study on 34 releases of 10 open-source projects, we have elaborately compared the prediction performance of different defect predictors built with five well-known classifiers using training data simplified at different levels of granularity and with two popular filters. The results indicate that when using the multi-granularity simplification method with an appropriate filter, the prediction models based on Naive Bayes can achieve fairly good performance and outperform the benchmark method.

cs.SE↗

arXiv2014

Random affine code tree fractals and Falconer-Sloan condition

We calculate the almost sure dimension for a general class of random affine code tree fractals in $\mathbb R^d$. The result is based on a probabilistic version of the Falconer-Sloan condition $C(s)$ introduced in \cite{FS}. We verify that, in general, systems having a small number of maps do not satisfy condition $C(s)$. However, there exists a natural number $n$ such that for typical systems the family of all iterates up to level $n$ satisfies condition $C(s)$.

math.DS↗

arXiv2014

Linear Contour Learning: A Method for Supervised Dimension Reduction

We propose a novel approach to sufficient dimension reduction in regression, based on estimating contour directions of negligible variation for the response surface. These directions span the orthogonal complement of the minimal space relevant for the regression, and can be extracted according to a measure of the variation in the response, leading to General Contour Regression(GCR). In comparison to exiisting sufficient dimension reduction techniques, this sontour-based mothology guarantees exhaustive estimation of the central space under ellipticity of the predictoor distribution and very mild additional assumptions, while maintaining vn-consisytency and somputational ease. Moreover, it proves to be robust to departures from ellipticity. We also establish some useful population properties for GCR. Simulations to compare performance with that of standard techniques such as ordinary least squares, sliced inverse regression, principal hessian directions, and sliced average variance estimation confirm the advntages anticipated by theoretical analyses. We also demonstrate the use of contour-based methods on a data set concerning grades of students from Massachusetts colleges.

cs.LG↗

arXiv2014

An Analysis of Research in Software Engineering: Assessment and Trends

Glass published the first report on the assessment of systems and software engineering scholars and institutions two decades ago. The ongoing, annual survey of publications in this field provides fund managers, young scholars, graduate students, etc. with useful information for different purposes. However, the studies have been questioned by some critics because of a few shortcomings of the evaluation method. It is actually very hard to reach a widely recognized consensus on such an assessment of scholars and institutions. This paper presents a module and automated method for assessment and trends analysis in software engineering compared with the prior studies. To achieve a more reasonable evaluation result, we take into consideration more high-quality publications, the rank of each publication analyzed, and the different roles of authors named on each paper in question. According to the 7638 papers published in 36 publications from 2008 to 2013, the statistics of research subjects roughly follow power laws, implying the interesting Matthew Effect. We then identify the Top 20 scholars, institutions and countries or regions in terms of a new evaluation rule based on the frequently-used one. The top-ranked scholar is Mark Harman of the University College London, UK, the top-ranked institution is the University of California, USA, and the top-ranked country is the USA. Besides, we also show two levels of trend changes based on the EI classification system and user-defined uncontrolled keywords, as well as noteworthy scholars and institutions in a specific research area. We believe that our results would provide a valuable insight for young scholars and graduate students to seek possible potential collaborators and grasp the popular research topics in software engineering.

cs.SE↗

arXiv2014

On efficient dimension reduction with respect to a statistical functional of interest

We introduce a new sufficient dimension reduction framework that targets a statistical functional of interest, and propose an efficient estimator for the semiparametric estimation problems of this type. The statistical functional covers a wide range of applications, such as conditional mean, conditional variance and conditional quantile. We derive the general forms of the efficient score and efficient information as well as their specific forms for three important statistical functionals: the linear functional, the composite linear functional and the implicit functional. In conjunction with our theoretical analysis, we also propose a class of one-step Newton-Raphson estimators and show by simulations that they substantially outperform existing methods. Finally, we apply the new method to construct the central mean and central variance subspaces for a data set involving the physical measurements and age of abalones, which exhibits a strong pattern of heteroscedasticity.

math.ST↗

arXiv2014

Removing Mixture of Gaussian and Impulse Noise by Patch-Based Weighted Means

We first establish a law of large numbers and a convergence theorem in distribution to show the rate of convergence of the non-local means filter for removing Gaussian noise. We then introduce the notion of degree of similarity to measure the role of similarity for the non-local means filter. Based on the convergence theorems, we propose a patch-based weighted means filter for removing impulse noise and its mixture with Gaussian noise by combining the essential idea of the trilateral filter and that of the non-local means filter. Our experiments show that our filter is competitive compared to recently proposed methods.

cs.CV↗

arXiv2013

Projections of random covering sets

We show that, almost surely, the Hausdorff dimension $s_0$ of a random covering set is preserved under all orthogonal projections to linear subspaces with dimension $k>s_0$. The result holds for random covering sets with a generating sequence of ball-like sets, and is obtained by investigating orthogonal projections of a class of random Cantor sets.

math.CA↗

arXiv2013

A note on the hitting probabilities of random covering sets

Let $E=\limsup\limits_{n\to\infty}(g_n+ξ_n)$ be the random covering set on the torus $\mathbb{T}^d$, where $\{g_n\}$ is a sequence of ball-like sets and $ξ_n$ is a sequence of independent random variables uniformly distributed on $\T^d$. We prove that $E\cap F\neq\emptyset$ almost surely whenever $F\subset\mathbb{T}^d$ is an analytic set with Hausdorff dimension, $\dim_H(F)>d-α$, where $α$ is the almost sure Hausdorff dimension of $E$. Moreover, examples are given to show that the condition on $\dim_H(F)$ cannot be replaced by the packing dimension of $F$.

math.CA↗

arXiv2013

Hausdorff dimension of affine random covering sets in torus

We calculate the almost sure Hausdorff dimension of the random covering set $\limsup_{n\to\infty}(g_n + ξ_n)$ in $d$-dimensional torus $\mathbb T^d$, where the sets $g_n\subset\mathbb T^d$ are parallelepipeds, or more generally, linear images of a set with nonempty interior, and $ξ_n\in\mathbb T^d$ are independent and uniformly distributed random points. The dimension formula, derived from the singular values of the linear mappings, holds provided that the sequences of the singular values are decreasing.

math.PR↗

arXiv2013

A general theory for nonlinear sufficient dimension reduction: Formulation and estimation

In this paper we introduce a general theory for nonlinear sufficient dimension reduction, and explore its ramifications and scope. This theory subsumes recent work employing reproducing kernel Hilbert spaces, and reveals many parallels between linear and nonlinear sufficient dimension reduction. Using these parallels we analyze the properties of existing methods and develop new ones. We begin by characterizing dimension reduction at the general level of $σ$-fields and proceed to that of classes of functions, leading to the notions of sufficient, complete and central dimension reduction classes. We show that, when it exists, the complete and sufficient class coincides with the central class, and can be unbiasedly and exhaustively estimated by a generalized sliced inverse regression estimator (GSIR). When completeness does not hold, this estimator captures only part of the central class. However, in these cases we show that a generalized sliced average variance estimator (GSAVE) can capture a larger portion of the class. Both estimators require no numerical optimization because they can be computed by spectral decomposition of linear operators. Finally, we compare our estimators with existing methods by simulation and on actual data sets.

math.ST↗

arXiv2013

Diophantine approximation of the orbit of 1 in the dynamical system of bete expansions

We consider the distribution of the orbits of the number 1 under the $β$-transformations $T_β$ as $β$ varies. Mainly, the size of the set of $β>1$ for which a given point can be well approximated by the orbit of 1 is measured by its Hausdorff dimension. That is, the dimension of the following set $$ E\big({\ell_n}_{n\ge 1}, x_0\big)=\Big{β>1: |T^n_β1-x_0|<β^{-\ell_n}, {for infinitely many} n\in \N\Big} $$ is determined, where $x_0$ is a given point in $[0,1]$ and ${\ell_n}_{n\ge 1}$ is a sequence of integers tending to infinity as $n\to \infty$. For the proof of this result, the notion of the recurrence time of a word in symbolic space is introduced to characterize the lengths and the distribution of cylinders (the set of $β$ with a common prefix in the expansion of 1) in the parameter space ${β\in \R: β>1}$.

math.DS↗

arXiv2013

The hybrid lattice of KxFe2-ySe2: why superconductivity and magnetism can coexist

Much remains unknown of the microscopic origin of superconductivity when it materializes in atomically disordered systems as in amorphous alloys (1) or in crystals riddled with defects(2). A manifestation of this conundrum is envisaged in the highly defective iron chalcogenide superconductors of KxFe2-ySe2 (3-6). How can superconductivity survive under such crude conditions that call for strong electron localization (7)? With vacancies present both at the K and Fe sites, superconductivity is bordering a semi-metallic region below x ~ 0.7 and an insulating and antiferromagnetic region above x ~ 0.85 (8,9). Here, we report on the bulk local atomic structure and show that the Fe sublattice is locally distorted in a way that it accommodates two kinds of Fe valence environments giving rise to a bimodal bond distribution. While the bond length distribution is driven by K and Fe contents, the superconducting state is characterized by the coexistence of both short (metallic) and long (insulating) Fe bond environments and is not phase separated. In contrast to other Fe-based materials in which only one kind of Fe to Fe bond is present, the dual nature of the Fe correlations explains why superconductivity is intertwined with magnetic order. Such a hybrid state is most likely present in cuprate superconductors as well (10,11) while our results point to the importance of the local atomic symmetry by which the exchange interactions between local moments can materialize (12).

cond-mat.supr-con↗

arXiv2012

Color Constancy based on Image Similarity via Bilayer Sparse Coding

Computational color constancy is a very important topic in computer vision and has attracted many researchers' attention. Recently, lots of research has shown the effects of high level visual content information for illumination estimation. However, all of these existing methods are essentially combinational strategies in which image's content analysis is only used to guide the combination or selection from a variety of individual illumination estimation methods. In this paper, we propose a novel bilayer sparse coding model for illumination estimation that considers image similarity in terms of both low level color distribution and high level image scene content simultaneously. For the purpose, the image's scene content information is integrated with its color distribution to obtain optimal illumination estimation model. The experimental results on two real-world image sets show that our algorithm is superior to other prevailing illumination estimation methods, even better than combinational methods.

cs.CV↗

arXiv2012

Sufficient dimension reduction based on an ensemble of minimum average variance estimators

We introduce a class of dimension reduction estimators based on an ensemble of the minimum average variance estimates of functions that characterize the central subspace, such as the characteristic functions, the Box--Cox transformations and wavelet basis. The ensemble estimators exhaustively estimate the central subspace without imposing restrictive conditions on the predictors, and have the same convergence rate as the minimum average variance estimates. They are flexible and easy to implement, and allow repeated use of the available sample, which enhances accuracy. They are applicable to both univariate and multivariate responses in a unified form. We establish the consistency and convergence rate of these estimators, and the consistency of a cross validation criterion for order determination. We compare the ensemble estimators with other estimators in a wide variety of models, and establish their competent performance.

math.ST↗