Results for "Difan Zou"

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An Improved Analysis of Training Over-parameterized Deep Neural NetworksJun 11 2019A recent line of research has shown that gradient-based algorithms with random initialization can converge to the global minima of the training loss for over-parameterized (i.e., sufficiently wide) deep neural networks. However, the condition on the width ... More
Signal Detection under Short-Interval Sampling of Continuous Waveforms for Optical Wireless Scattering CommunicationDec 13 2016In optical wireless scattering communication, received signal in each symbol interval is captured by a photomultiplier tube (PMT) and then sampled through very short but finite interval sampling. The resulting samples form a signal vector for symbol detection. ... More
Stochastic Variance-Reduced Hamilton Monte Carlo MethodsFeb 13 2018We propose a fast stochastic Hamilton Monte Carlo (HMC) method, for sampling from a smooth and strongly log-concave distribution. At the core of our proposed method is a variance reduction technique inspired by the recent advance in stochastic optimization. ... More
Two Dimension Intensity Distribution of Ultraviolet Scattering CommunicationApr 07 2019Consider a ultraviolet (UV) scattering communication system where the position of the transmitter is fixed and the receiver can move around on the ground. To obtain the link gain effectively and economically, we propose an algorithm based on one-dimensional ... More
Saving Gradient and Negative Curvature Computations: Finding Local Minima More EfficientlyDec 11 2017We propose a family of nonconvex optimization algorithms that are able to save gradient and negative curvature computations to a large extent, and are guaranteed to find an approximate local minimum with improved runtime complexity. At the core of our ... More
Characterization on Practical Photon Counting Receiver in Optical Scattering CommunicationFeb 22 2017Mar 13 2017We characterize the practical photon-counting receiver in optical scattering communication with finite sampling rate and electrical noise. In the receiver side, the detected signal can be characterized as a series of pulses generated by photon-multiplier ... More
Global Convergence of Langevin Dynamics Based Algorithms for Nonconvex OptimizationJul 20 2017Feb 19 2018We present a unified framework to analyze the global convergence of Langevin dynamics based algorithms for nonconvex finite-sum optimization with $n$ component functions. At the core of our analysis is a direct analysis of the ergodicity of the numerical ... More
Stochastic Gradient Descent Optimizes Over-parameterized Deep ReLU NetworksNov 21 2018Dec 27 2018We study the problem of training deep neural networks with Rectified Linear Unit (ReLU) activation function using gradient descent and stochastic gradient descent. In particular, we study the binary classification problem and show that for a broad family ... More
A 1Mbps Real-time NLOS UV Scattering Communication System with Receiver Diversity over 1kmFeb 12 2018In the non-line of sight (NLOS) ultraviolet (UV) scattering communication, the received signals exhibit the characteristics of discrete photoelectrons due to the extremely large path loss. We design and demonstrate an NLOS UV scattering communication ... More
The magnetocaloric and barocaloric effects in Gd5Si2Ge2 compoundDec 09 2010Oct 10 2011The caloric effect in Gd5Si2Ge2 compound is studied experimentally and theoretically. The first-order phase transition is sensitive to both magnetic field and pressure. It indicates that the influences of magnetic field and pressure on the phase transition ... More
Quantum information processing and multi-qubit entanglement with Josephson-junction charge qubits in a thermal cavityJun 10 2003We propose a scheme to implement the two-qubit quantum phase gate with Josephson-junction charge qubits in a thermal cavity. In this scheme, the photon-number-dependent parts in the time evolution operator are canceled at the special time. Thus the scheme ... More
Intelligent Interference Exploitation for Heterogeneous Cellular Networks against EavesdroppingOct 29 2017Jul 24 2018This paper explores the co-existence of a macro cell and a small cell for heterogeneous cellular networks, where a macro base station (MBS) and small base station (SBS) transmit to respective macro user (MU) and small user (SU) through their shared spectrum ... More
Bulk characterization of topological crystalline insulators: stability under interactions and relations to symmetry enriched U(1) quantum spin liquidsNov 08 2017Jan 16 2018Topological crystalline insulators (TCIs) are nontrivial quantum phases of matter protected by crystalline (and other) symmetries. They are originally predicted by band theories, so an important question is their stability under interactions. In this ... More
Entanglement of three cavity fields via resonant interactions with dressed three-level atomsNov 09 2013In this paper we show that three cavity fields can be entangled when they are tuned on resonance with an ensemble of dressed three-level atoms. The master equation for the three cavity modes is derived by using atomic dressed states and the inseparability ... More
A Rational Model of Large-Scale Motion in TurbulenceMay 30 2011A rational theory is proposed to describe the large-scale motion in turbulence. The fluid element with inner orientational structures is proposed to be the building block of fluid dynamics. The variance of the orientational structures then constitutes ... More
Non-Abrikosov vortices in liquid metallic hydrogenJul 05 2013We consider non-Abrikosov vortex solutions in liquid metallic hydrogen (LMH) in the framework of two-component Ginzburg-Landau model. We have shown that there are three types of non-Abrikosov vortices depending on chosen boundary conditions at the core ... More
On the Morse--Novikov Cohomology of blowing up complex manifoldsJul 31 2019Inspired by the recent works of S. Rao--S. Yang--X.-D. Yang and L. Meng on the blow-up formulae for de Rham and Morse--Novikov cohomology groups, we give a new simple proof of the blow-up formula for Morse--Novikov cohomology by introducing the relative ... More
Physical-Layer Security for Spectrum Sharing SystemsDec 20 2016Dec 22 2016In this paper, we examine the physical-layer security for a spectrum sharing system consisting of multiple source-destination pairs, which dynamically access their shared spectrum for data transmissions in the presence of an eavesdropper. We propose a ... More
A Deep, Forgetful Novelty-Seeking Movie Recommender ModelSep 02 2019As more and more people shift their movie watching online, competition between movie viewing websites are getting more and more intense. Therefore, it has become incredibly important to accurately predict a given user's watching list to maximize the chances ... More
The complex Monge-Ampére equation on the complement of a divisorMar 28 2018We consider the complex Monge-Amp\'{e}re equation on complete K\"{a}hler manifolds with cusp singularity along a divisor when the right hand side $F$ has rather weak regularity. We proved that when the right hand side $F$ is in some \emph{weighted} $W^{1,p_0}$ ... More
An upper bound on distance degenerate handle additionsJul 17 2017We prove that for any distance at least 3 Heegaard splitting and a boundary component $F$, there is a diameter finite ball in the curve complex $\mathcal {C}(F)$ so that it contains all distance degenerate curves or slopes in $F$.
A Sublinear Algorithm of Sparse Fourier Transform for Nonequispaced DataFeb 16 2005We present a sublinear randomized algorithm to compute a sparse Fourier transform for nonequispaced data. Suppose a signal S is known to consist of N equispaced samples, of which only L<N are available. If the ratio p=L/N is not close to 1, the available ... More
The Five Elements of Th1-Th2 SystemMar 18 2008The T helper (Th) phenotypes, Th1/Th2, are acquired upon interaction of a naive T helper cell and an antigen presenting cell (APC). Naive T helper cells may differentiate into either phenotype, and the actual outcome is determined by the density and avidity ... More
Comparison of SVM and Spectral Embedding in Promoter Biobricks' Categorizing and ClusteringFeb 15 2019Feb 18 2019Background: In organisms' genomes, promoters are short DNA sequences on the upstream of structural genes, with the function of controlling genes' transcription. Promoters can be roughly divided into two classes: constitutive promoters and inducible promoters. ... More
Reconstructing fluid dynamics with micro-finite elementAug 21 2017In the theory of the Navier-Stokes equations, the viscous fluid in incompressible flow is modelled as a homogeneous and dense assemblage of constituent "fluid particles" with viscous stress proportional to rate of strain. The crucial concept of fluid ... More
Global Entropy Solutions to Multi-Dimensional Isentropic Gas Dynamics with Spherical SymmetryNov 13 2017Jul 24 2018We are concerned with spherically symmetric solutions to the Euler equations for the multi-dimensional compressible fluids, which have many applications in diverse real physical situations. The system can be reduced to one dimensional isentropic gas dynamics ... More
Global Entropy Solutions to the Gas Flow in General NozzleMar 10 2019Aug 17 2019We are concerned with the global existence of entropy solutions for the compressible Euler equations describing the gas flow in a nozzle with general cross-sectional area, for both isentropic and isothermal fluids. New viscosities are delicately designed ... More
Optimal Investment with Transaction Costs under Cumulative Prospect Theory in Discrete TimeNov 15 2015We study optimal investment problems with transaction costs under Kahneman and Tversky's cumulative prospective theory (CPT). A CPT investor makes investment decisions in a single-period discrete time financial market consisting of one risk-free asset ... More
Five-quark components in baryonsJan 07 2010Evidence has been accumulating for the existence of significant intrinsic non-perturbative five-quark components in various baryons. The inclusion of the five-quark components gives a natural explanation of the excess of $\bar d$ over $\bar u$, significant ... More
Multi-quark components in baryonsSep 30 2005A brief review on some recent progresses in our understanding of multi-quark components in baryons is presented. The multi-quark components in baryons seem to be mainly in colored quark cluster configurations rather than in ``meson cloud'' configurations ... More
Light Hadron Spectroscopy at BEPCNov 14 2000The $J/\Psi$ and $\Psi'$ experiments at the Beijing Electron Positron Collider (BEPC) play a unique role in many aspects of light hadron spectroscopy, such as hunting for glueballs and hybrids, extracting $u\bar u+d\bar d$ and $s\bar s$ components of ... More
Okubo-Zweig-Iizuka Rule Violation and Possible ExplanationsNov 05 1996Violations of the Okubo-Zweig-Iizuka (OZI) rule in $s\bar s <-> n\bar n = 1/2 (u\bar u + d\bar d)$ mixing and $\phi$ production from nucleon-antinucleon annihilation are reviewed. Possible explanations are examined. We conclude that the two-step hadronic ... More
How much does your data exploration overfit? Controlling bias via information usageNov 16 2015Oct 06 2016Modern data is messy and high-dimensional, and it is often not clear a priori what are the right questions to ask. Instead, the analyst typically needs to use the data to search for interesting analyses to perform and hypotheses to test. This is an adaptive ... More
Stochastic EM for Shuffled Linear RegressionApr 02 2018We consider the problem of inference in a linear regression model in which the relative ordering of the input features and output labels is not known. Such datasets naturally arise from experiments in which the samples are shuffled or permuted during ... More
On Isolated Singularities of Fractional Semi-Linear Elliptic EquationsApr 03 2018In this paper, we study the local behavior of nonnegative solutions of fractional semi-linear equations $(-\Delta)^\sigma u = u^p$ with an isolated singularity, where $\sg \in (0, 1)$ and $\frac{n}{n-2\sg} < p < \frac{n+2\sg}{n-2\sg}$. We first use blow ... More
Positive Least Energy Solutions and Phase Separation for Coupled Schrodinger Equations with Critical Exponent: Higher Dimensional CaseSep 12 2012Aug 15 2013We study the following nonlinear Schr\"{o}dinger system which is related to Bose-Einstein condensate: {displaymath} {cases}-\Delta u +\la_1 u = \mu_1 u^{2^\ast-1}+\beta u^{\frac{2^\ast}{2}-1}v^{\frac{2^\ast}{2}}, \quad x\in \Omega, -\Delta v +\la_2 v ... More
Charmless $B \to PV, VV $ decays and new physics effects in the mSUGRA modelJul 11 2005Oct 24 2005By employing the QCD factorization approach, we calculate the new physics contributions to the branching radios of the two-body charmless $ B \to PV$ and $B \to VV$ decays in the framework of the minimal supergravity (mSUGRA) model. we choose three typical ... More
Transport in gapped bilayer graphene: the role of potential fluctuationsAug 04 2010We employ a dual-gated geometry to control the band gap \Delta in bilayer graphene and study the temperature dependence of the resistance at the charge neutrality point, RNP(T), from 220 to 1.5 K. Above 5 K, RNP(T) is dominated by two thermally activated ... More
Stochastic Kriging for Inadequate Simulation ModelsFeb 02 2018Feb 13 2018Stochastic kriging is a popular metamodeling technique for representing the unknown response surface of a simulation model. However, the simulation model may be inadequate in the sense that there may be a non-negligible discrepancy between it and the ... More
Hall Resistivity in Ferromagnetic Manganese-Oxide CompoundsJun 05 1996Temperature-dependence and magnetic field-dependence of the Hall effect and the magnetic property in manganese-oxide thin films are studied. The spontaneous magnetization and the Hall resistivity are obtained for a various of magnetic fields over all ... More
Quantum Hydrodynamics of VorticityAug 27 2019We formulate a quantum theory of vorticity (hydro)dynamics on a general two-dimensional bosonic lattice. In the classical limit of a bosonic condensate, it reduces to conserved plasma-like vortex-antivortex dynamics. The nonlocal topological character ... More
Sampling of surfaces and functions in high dimensional spacesMar 03 2019We introduce a sampling theoretic framework for the recovery of smooth surfaces and functions living on smooth surfaces from few samples. The proposed approach can be thought of as a nonlinear generalization of union of subspace models widely used in ... More
CoCoLasso for High-dimensional Error-in-variables RegressionOct 24 2015Jan 01 2016Much theoretical and applied work has been devoted to high-dimensional regression with clean data. However, we often face corrupted data in many applications where missing data and measurement errors cannot be ignored. Loh and Wainwright (2012) proposed ... More
Rejoinder: One-step sparse estimates in nonconcave penalized likelihood modelsAug 07 2008We would like to take this opportunity to thank the discussants for their thoughtful comments and encouragements on our work [arXiv:0808.1012]. The discussants raised a number of issues from theoretical as well as computational perspectives. Our rejoinder ... More
Joint Detection and Location of English PunsAug 31 2019A pun is a form of wordplay for an intended humorous or rhetorical effect, where a word suggests two or more meanings by exploiting polysemy (homographic pun) or phonological similarity to another word (heterographic pun). This paper presents an approach ... More
Indices of Coincidence Isometries of the Hyper Cubic Lattice $Z^n$Aug 29 2006The problem of computing the index of a coincidence isometry of the hyper cubic lattice $\mathbb{Z}^{n}$ is considered. The normal form of a rational orthogonal matrix is analyzed in detail, and explicit formulas for the index of certain coincidence isometries ... More
Learning to Ask: Question-based Sequential Bayesian Product SearchAug 30 2019Product search is generally recognized as the first and foremost stage of online shopping and thus significant for users and retailers of e-commerce. Most of the traditional retrieval methods use some similarity functions to match the user's query and ... More
Composite quantile regression and the oracle Model Selection TheoryJun 18 2008Coefficient estimation and variable selection in multiple linear regression is routinely done in the (penalized) least squares (LS) framework. The concept of model selection oracle introduced by Fan and Li [J. Amer. Statist. Assoc. 96 (2001) 1348--1360] ... More
A Framework towards Quantifying Human Restorativeness in Virtual Built EnvironmentsFeb 14 2019The impact of built environment on the human restorativeness has long been argued; however, the interrelations between neuroscience and the built environment, and the degree to which the built environment contributes to increased human restorativeness ... More
The Impact of Countdown Clocks on Subway Ridership in New York CityDec 26 2018Protecting the passengers' safety and increasing ridership are two never ending pursuits of public transit agencies. One of the proposed methods to achieve both goals for subway service is to implement real time train arriving countdown clocks in subway ... More
Asynchronous Time-Parallel Method based on Laplace TransformSep 03 2019Laplace transform method has proved to be very efficient and easy to parallelize for the solution of time-dependent problems. However, the synchronization delay among processors implies an upper bound on the expectable acceleration factor, which leads ... More
On Elliptic Systems involving critical Hardy-Sobolev exponents (Part II)Apr 12 2015Jul 07 2015This paper is the second part of a work devoted to the study of elliptic systems involving multiple Hardy-Sobolev critical exponents: $$\begin{cases} -\Delta u-\lambda \frac{|u|^{2^*(s_1)-2}u}{|x|^{s_1}}=\kappa\alpha \frac{1}{|x|^{s_2}}|u|^{\alpha-2}u|v|^\beta\quad ... More
On Elliptic Systems involving critical Hardy-Sobolev exponentsApr 04 2015Jul 07 2015Let $\Omega\subset \R^N$ ($N\geq 3$) be an open domain which is not necessarily bounded. By using variational methods, we consider the following elliptic systems involving multiple Hardy-Sobolev critical exponents: $$\begin{cases} -\Delta u-\lambda \frac{|u|^{2^*(s_1)-2}u}{|x|^{s_1}}=\kappa\alpha ... More
On a problem of countable expansionsMar 25 2015Aug 01 2015For a real number $q\in(1,2)$ and $x\in[0,1/(q-1)]$, the infinite sequence $(d_i)$ is called a \emph{$q$-expansion} of $x$ if $$ x=\sum_{i=1}^\infty\frac{d_i}{q^i},\quad d_i\in\{0,1\}\quad\textrm{for all}~ i\ge 1. $$ For $m=1, 2, \cdots$ or $\aleph_0$ ... More
3-manifolding admitting locally large distance 2 Heegaard splittingsSep 17 2015Oct 26 2015From the view of Heegaard splitting, it is known that if a closed orientable 3-manifold admits a distance at least three Heegaard splitting, then it is hyperbolic. However, for a closed orientable 3-manifold admitting only distance at most two Heegaard ... More
Minimizing Close-k Aggregate Loss Improves ClassificationNov 01 2018Nov 03 2018In classification, the de facto method for aggregating individual losses is the average loss. When the actual metric of interest is 0-1 loss, it is common to minimize the average surrogate loss for some well-behaved (e.g. convex) surrogate. Recently, ... More
Global Entropy Solutions to the Gas Flow in general NozzleMar 10 2019We are concerned with the global existence of entropy solutions for the compressible Euler equations describing the gas flow in a nozzle with general cross section area, for both isentropic and isothermal fluids. New viscosities are delicately designed ... More
Nonlinear stability and existence of vortex sheets for inviscid liquid-gas two-phase flowAug 17 2018Jan 01 2019We are concerned with the vortex sheet solutions for the inviscid two-phase flow in two dimensions. In particular, the nonlinear stability and existence of compressible vortex sheet solutions under small perturbations are established by using a modification ... More
Hadron spectroscopy from strangeness to charm and beautyJan 07 2013Quarks of different flavors have different masses, which will cause breaking of flavor symmetries of QCD. Flavor symmetries and their breaking in hadron spectroscopy play important role for understanding the internal structures of hadrons. Hadron spectroscopy ... More
Baryon Resonances Observed at BESFeb 01 2008The $\psi$ decays provide a novel way to explore baryon spectroscopy and baryon structure. The baryon resonances observed from $\psi$ decays at BES are reviewed. The implications and prospects at upgraded BESIII/BEPCII are discussed.
On the nature of the lowest $1/2^-$ baryon nonet and decupletNov 30 2007From recent study of properties of the lowest spin-parity $1/2^-$ baryons, $N^*(1535)$ and $\Delta^*(1620)$, new pictures for the internal structure of the lowest $1/2^-$ baryon octet and decuplet are proposed. While the lowest $1/2^-$ baryon octet may ... More
Complementary studies on $N^*$ from $e^+e^-$, $pp$ and $p\bar p$ collisionsJul 27 2009Aug 05 2009Complementary to the conventional experimental studies on $N^*$ from $\pi N$ and $\gamma^{(*)}N$ reactions, the $e^+e^-$, $pp$ and $p\bar p$ collisions can give novel insights into these $N^*$ resonances. While the $e^+e^-$ collisions through production ... More
Strangeness in the proton and N*(1535)Oct 15 2006The newest progress on the study of the strangeness in the proton and in the lowest negative parity nucleon excited state $N^*(1535)$ is reviewed. Implications on the internal quark structure of the proton, $N^*(1535)$ and other baryons are discussed. ... More
On the Convergence of Weighted AdaGrad with Momentum for Training Deep Neural NetworksAug 10 2018Sep 28 2018Adaptive stochastic gradient descent methods, such as AdaGrad, RMSProp, Adam, AMSGrad, etc., have been demonstrated efficacious in solving non-convex stochastic optimization, such as training deep neural networks. However, their convergence rates have ... More
Existence and symmetry of positive ground states for a doubly critical Schrodinger systemNov 07 2012Mar 31 2014We study the following doubly critical Schr\"{o}dinger system $$-\Delta u -\frac{\la_1}{|x|^2}u=u^{2^\ast-1}+ \nu \al u^{\al-1}v^\bb, \quad x\in \RN, -\Delta v -\frac{\la_2}{|x|^2}v=v^{2^\ast-1} + \nu \bb u^{\al}v^{\bb-1}, \quad x\in \RN, u, v\in D^{1, ... More
Exact Asymptotic Behavior of Singular Positive Solutions of Fractional Semi-Linear Elliptic EquationsMay 10 2018In this paper, we prove the exact asymptotic behavior of singular positive solutions of fractional semi-linear equations $$(-\Delta)^\sigma u = u^p~~~~~~~~in ~~ B_1\backslash \{0\}$$ with an isolated singularity, where $\sigma \in (0, 1)$ and $\frac{n}{n-2\sigma} ... More
Asymptotic behavior of positive singular solutions to fractional Hardy-Hénon equationsMar 31 2019In this paper, we study the asymptotic behavior of positive solutions of fractional Hardy-H\'enon equation $$ (-\Delta)^\sigma u = |x|^\alpha u^p, ~~~~~~~ x \in B_1 \backslash \{0\} $$ with an isolated singularity at the origin, where $\sigma \in (0, ... More
Qualitative analysis for an elliptic system in the punctured spaceNov 17 2018In this paper, we investigate the qualitative properties of positive solutions for the following two-coupled elliptic system in the punctured space: $$ \begin{cases} -\Delta u =\mu_1 u^{2q+1} + \beta u^q v^{q+1} \\ -\Delta v =\mu_2 v^{2q+1} + \beta v^q ... More
Contrastive Variational Autoencoder Enhances Salient FeaturesFeb 12 2019Variational autoencoders are powerful algorithms for identifying dominant latent structure in a single dataset. In many applications, however, we are interested in modeling latent structure and variation that are enriched in a target dataset compared ... More
GPU Accelerated Contactless Human Machine Interface for Driving CarJul 09 2019In this paper we present an original contactless human machine interface for driving car. The proposed framework is based on the image sent by a simple camera device, which is then processed by various computer vision algorithms. These algorithms allow ... More
Linear Process Bootstrap Unit Root TestOct 20 2016One of the most widely applied unit root test, Phillips-Perron test, enjoys in general highpowers, but suffers from size distortions when moving average noise exists. As a remedy, thispaper proposes a nonparametric bootstrap unit root test that specifically ... More
HEGY test under seasonal heterogeneityAug 14 2016Sep 22 2016Both seasonal unit roots and seasonal heterogeneity are common in seasonal data. When testing seasonal unit roots under seasonal heterogeneity, it is unclear if we can apply tests designed for seasonal homogeneous settings, for example the non-periodic ... More
A Note on Chern-Yamabe ProblemApr 08 2019We propose a flow to study the Chern-Yamabe problem and discuss the long time existence of the flow. In the balanced case we show that the Chern-Yamabe problem is the Euler-Lagrange equation of some functional. The monotonicity of the functional along ... More
On the Very-well-poised Bilateral Basic Hypergeometric $_5ψ_5$ SeriesJan 09 2016Mar 29 2016In this paper, we prove several transformation formulas for the very-well-poised bilateral basic hypergeometric $_5\psi_5$ series by using the relationship between the bilateral basic hypergeometric $_5\psi_5$ series and basic hypergeometric $_8\phi_7$ ... More
Analysis and boundary condition of the lattice Boltzmann BGK model with two velocity componentsJul 22 1995In this paper, we study the two dimensional lattice Boltzmann BGK model (LBGK) by analytically solving a simple flow in a 2~-D channel. The flow is driven by the movement of upper boundary with vertical injection fluid at the porous boundaries. The velocity ... More
Complex RG flows for 2D nonlinear O(N) sigma modelsJan 06 2011Mar 25 2011Motivated by recent attempts to find nontrivial infrared fixed points in 4-dimensional lattice gauge theories, we discuss the extension of the renormalization group (RG) transformations to complex coupling spaces for O(N) models on LxL lattices, in the ... More
Inferring Gene Regulatory Network Using An Evolutionary Multi-Objective MethodDec 16 2015Inference of gene regulatory networks (GRNs) based on experimental data is a challenging task in bioinformatics. In this paper, we present a bi-objective minimization model (BoMM) for inference of GRNs, where one objective is the fitting error of derivatives, ... More
On a double-variable inequality and elliptic systems involving critical Hardy-Sobolev exponentsNov 27 2017Let $\Omega\subset \mathbb{R}^N$ ($N\geq 3$) be an open domain which is not necessarily bounded. The sharp constant and extremal functions to the following kind of double-variable inequalities $$ S_{\alpha,\beta,\lambda,\mu}(\Omega) \Big(\int_\Omega \big(\lambda ... More
A nonlinear elliptic PDE with multiple Hardy-Sobolev critical exponents in $\mathbb{R}^N$Apr 05 2015Dec 27 2017In this paper, we will study the following PDE in $\mathbb{R}^N$ involving multiple Hardy-Sobolev critical exponents: $$ \begin{cases} \Delta u+\sum_{i=1}^{l}\lambda_i \frac{u^{2^*(s_i)-1}}{|x|^{s_i}}+u^{2^*-1}=0\;\hbox{in}\;\mathbb{R}^N, u\in D_{0}^{1,2}(\mathbb{R}^N), ... More
On coupled Schrödinger systems with double critical exponents and indefinite weightsMar 31 2015By using variational methods, we study the existence of mountain pass solution to the following doubly critical Schr\"{o}dinger system: $$ \begin{cases} -\Delta u-\mu_1\frac{u}{|x|^2}-|u|^{2^{*}-2}u &=h(x)\alpha|u|^{\alpha-2}|v|^\beta u\quad \rm{in}\; ... More
Quantity Tagger: A Latent-Variable Sequence Labeling Approach to Solving Addition-Subtraction Word ProblemsAug 31 2019An arithmetic word problem typically includes a textual description containing several constant quantities. The key to solving the problem is to reveal the underlying mathematical relations (such as addition and subtraction) among quantities, and then ... More
Dynamics of Boolean NetworksJul 02 2013Boolean networks are special types of finite state time-discrete dynamical systems. A Boolean network can be described by a function from an n-dimensional vector space over the field of two elements to itself. A fundamental problem in studying these dynamical ... More
An Algorithm for Detecting Fixed Points of Boolean NetworksApr 22 2014In the applications of Boolean networks to modeling biological systems, an important computational problem is the detection of the fixed points of these networks. This is an NP-complete problem in general. There have been various attempts to develop algorithms ... More
Characterization of Boolean Networks with Single or Bistable StatesJul 02 2013Many biological systems, such as metabolic pathways, exhibit bistability behavior: these biological systems exhibit two distinct stable states with switching between the two stable states controlled by certain conditions. Since understanding bistability ... More
Gaussian binomials and the number of sublatticesOct 23 2006The purpose of this short communication is to make some observations on the connections between various existing formulas of counting the number of sublattices of a fixed index in an $n$-dimensional lattice and their connection with the Gaussian binomials. ... More
Optimal Investment and Risk Control Problem for an Insurer: Expected Utility MaximizationFeb 14 2014Mar 07 2014Motivated by the AIG bailout case in the financial crisis of 2007-2008, we consider an insurer who wants to maximize the expected utility of the terminal wealth by selecting optimal investment and risk control strategies. The insurer's risk process is ... More
Spectral responses in granular compactionNov 06 2009The slow compaction of a gently tapped granular packing is reminiscent of the low-temperature dynamics of structural and spin glasses. Here, I probe the dynamical spectrum of granular compaction by measuring a complex (frequency-dependent) volumetric ... More
Instance Influence Estimation for Hyperspectral Target Signature Characterization using Extended Functions of Multiple InstancesMar 21 2016The Extended Functions of Multiple Instances (eFUMI) algorithm is a generalization of Multiple Instance Learning (MIL). In eFUMI, only bag level (i.e. set level) labels are needed to estimate target signatures from mixed data. The training bags in eFUMI ... More
Regularized rank-based estimation of high-dimensional nonparanormal graphical modelsFeb 13 2013A sparse precision matrix can be directly translated into a sparse Gaussian graphical model under the assumption that the data follow a joint normal distribution. This neat property makes high-dimensional precision matrix estimation very appealing in ... More
Convergence of an Adaptive Finite Element Method for Distributed Flux ReconstructionSep 09 2013We shall establish the convergence of an adaptive conforming finite element method for the reconstruction of the distributed flux in a diffusion system. The adaptive method is based on a posteriori error estimators for the distributed flux, state and ... More
SURE Information Criteria for Large Covariance Matrix Estimation and Their Asymptotic PropertiesJun 25 2014Mar 04 2016Consider $n$ independent and identically distributed $p$-dimensional Gaussian random vectors with covariance matrix $\Sigma.$ The problem of estimating $\Sigma$ when $p$ is much larger than $n$ has received a lot of attention in recent years. Yet little ... More
Phase Retrieval using Lipschitz Continuous MapsMar 10 2014In this note we prove that reconstruction from magnitudes of frame coefficients (the so called "phase retrieval problem") can be performed using Lipschitz continuous maps. Specifically we show that when the nonlinear analysis map $\alpha:{\mathcal H}\rightarrow\mathbb{R}^m$ ... More
Orlicz-Legendre EllipsoidsAug 24 2014The Orlicz-Legendre ellipsoids, which are in the framework of emerging dual Orlicz Brunn-Minkowski theory, are introduced for the first time. They are in some sense dual to the recently found Orlicz-John ellipsoids, and have largely generalized the classical ... More
Emergence of conformal symmetry in quantum spin chains: anti-periodic boundary conditions and supersymmetryJul 24 2019Universal properties of a critical quantum spin chain are encoded in the underlying conformal field theory (CFT). This underlying CFT is fully characterized by its conformal data. We propose a method to extract the conformal data from a critical quantum ... More
Local Lipschitz Stability for Inverse Robin Problems in Elliptic and Parabolic SystemsMar 08 2016In this work, we shall study the nonlinear inverse problems of recovering the Robin coefficients in elliptic and parabolic systems of second order, and establish their local Lipschitz stabilities. Some local Lipschitz stability was derived for an elliptic ... More
N*, Lambda*, Sigma* and Xi* Resonances from J/Psi and Psi' DecaysJun 04 2000Vector charmonium states $J/\Psi$ and $\Psi'$ are copiously produced by $e^+e^-$ annihilations at the Beijing Electron Positron Collider (BEPC). Their decays provide an excellent place for studying excited nucleons and hyperons -- $N^*$, $\Lambda^*$, ... More
Search for Glueballs from Three-body Annihilation of Antiproton-Proton in-FlightDec 04 1998Lattice QCD and other theoretical models predict that the 0(-+), 2(++) and 2(-+) glueballs have masses in the range of 2.0 to 2.4 GeV. For resonances in such an energy range, three-body decay modes are expected to be large. The strategy for looking for ... More
pi-pi S-Wave Interaction and 0++ ParticlesNov 05 1996From a re-analysis of pi+ pi- -> pi+ pi- and pi+ pi- -> K K data, we found for pi-pi S-wave interaction below 2 GeV, sigma(400), f0(980), f0(1500) and f0(1780) clearly show up. f0(1370) can be included with a very small branching ratio to pi-pi. f0(1300) ... More
Perspectival Knowledge in PSOA RuleML: Representation, Model Theory, and TranslationDec 07 2017May 02 2018In Positional-Slotted Object-Applicative (PSOA) RuleML, a predicate application (atom) can have an Object IDentifier (OID) and descriptors that may be positional arguments (tuples) or attribute-value pairs (slots). PSOA RuleML 1.0 specifies for each descriptor ... More