arXiv subjects

Ping Li

Publications and source records attributed to Ping Li.

At least 361 records · Page 20Linked to original sources

arXiv2018

Generalized Birkhoff theorem and its applications in mimetic gravity

There is undetermined potential function $V(ϕ)$ in the action of mimetic gravity which should be resolved through physical means. In general relativity(GR), the static spherically symmetric(SSS) solution to the Einstein equation is a benchmark and its deformation also plays a crucial role in mimetic gravity. The equation of motion is provided with high nonlinearity, but we can reduce primal nonlinearity to a frequent Riccati form in the SSS case of mimetic gravity. In other words, we obtain an expression of solution to the functional differential equation of motion with any potential function. Remarkably, we proved rigorously that there is a zero point of first order for the metric function $β(r)$ if another metric function $α(r)$ possesses a pole of first order within mimetic gravity. The zero point theorem may be regarded as the generalization of Birkhoff theorem $αβ=1$ in GR. As a corollary, we show that there is a modified black hole solution for any given $V(ϕ)$, which can pass the test of solar system. As another corollary, the zero point theorem provides a dynamical mechanism for the maximum size of galaxies. Especially, there are two analytic solutions which provide good fits to the rotation curves of galaxies without the demand for particle dark matter.

gr-qc↗

arXiv2018

A Tight Bound of Hard Thresholding

This paper is concerned with the hard thresholding operator which sets all but the $k$ largest absolute elements of a vector to zero. We establish a {\em tight} bound to quantitatively characterize the deviation of the thresholded solution from a given signal. Our theoretical result is universal in the sense that it holds for all choices of parameters, and the underlying analysis depends only on fundamental arguments in mathematical optimization. We discuss the implications for two domains: Compressed Sensing. On account of the crucial estimate, we bridge the connection between the restricted isometry property (RIP) and the sparsity parameter for a vast volume of hard thresholding based algorithms, which renders an improvement on the RIP condition especially when the true sparsity is unknown. This suggests that in essence, many more kinds of sensing matrices or fewer measurements are admissible for the data acquisition procedure. Machine Learning. In terms of large-scale machine learning, a significant yet challenging problem is learning accurate sparse models in an efficient manner. In stark contrast to prior work that attempted the $\ell_1$-relaxation for promoting sparsity, we present a novel stochastic algorithm which performs hard thresholding in each iteration, hence ensuring such parsimonious solutions. Equipped with the developed bound, we prove the {\em global linear convergence} for a number of prevalent statistical models under mild assumptions, even though the problem turns out to be non-convex.

stat.ML↗

arXiv2018

The evolving networks of debtor-creditor relationships with addition and deletion of nodes: a case of P2P lending

P2P lending activities have grown rapidly and have caused the huge and complex networks of debtor-creditor relationships. The aim of this study was to study the underlying structural characteristics of networks formed by debtor-creditor relationships. According attributes of P2P lending, this paper model the networks of debtor-creditor relationships as an evolving networks with addition and deletion of nodes. It was found that networks of debtor-creditor relationships are scale-free networks. Moreover, the exponent of power-law was calculated by an empirical study. In addition, this paper study what factors impact on the exponent of power-law besides the number of nodes. It was found that the both interest rate and term have significantly influence on the exponent of power-law. Interest rate is negatively correlated with the exponent of power-law and term is positively correlated with the exponent of power-law. Our results enriches the application of complex networks

q-fin.GN↗

arXiv2018

Several Tunable GMM Kernels

While tree methods have been popular in practice, researchers and practitioners are also looking for simple algorithms which can reach similar accuracy of trees. In 2010, (Ping Li UAI'10) developed the method of "abc-robust-logitboost" and compared it with other supervised learning methods on datasets used by the deep learning literature. In this study, we propose a series of "tunable GMM kernels" which are simple and perform largely comparably to tree methods on the same datasets. Note that "abc-robust-logitboost" substantially improved the original "GDBT" in that (a) it developed a tree-split formula based on second-order information of the derivatives of the loss function; (b) it developed a new set of derivatives for multi-class classification formulation. In the prior study in 2017, the "generalized min-max" (GMM) kernel was shown to have good performance compared to the "radial-basis function" (RBF) kernel. However, as demonstrated in this paper, the original GMM kernel is often not as competitive as tree methods on the datasets used in the deep learning literature. Since the original GMM kernel has no parameters, we propose tunable GMM kernels by adding tuning parameters in various ways. Three basic (i.e., with only one parameter) GMM kernels are the "$e$GMM kernel", "$p$GMM kernel", and "$γ$GMM kernel", respectively. Extensive experiments show that they are able to produce good results for a large number of classification tasks. Furthermore, the basic kernels can be combined to boost the performance.

cs.LG↗

arXiv2018

Sign-Full Random Projections

The method of 1-bit ("sign-sign") random projections has been a popular tool for efficient search and machine learning on large datasets. Given two $D$-dim data vectors $u$, $v\in\mathbb{R}^D$, one can generate $x = \sum_{i=1}^D u_i r_i$, and $y = \sum_{i=1}^D v_i r_i$, where $r_i\sim N(0,1)$ iid. The "collision probability" is ${Pr}\left(sgn(x)=sgn(y)\right) = 1-\frac{\cos^{-1}ρ}π$, where $ρ= ρ(u,v)$ is the cosine similarity. We develop "sign-full" random projections by estimating $ρ$ from (e.g.,) the expectation $E(sgn(x)y)=\sqrt{\frac{2}π} ρ$, which can be further substantially improved by normalizing $y$. For nonnegative data, we recommend an interesting estimator based on $E\left(y_- 1_{x\geq 0} + y_+ 1_{x<0}\right)$ and its normalized version. The recommended estimator almost matches the accuracy of the (computationally expensive) maximum likelihood estimator. At high similarity ($ρ\rightarrow1$), the asymptotic variance of recommended estimator is only $\frac{4}{3π} \approx 0.4$ of the estimator for sign-sign projections. At small $k$ and high similarity, the improvement would be even much more substantial.

stat.ME↗

arXiv2018

On the spectral rigidity of Einstein-type Kähler manifolds

We are concerned in this article with a classical question in spectral geometry dating back to McKean-Singer, Patodi and Tanno: whether or not the constancy of holomorphic sectional curvature of a complex $n$-dimensional compact Kähler manifold can be completely determined by the eigenvalues of its $p$-Laplacian for a \emph{single} integer $p$? We treat this question in this article under two Einstein-type conditions: cohomologically Einstein and Fano Einstein. Building on our previous work, we show that for cohomologically Einstein Kähler manifolds this is true for all but finitely many pairs $(p,n)$. As a consequence, the standard complex projective spaces can be characterized among cohomologically Einstein Kähler manifolds in terms of a single spectral set in all these cases. Moreover, in the case of $p=0$, we show that the complex projective spaces can be characterized among Fano Kähler-Einstein manifolds only in terms of the first nonzero eigenvalue with multiplicity, which has a similar flavor to a recent remarkable result due to Kento Fujita.

math.DG↗

arXiv2017

Conformal transformation route to gravity's rainbow

Conformal transformation as a mathematical tool has been used in many areas of gravitational physics. In this paper, we would consider the gravity's rainbow, in which the metric could be treated as a conformal rescaling of the original metric. By using the conformal transformation technique, we get a specific form of modified Newton's constant and cosmological constant in gravity's rainbow, which implies that the total vacuum energy is dependent on probe energy. Moreover, the result shows that the Einstein gravity's rainbow could be described by an energy-dependent $f(E,\tilde R)$ gravity. At last, we study the $f(R)$ gravity, when the gravity's rainbow is considered, it can also be described as another energy-dependent $\tilde f(E,\tilde R)$ gravity.

gr-qc↗

arXiv2017

Prediction of Topological Crystalline Insulator and Topological Phase Transitions in Two-dimensional PbTe Films

Topological phases, especially topological crystalline insulators (TCIs), have been intensively explored observed experimentally in three-dimensional (3D) materials. However, the two-dimensional (2D) films are explored much less than 3D TCI, and even 2D topological insulators. Based on ab initio calculations, here we investigate the electronic and topological properties of 2D PbTe(001) few-layers. The monolayer and trilayer PbTe are both intrinsic 2D TCIs with a large band gap reaching 0.27 eV, indicating a high possibility for room-temperature observation of quantized conductance. The origin of TCI phase can be attributed to the p band inversion,which is determined by the competitions of orbital hybridization and quantum confinement. We also observe a semimetal-TCI-normal insulator transition under biaxial strains, whereas a uniaxial strains lead to Z2 nontrivial states. Especially, the TCI phase of PbTe monolayer remains when epitaxial grow on NaI semiconductor substrate. Our findings on the controllable quantum states with sizable band gaps present an ideal platform for realizing future topological quantum devices with ultralow dissipation.

cond-mat.mtrl-sci↗

arXiv2017

Image matting with normalized weight and semi-supervised learning

Image matting is an important vision problem. The main stream methods for it combine sampling-based methods and propagation-based methods. In this paper, we deal with the combination with a normalized weighting parameter, which could well control the relative relationship between information from sampling and from propagation. A reasonable value range for this parameter is given based on statistics from the standard benchmark dataset. The matting is further improved by introducing semi-supervised learning iterations, which automatically refine the trimap without user's interaction. This is especially beneficial when the trimap is coarse. The experimental results on standard benchmark dataset have shown that both the normalized weighting parameter and the semi-supervised learning iteration could significantly improve the matting performance.

cs.CV↗

arXiv2017

Efficient Online Minimization for Low-Rank Subspace Clustering

Low-rank representation~(LRR) has been a significant method for segmenting data that are generated from a union of subspaces. It is, however, known that solving the LRR program is challenging in terms of time complexity and memory footprint, in that the size of the nuclear norm regularized matrix is $n$-by-$n$ (where $n$ is the number of samples). In this paper, we thereby develop a fast online implementation of LRR that reduces the memory cost from $O(n^2)$ to $O(pd)$, with $p$ being the ambient dimension and $d$ being some estimated rank~($d < p \ll n$). The crux for this end is a non-convex reformulation of the LRR program, which pursues the basis dictionary that generates the (uncorrupted) observations. We build the theoretical guarantee that the sequence of the solutions produced by our algorithm converges to a stationary point of the empirical and the expected loss function asymptotically. Extensive experiments on synthetic and realistic datasets further substantiate that our algorithm is fast, robust and memory efficient.

stat.ML↗

arXiv2017

Topological Dirac states beyond $π$ orbitals for silicene on SiC(0001) surface

The discovery of intriguing properties related to the Dirac states in graphene has spurred huge interest in exploring its two-dimensional group-IV counterparts, such as silicene, germanene, and stanene. However, these materials have to be obtained via synthesizing on substrates with strong interfacial interactions, which usually destroy their intrinsic $π$($p_z$)-orbital Dirac states. Here we report a theoretical study on the existence of Dirac states arising from the $p_{x,y}$ orbitals instead of $p_z$ orbitals in silicene on 4H-SiC(0001), which survive in spite of the strong interfacial interactions. We also show that the exchange field together with the spin-orbital coupling give rise to a detectable band gap of 1.3 meV. Berry curvature calculations demonstrate the nontrivial topological nature of such Dirac states with a Chern number $C = 2$, presenting the potential of realizing quantum anomalous Hall effect for silicene on SiC(0001). Finally, we construct a minimal effective model to capture the low-energy physics of this system. This finding is expected to be also applicable to germanene and stanene, and imply great application potentials in nanoelectronics.

cond-mat.mes-hall↗

arXiv2017

Discovery of Intrinsic Quantum Anomalous Hall Effect in Organic Mn-DCA Lattice

The quantum anomalous Hall (QAH) phase is a novel topological state of matter characterized by a nonzero quantized Hall conductivity without an external magnetic field. The realizations of QAH effect, however, are experimentally challengeable. Based on ab initio calculations, here we propose an intrinsic QAH phase in DCA Kagome lattice. The nontrivial topology in Kagome bands are confirmed by the nonzero chern number, quantized Hall conductivity, and gapless chiral edge states of Mn-DCA lattice. A tight-binding (TB) model is further constructed to clarify the origin of QAH effect. Furthermore, its Curie temperature, estimated to be ~ 253 K using Monte-Carlo simulation, is comparable with room temperature and higher than most of two-dimensional ferromagnetic thin films. Our findings present a reliable material platform for the observation of QAH effect in covalent-organic frameworks.

cond-mat.mtrl-sci↗

arXiv2017

Object Proposal with Kernelized Partial Ranking

Object proposals are an ensemble of bounding boxes with high potential to contain objects. In order to determine a small set of proposals with a high recall, a common scheme is extracting multiple features followed by a ranking algorithm which however, incurs two major challenges: {\bf 1)} The ranking model often imposes pairwise constraints between each proposal, rendering the problem away from an efficient training/testing phase; {\bf 2)} Linear kernels are utilized due to the computational and memory bottleneck of training a kernelized model. In this paper, we remedy these two issues by suggesting a {\em kernelized partial ranking model}. In particular, we demonstrate that {\bf i)} our partial ranking model reduces the number of constraints from $O(n^2)$ to $O(nk)$ where $n$ is the number of all potential proposals for an image but we are only interested in top-$k$ of them that has the largest overlap with the ground truth; {\bf ii)} we permit non-linear kernels in our model which is often superior to the linear classifier in terms of accuracy. For the sake of mitigating the computational and memory issues, we introduce a consistent weighted sampling~(CWS) paradigm that approximates the non-linear kernel as well as facilitates an efficient learning. In fact, as we will show, training a linear CWS model amounts to learning a kernelized model. Extensive experiments demonstrate that equipped with the non-linear kernel and the partial ranking algorithm, recall at top-$k$ proposals can be substantially improved.

cs.CV↗

arXiv2017

Two-Dimensional Arsenene Oxide: A Realistic Large-gap Quantum Spin Hall Insulator

Searching for two-dimensional (2D) realistic materials able to realize room-temperature quantum spin Hall (QSH) effects is currently a growing field. Here, we through ab initio calculations to identify arsenene oxide, AsO, as an excellent candidate, which demonstrates high stability, flexibility, and tunable spin-orbit coupling (SOC) gaps. In contrast to known pristine or functionalized arsenene, the maximum nontrivial band gap of AsO reaches 89 meV, and can be further enhanced to 130 meV under biaxial strain. By sandwiching 2D AsO between BN sheets, we propose a quantum well in which the band topology of AsO is preserved with a sizeable band gap. Considering that AsO having fully oxidized surfaces are naturally stable against surface oxidization and degradation, this functionality provides a viable strategy for designing topological quantum devices operating at room temperature.

cond-mat.mtrl-sci↗

arXiv2017

Tunable GMM Kernels

The recently proposed "generalized min-max" (GMM) kernel can be efficiently linearized, with direct applications in large-scale statistical learning and fast near neighbor search. The linearized GMM kernel was extensively compared in with linearized radial basis function (RBF) kernel. On a large number of classification tasks, the tuning-free GMM kernel performs (surprisingly) well compared to the best-tuned RBF kernel. Nevertheless, one would naturally expect that the GMM kernel ought to be further improved if we introduce tuning parameters. In this paper, we study three simple constructions of tunable GMM kernels: (i) the exponentiated-GMM (or eGMM) kernel, (ii) the powered-GMM (or pGMM) kernel, and (iii) the exponentiated-powered-GMM (epGMM) kernel. The pGMM kernel can still be efficiently linearized by modifying the original hashing procedure for the GMM kernel. On about 60 publicly available classification datasets, we verify that the proposed tunable GMM kernels typically improve over the original GMM kernel. On some datasets, the improvements can be astonishingly significant. For example, on 11 popular datasets which were used for testing deep learning algorithms and tree methods, our experiments show that the proposed tunable GMM kernels are strong competitors to trees and deep nets. The previous studies developed tree methods including "abc-robust-logitboost" and demonstrated the excellent performance on those 11 datasets (and other datasets), by establishing the second-order tree-split formula and new derivatives for multi-class logistic loss. Compared to tree methods like "abc-robust-logitboost" (which are slow and need substantial model sizes), the tunable GMM kernels produce largely comparable results.

stat.ML↗

arXiv2017

Two-Dimensional Large Gap Topological Insulators with Large Rashba Spin-Orbit Coupling in Group-IV films

Rashba spin orbit coupling in topological insulators has attracted much interest due to its exotic properties closely related to spintronic devices. The coexistence of nontrivial topology and giant Rashba splitting, however, has rare been observed in two-dimensional films, limiting severely its potential applications at room temperature. Here, we propose a series of inversion asymmetric group IV films, ABZ2, whose stability are confirmed by phonon spectrum calculations. The analyses of electronic structures reveal that they are intrinsic 2D TIs with a bulk gap as large as 0.74 eV, except for GeSiF2, SnSiCl2, GeSiCl2 and GeSiBr2 monolayers which can transform from normal to topological phases under appropriate tensile strains. Another prominent intriguing feature is the giant Rashba spin splitting with a magnitude reaching 0.15 eV, the largest value reported in 2D films. These results present a platform to explore 2D TIs for room temperature device applications.

cond-mat.mtrl-sci↗

arXiv2017

L2GSCI: Local to Global Seam Cutting and Integrating for Accurate Face Contour Extraction

Current face alignment algorithms can robustly find a set of landmarks along face contour. However, the landmarks are sparse and lack curve details, especially in chin and cheek areas where a lot of concave-convex bending information exists. In this paper, we propose a local to global seam cutting and integrating algorithm (L2GSCI) to extract continuous and accurate face contour. Our method works in three steps with the help of a rough initial curve. First, we sample small and overlapped squares along the initial curve. Second, the seam cutting part of L2GSCI extracts a local seam in each square region. Finally, the seam integrating part of L2GSCI connects all the redundant seams together to form a continuous and complete face curve. Overall, the proposed method is much more straightforward than existing face alignment algorithms, but can achieve pixel-level continuous face curves rather than discrete and sparse landmarks. Moreover, experiments on two face benchmark datasets (i.e., LFPW and HELEN) show that our method can precisely reveal concave-convex bending details of face contours, which has significantly improved the performance when compared with the state-ofthe- art face alignment approaches.

cs.CV↗

arXiv2017

Linearized GMM Kernels and Normalized Random Fourier Features

The method of "random Fourier features (RFF)" has become a popular tool for approximating the "radial basis function (RBF)" kernel. The variance of RFF is actually large. Interestingly, the variance can be substantially reduced by a simple normalization step as we theoretically demonstrate. We name the improved scheme as the "normalized RFF (NRFF)". We also propose the "generalized min-max (GMM)" kernel as a measure of data similarity. GMM is positive definite as there is an associated hashing method named "generalized consistent weighted sampling (GCWS)" which linearizes this nonlinear kernel. We provide an extensive empirical evaluation of the RBF kernel and the GMM kernel on more than 50 publicly available datasets. For a majority of the datasets, the (tuning-free) GMM kernel outperforms the best-tuned RBF kernel. We conduct extensive experiments for comparing the linearized RBF kernel using NRFF with the linearized GMM kernel using GCWS. We observe that, to reach a comparable classification accuracy, GCWS typically requires substantially fewer samples than NRFF, even on datasets where the original RBF kernel outperforms the original GMM kernel. The empirical success of GCWS (compared to NRFF) can also be explained from a theoretical perspective. Firstly, the relative variance (normalized by the squared expectation) of GCWS is substantially smaller than that of NRFF, except for the very high similarity region (where the variances of both methods are close to zero). Secondly, if we make a model assumption on the data, we can show analytically that GCWS exhibits much smaller variance than NRFF for estimating the same object (e.g., the RBF kernel), except for the very high similarity region.

cs.LG↗