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Li Chen

Publications and source records attributed to Li Chen.

At least 649 records · Page 36Linked to original sources
arXiv2017

Algorithms for Deforming and Contracting Simply Connected Discrete Closed Manifolds (II)

In an exploration paper, {\it L. Chen, Algorithms for Deforming and Contracting Simply Connected Discrete Closed Manifolds (I)}, we designed algorithms for deforming and contracting a simply connected discrete closed manifold to a discrete sphere. However, the algorithms could not guarantee to be applicable to every case. This paper will be the continuation of the exploration. This paper contains two main procedures: (1) A shrinking procedure to contract a simply connected closed manifold. Unlike ones in the previous paper, we added a tree structure to support the process. (2) A more direct procedure for mapping a component from a separated simply connected closed manifold to a disk. We also discuss the practical use of these algorithms in topological data analysis. We think that we have an algorithmic solution, but careful detailed analysis should be done next.

math.GN↗
arXiv2017

Stochastic Variance Reduction Gradient for a Non-convex Problem Using Graduated Optimization

In machine learning, nonconvex optimization problems with multiple local optimums are often encountered. Graduated Optimization Algorithm (GOA) is a popular heuristic method to obtain global optimums of nonconvex problems through progressively minimizing a series of convex approximations to the nonconvex problems more and more accurate. Recently, such an algorithm GradOpt based on GOA is proposed with amazing theoretical and experimental results, but it mainly studies the problem which consists of one nonconvex part. This paper aims to find the global solution of a nonconvex objective with a convex part plus a nonconvex part based on GOA. By graduating approximating non-convex part of the problem and minimizing them with the Stochastic Variance Reduced Gradient (SVRG) or proximal SVRG, two new algorithms, SVRG-GOA and PSVRG-GOA, are proposed. We prove that the new algorithms have lower iteration complexity ($O(1/\varepsilon)$) than GradOpt ($O(1/\varepsilon^2)$). Some tricks, such as enlarging shrink factor, using project step, stochastic gradient, and mini-batch skills, are also given to accelerate the convergence speed of the proposed algorithms. Experimental results illustrate that the new algorithms with the similar performance can converge to 'global' optimums of the nonconvex problems, and they converge faster than the GradOpt and the nonconvex proximal SVRG.

cs.LG↗
arXiv2017

Simultaneous constraints on the mass and radius of Aql X-1 from quiescence and X-ray burst observations

The measurement of neutron star mass and radius is one of the most direct way to distinguish between various dense matter equations of state. The mass and radius of accreting neutron stars hosted in low mass X-ray binaries can be constrained by several methods, including photospheric radius expansion from type-I X-ray bursts and from quiescent spectra. In this paper, we apply for the first time these two methods simultaneously to constrain the mass and radius of Aql X-1, as a reliable distance estimation, high signal-to-noise ratio quiescent spectra from Chandra and XMM-Newton, and photospheric radius expansion bursts from RXTE are available. This is also used to verify the consistency between the two methods, and to narrow down the uncertainties of the neutron star mass and radius. It is found that the distance to Aql X-1 should be in the range of $4.0-5.75$ kpc, based on the overlapping confidence regions between photospheric radius expansion burst and quiescent spectra methods. In addition, we show that the mass and radius determined for the compact star in Aql X-1 are compatible with strange star equations of state and conventional neutron star models.

astro-ph.HE↗
arXiv2017

Conical square functions for degenerate elliptic operators

The aim of this paper is to study the boundedness of different conical square functions that arise naturally from second order divergence form degenerate elliptic operators. More precisely, let $L_w=w^{-1}\,{\rm div}(w\,A\,\nabla)$ where $w\in A_2$ and $A$ is an $n\times n$ bounded, complex-valued, uniformly elliptic matrix. D. Cruz-Uribe and C. Rios solved the $L^2(w)$-Kato square root problem obtaining that $\sqrt{L_w}$ is equivalent to the gradient on $L^2(w)$. The same authors in collaboration with the second named author of this paper studied the $L^p(w)$-boundedness of operators that are naturally associated with $L_w$, such as the functional calculus, Riesz transforms, or vertical square functions. The theory developed admitted also weighted estimates (i.e., estimates in $L^p(v dw)$ for $v\in A_\infty(w)$), and in particular a class of "degeneracy" weights $w$ was found in such a way that the classical $L^2$-Kato problem can be solved. In this paper, continuing this line of research, and also that originated in some recent results by the second and third named authors of the current paper, we study the boundedness on $L^p(w)$ and on $L^p(v dw)$, with $v\in A_\infty(w)$, of the conical square functions that one can construct using the heat or Poisson semigroup associated with $L_w$. As a consequence of our methods, we find a class of degeneracy weights $w$ for which $L^2$-estimates for these conical square functions hold. This opens the door to the study of weighted and unweighted Hardy spaces and of boundary value problems associated with $L_w$.

math.CA↗
arXiv2017

Inverse mean curvature flow inside a cone in warped products

Given a convex cone in the \emph{prescribed} warped product, we consider hypersurfaces with boundary which are star-shaped with respect to the center of the cone and which meet the cone perpendicularly. If those hypersurfaces inside the cone evolve along the inverse mean curvature flow, then, by using the convexity of the cone, we can prove that this evolution exists for all the time and the evolving hypersurfaces converge smoothly to a piece of round sphere as time tends to infinity.

math.DG↗
arXiv2017

Keeping the Bad Guys Out: Protecting and Vaccinating Deep Learning with JPEG Compression

Deep neural networks (DNNs) have achieved great success in solving a variety of machine learning (ML) problems, especially in the domain of image recognition. However, recent research showed that DNNs can be highly vulnerable to adversarially generated instances, which look seemingly normal to human observers, but completely confuse DNNs. These adversarial samples are crafted by adding small perturbations to normal, benign images. Such perturbations, while imperceptible to the human eye, are picked up by DNNs and cause them to misclassify the manipulated instances with high confidence. In this work, we explore and demonstrate how systematic JPEG compression can work as an effective pre-processing step in the classification pipeline to counter adversarial attacks and dramatically reduce their effects (e.g., Fast Gradient Sign Method, DeepFool). An important component of JPEG compression is its ability to remove high frequency signal components, inside square blocks of an image. Such an operation is equivalent to selective blurring of the image, helping remove additive perturbations. Further, we propose an ensemble-based technique that can be constructed quickly from a given well-performing DNN, and empirically show how such an ensemble that leverages JPEG compression can protect a model from multiple types of adversarial attacks, without requiring knowledge about the model.

cs.CV↗
arXiv2017

Semi-supervised classification for dynamic Android malware detection

A growing number of threats to Android phones creates challenges for malware detection. Manually labeling the samples into benign or different malicious families requires tremendous human efforts, while it is comparably easy and cheap to obtain a large amount of unlabeled APKs from various sources. Moreover, the fast-paced evolution of Android malware continuously generates derivative malware families. These families often contain new signatures, which can escape detection when using static analysis. These practical challenges can also cause traditional supervised machine learning algorithms to degrade in performance. In this paper, we propose a framework that uses model-based semi-supervised (MBSS) classification scheme on the dynamic Android API call logs. The semi-supervised approach efficiently uses the labeled and unlabeled APKs to estimate a finite mixture model of Gaussian distributions via conditional expectation-maximization and efficiently detects malwares during out-of-sample testing. We compare MBSS with the popular malware detection classifiers such as support vector machine (SVM), $k$-nearest neighbor (kNN) and linear discriminant analysis (LDA). Under the ideal classification setting, MBSS has competitive performance with 98\% accuracy and very low false positive rate for in-sample classification. For out-of-sample testing, the out-of-sample test data exhibit similar behavior of retrieving phone information and sending to the network, compared with in-sample training set. When this similarity is strong, MBSS and SVM with linear kernel maintain 90\% detection rate while $k$NN and LDA suffer great performance degradation. When this similarity is slightly weaker, all classifiers degrade in performance, but MBSS still performs significantly better than other classifiers.

cs.CR↗
arXiv2017

Powerful CMD: A Tool for Colour-Magnitude Diagram Studies

We present a new tool for colour-magnitude diagram (CMD) studies, $Powerful~CMD$. This tool is built on the basis of the advanced stellar population synthesis (ASPS) model, in which single stars, binary stars, rotating stars, and star formation history have been taken into account. Via $Powerful~CMD$, the distance modulus, colour excess, metallicity, age, binary fraction, rotating star fraction, and star formation history of star clusters can be determined simultaneously from observed CMDs. The new tool is tested via both simulated and real star clusters. Five parameters of clusters NGC6362, NGC6652, NGC6838 and M67 are determined and compared to other works. It is shown that this tool is useful for CMD studies, in particular for those with the data of the Hubble Space Telescope (HST). Moreover, we find that the inclusion of binaries in theoretical stellar population models may lead to smaller colour excess compared to the case of single star population models.

astro-ph.GA↗
arXiv2017

Collective excitation of a trapped Bose-Einstein condensate with spin-orbit coupling

We investigate the collective excitations of a Raman-induced spin-orbit coupled Bose-Einstein condensate confined in a quasi one-dimension harmonic trap using the Bogoliubov method. By tuning the Raman coupling strength, three phases of the system can be identified. By calculating the transition strength, we are able to classify various excitation modes that are experimentally relevant. We show that the three quantum phases possess distinct features in their collective excitation properties. In particular, the spin dipole and the spin breathing modes can be used to clearly map out the phase boundaries. We confirm these predictions by direct numerical simulations of the quench dynamics that excites the relevant collective modes.

cond-mat.quant-gas↗
arXiv2017

Fundamental properties of cooperative contagion processes

We investigate the effects of cooperativity between contagion processes that spread and persist in a host population. We propose and analyze a dynamical model in which individuals that are affected by one transmissible agent $A$ exhibit a higher than baseline propensity of being affected by a second agent $B$ and vice versa. The model is a natural extension of the traditional SIS (Susceptible-Infected-Susceptible) model used for modeling single contagion processes. We show that cooperativity changes the dynamics of the system considerably when cooperativity is strong. The system exhibits discontinuous phase transitions not observed in single agent contagion, multi-stability, a separation of the traditional epidemic threshold into different thresholds for inception and extinction as well as hysteresis. These properties are robust and are corroborated by stochastic simulations on lattices and generic network topologies. Finally, we investigate wave propagation and transients in a spatially extended version of the model and show that especially for intermediate values of baseline reproduction ratios the system is characterized by various types of wave-front speeds. The system can exhibit spatially heterogeneous stationary states for some parameters and negative front speeds (receding wave fronts). The two agent model can be employed as a starting point for more complex contagion processes, involving several interacting agents, a model framework particularly suitable for modeling the spread and dynamics of microbiological ecosystems in host populations.

physics.soc-ph↗
arXiv2017

Sparse Algorithm for Robust LSSVM in Primal Space

As enjoying the closed form solution, least squares support vector machine (LSSVM) has been widely used for classification and regression problems having the comparable performance with other types of SVMs. However, LSSVM has two drawbacks: sensitive to outliers and lacking sparseness. Robust LSSVM (R-LSSVM) overcomes the first partly via nonconvex truncated loss function, but the current algorithms for R-LSSVM with the dense solution are faced with the second drawback and are inefficient for training large-scale problems. In this paper, we interpret the robustness of R-LSSVM from a re-weighted viewpoint and give a primal R-LSSVM by the representer theorem. The new model may have sparse solution if the corresponding kernel matrix has low rank. Then approximating the kernel matrix by a low-rank matrix and smoothing the loss function by entropy penalty function, we propose a convergent sparse R-LSSVM (SR-LSSVM) algorithm to achieve the sparse solution of primal R-LSSVM, which overcomes two drawbacks of LSSVM simultaneously. The proposed algorithm has lower complexity than the existing algorithms and is very efficient for training large-scale problems. Many experimental results illustrate that SR-LSSVM can achieve better or comparable performance with less training time than related algorithms, especially for training large scale problems.

cs.LG↗
arXiv2017

The Jain-2/5 parent Hamiltonian: structure of zero modes, dominance patterns, and zero mode generators

We analyze general zero mode properties of the parent Hamiltonian of the unprojected Jain-2/5 state. We characterize the zero mode condition associated to this Hamiltonian via projection onto a four-dimensional two-particle subspace for given pair angular momentum, for the disk and similarly for the spherical geometry. Earlier numerical claims in the literature about ground state uniqueness on the sphere are substantiated on analytic grounds, and related results are derived. Preference is given to second quantized methods, where zero mode properties are derived not from given analytic wave functions, but from a "lattice" Hamiltonian and associated zero mode conditions. This method reveals new insights into the guiding-center structure of the unprojected Jain-2/5 state, in particular a system of dominance patterns following a "generalized Pauli principle", which establishes a complete one-to-one correspondence with the edge mode counting. We also identify one-body operators that function as generators of zero modes.

cond-mat.str-el↗
arXiv2017

Wavefronts for a nonlinear nonlocal bistable reaction-diffusion equation in population dynamics

The wavefronts of a nonlinear nonlocal bistable reaction-diffusion equation, \begin{align*} \frac{\partial u}{\partial t}=\frac{\partial^2u}{\partial x^2}+u^2(1-J_σ*u)-du,\quad(t,x)\in(0,\infty)\times\mathbb R, \end{align*} with $J_σ(x)=(1/σ)= J(x/σ)$ and $ \int_{\mathbb R} J(x)dx=1 $ are investigated in this article. It is proven that there exists a $c_*(σ)$ such that for all $c\geq c_*(σ)$, a monotone wavefront $(c,ω)$ can be connected by the two positive equilibrium points. On the other hand, there exists a $c^*(σ)$ such that the model admits a semi-wavefront $(c^*(σ),ω)$ with $ω(-\infty)=0$. Furthermore, it is shown that for sufficiently small $σ$, the semi-wavefronts are in fact wavefronts connecting $0$ to the largest equilibrium. In addition, the wavefronts converge to those of the local problem as $σ\to0$.

math.AP↗
arXiv2017

On Abrikosov Lattice Solutions of the Ginzburg-Landau Equations

We prove existence of Abrikosov vortex lattice solutions of the Ginzburg-Landau equations of superconductivity, with multiple magnetic flux quanta per a fundamental cell. We also revisit the existence proof for the Abrikosov vortex lattices, streamlining some arguments and providing some essential details missing in earlier proofs for a single magnetic flux quantum per a fundamental cell.

math-ph↗
arXiv2017

A global study of Type B quasi-periodic oscillation in black hole X-ray binaries

We performed a global study on the timing and spectral properties of type-B quasi-periodic oscillations (QPOs) in the outbursts of black hole X-ray binaries. The sample is built based on the observations of {\it Rossi X-ray Timing Explorer}, via searching in the literature in RXTE era for all the identified type-B QPOs. To enlarge the sample, we also investigated some type-B QPOs that are reported but not yet fully identified. Regarding to the time lag and hard/soft flux ratio, we found that the sources with type-B QPOs behave in two subgroups. In one subgroup, type-B QPO shows a hard time lag that firstly decreases and then reverse into a soft time lag along with softening of the energy spectrum. In the other subgroup, type-B QPOs distribute only in a small region with hard time lag and relatively soft hardness. These findings may be understood with a diversity of the homogeneity showing up for the hot inner flow of different sources. We confirm the universality of a positive relation between the type-B QPO frequency and the hard component luminosity in different sources. We explain the results by considering that the type-B QPO photons are produced in the inner accretion flow around the central black hole, under a local Eddington limit. Using this relationship, we derived an mass estimation of $9.3-27.1$ $\rm{M_{\odot}}$ for the black hole in H 1743-322.

astro-ph.HE↗
arXiv2016

Non-parametric inverse curvature flows in the AdS-Schwarzschild manifold

We consider the inverse curvature flows in the anti-de Sitter-Schwarzschild manifold with star-shaped initial hypersurface, driven by the 1-homogeneous curvature function. We show that the solutions exist for all time and the principle curvatures of the hypersurface converges to 1 exponentially fast.

math.DG↗
arXiv2016

Mean Field Limit and Propagation of Chaos for a Pedestrian Flow Model

In this paper a rigorous proof of the mean field limit for a pedestrian flow model in two dimensions is given by using a probabilistic method. The model under investigation is an interacting particle system coupled to the eikonal equation on the microscopic scale. For stochastic initial data, it is proved that the solution of the $N$-particle pedestrian flow system with properly chosen cut-off converges in the probability sense to the solution of the characteristics of the non-cut-off Vlasov equation. Furthermore, the result on propagation of chaos is also deduced in terms of bounded Lipschitz distance.

math.AP↗