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Generative Hybrid Representations for Activity Forecasting with No-Regret LearningApr 12 2019Automatically reasoning about future human behaviors is a difficult problem with significant practical applications to assistive systems. Part of this difficulty stems from learning systems' inability to represent all kinds of behaviors. Some behaviors, ... More

Stochastic Perron for stochastic target gamesAug 28 2014Apr 06 2016We extend the stochastic Perron method to analyze the framework of stochastic target games, in which one player tries to find a strategy such that the state process almost surely reaches a given target no matter which action is chosen by the other player. ... More

Stochastic Perron for Stochastic Target ProblemsApr 13 2016May 17 2016In this paper, we adapt stochastic Perron's method to analyze a stochastic target problem with unbounded controls in a jump diffusion set-up. With this method, we construct a viscosity sub-solution and super-solution to the associated Hamiltonian-Jacobi-Bellman ... More

On the controller-stopper problems with controlled jumpsSep 13 2016We analyze the continuous time zero-sum and cooperative controller-stopper games of Karatzas and Sudderth [Annals of Probability, 2001], Karatzas and Zamfirescu [Annals of Probability, 2008] and Karatzas and Zamfirescu [Applied Mathematics and Optimization, ... More

On the controller-stopper problems with controlled jumpsSep 13 2016Oct 03 2016We analyze the continuous time zero-sum and cooperative controller-stopper games of Karatzas and Sudderth [Annals of Probability, 2001], Karatzas and Zamfirescu [Annals of Probability, 2008] and Karatzas and Zamfirescu [Applied Mathematics and Optimization, ... More

A description of transverse momentum distributions in p+p collisions at RHIC and LHC energiesNov 05 2018It has long been debated whether the hydrodynamics is suitable for the smaller colliding systems such as p+p collisions. In this paper, by assuming the existence of longitudinal collective motion and long-range interactions in the hot and dense matter ... More

Generation of Synthetic Electronic Medical Record TextDec 06 2018Machine learning (ML) and Natural Language Processing (NLP) have achieved remarkable success in many fields and have brought new opportunities and high expectation in the analyses of medical data. The most common type of medical data is the massive free-text ... More

Energy-efficient Amortized Inference with Cascaded Deep ClassifiersOct 10 2017Deep neural networks have been remarkable successful in various AI tasks but often cast high computation and energy cost for energy-constrained applications such as mobile sensing. We address this problem by proposing a novel framework that optimizes ... More

Asynchronous Decentralized Optimization in Directed NetworksJan 24 2019A popular asynchronous protocol for decentralized optimization is randomized gossip where a pair of neighbors concurrently update via pairwise averaging. In practice, this creates deadlocks and is vulnerable to information delays. It can also be problematic ... More

Superstructure evolution of tellurium atoms on Au(111) surface at different coveragesMay 03 2017We systematically investigated the superstructure evolution of Te atoms on Au(111) substrate at different coverages. As revealed by low temperature scanning tunneling microscopy and spectroscopy, Te atoms form one-dimensional root3 R30{\deg} chains near ... More

Epitaxial Growth and Band Structure of Te Film on GrapheneMar 21 2017Tellurium (Te) films with monolayer and few-layer thickness are obtained by molecular beam epitaxy on a graphene/6H-SiC(0001) substrate and investigated by in situ scanning tunneling microscopy and spectroscopy (STM/STS). We reveal that the Te films are ... More

Large Magnetic Anisotropy of an Iron-Porphyrin Complex on Metal SubstrateJul 18 2017Single magnetic atoms or molecules with large single-ion magnetic anisotropy are highly desired for future applications in high-density data storage and quantum computation. Here we have synthesized an Fe-porphyrin complex on Au(111) substrate in a controlled ... More

Representing Sentences as Low-Rank SubspacesApr 18 2017Sentences are important semantic units of natural language. A generic, distributional representation of sentences that can capture the latent semantics is beneficial to multiple downstream applications. We observe a simple geometry of sentences -- the ... More

Long-time dynamics of resonant weakly nonlinear CGL equationsJul 04 2014Consider a weakly nonlinear CGL equation on the torus~$\mathbb{T}^d$: \[u_t+i\Delta u=\epsilon [\mu(-1)^{m-1}\Delta^{m} u+b|u|^{2p}u+ ic|u|^{2q}u].\eqno{(*)}\] Here $u=u(t,x)$, $x\in\mathbb{T}^d$, $0<\epsilon<<1$, $\mu\geqslant0$, $b,c\in\mathbb{R}$ and ... More

An averaging theorem for nonlinear Schrödinger equations with small nonlinearitiesDec 03 2013Consider nonlinear Schr\"odinger equations with small nonlinearities \[\frac{d}{dt}u+i(-\triangle u+V(x)u)=\epsilon \mathcal{P}(\triangle u,u,x),\quad x\in \mathbb{T}^d.\eqno{(*)}\] Let $\{\zeta_1(x),\zeta_2(x),\dots\}$ be the $L_2$-basis formed by eigenfunctions ... More

Flattenings and Koszul Young flattenings arising in complexity theoryOct 03 2015Jun 03 2016I find new equations for Chow varieties, their secant varieties, and an additional variety that arises in the study of depth 5 circuits by flattenings and Koszul Young flattenings. This enables a new lower bound for symmetric border rank of $x_1x_2\cdots ... More

Important Notes on Lyapunov ExponentsJan 14 2014It is shown that the famous Lyapunov exponents cannot be used as the numerical characteristic for distinguishing different kinds of attractors, such as the equilibrium point, the limit closed curve, the stable torus and the strange attractor.

Geometry of PolysemyOct 24 2016Vector representations of words have heralded a transformational approach to classical problems in NLP; the most popular example is word2vec. However, a single vector does not suffice to model the polysemous nature of many (frequent) words, i.e., words ... More

On the energy equality for solutions to Newtonian and non-Newtonian fluidsJan 08 2019We are concerned with the energy equality for weak solutions to Newtonian and non-Newtonian incompressible fluids. In particular, the results obtained for non-Newtonian fluids, after restriction to the Newtonian case, equal or improve the known results. ... More

Accelerated Nonparametric Maximum Likelihood Density Deconvolution Using Bernstein PolynomialJan 24 2016A new method for deconvoluting density in measurement error models using the Bernstein type polynomial model which is actually a finite mixture of specific beta distributions is proposed and studied. The change-point detection method is used to choose ... More

The Dirichlet problem for fully nonlinear elliptic equations on Riemannian manifoldsMar 10 2014We study a class of fully nonlinear elliptic equations on Riemannian manifolds and solve the Dirichlet problem in a domain with no geometric restrictions to the boundary under essentially optimal structure conditions. It includes a new (and optimal) result ... More

Critical phenomena in one dimension from a Bethe ansatz perspectiveAug 20 2014Aug 31 2014This article briefly reviews recent theoretical developments in quantum critical phenomena in one-dimensional (1D) integrable quantum gases of cold atoms. We present a discussion on quantum phase transitions, universal thermodynamics, scaling functions ... More

Probing semiconductor quantum dot state and manipulation with superconducting transmission line resonatorDec 08 2013A coupled system of a superconducting transmission line resonator with a semiconductor double quantum dot is analyzed. We simulate the phase shift of the microwave signal in the resonator, which is sensitive to the quantum dot qubit state and manipulation. ... More

Equations for secant varieties of Chow varietiesFeb 13 2016Apr 24 2016The Chow variety of polynomials that decompose as a product of linear forms has been studied for more than 100 years. Finding equations in the ideal of secant varieties of Chow varieties would enable one to measure the complexity the permanent to prove ... More

Test Error Estimation after Model Selection Using Validation ErrorJan 09 2018Feb 11 2018When performing supervised learning with the model selected using validation error from sample splitting and cross validation, the minimum value of the validation error can be biased downward. We propose two simple methods that use the errors produced ... More

Bernstein Polynomial Model for Grouped Continuous DataJun 21 2015Jul 18 2015Grouped data are commonly encountered in applications. The Bernstein polynomial model is proposed as an approximate model in this paper for estimating a univariate density function based on grouped data. The coefficients of the Bernstein polynomial, as ... More

Cadlag curves of SLE driven by Levy processesMay 16 2007Sep 05 2008Schramm Loewner Evolutions (SLE) are random increasing hulls defined through the Loewner equation driven by Brownian motion. It is known that the increasing hulls are generated by continuous curves. When the driving process is of the form \sqrt{\kappa} ... More

Boundary Harnack inequalities for regional fractional LaplacianMay 11 2007Jul 17 2009We consider boundary Harnack inequalities for regional fractional Laplacian which are generators of censored stable-like processes on G taking \kappa(x,y)/|x-y|^{n+\alpha}dxdy, x,y\in G as the jumping measure. When G is a C^{1,\beta-1} open set, 1<\alpha<\beta\leq ... More

Accelerated Nonparametric Maximum Likelihood Density Deconvolution Using Bernstein PolynomialJan 24 2016Jan 26 2018A new maximum likelihood method for deconvoluting a continuous density with a positive lower bound on a known compact support in additive measurement error models with known error distribution using the approximate Bernstein type polynomial model, a finite ... More

The Gaussian Correlation Inequality for Symmetric Convex SetsDec 03 2010Mar 02 2013The paper is to prove the Gaussian correlation conjecture stating that, under the standard Gaussian measure, the measure of the intersection of any two symmetric convex sets is greater than or equal to the product of their measures. Characterization of ... More

Extremal function of intrinsic normsOct 12 2004Through the study of the degenerate complex Monge-Amp\`ere equation, we establish the optimal regularity of the extremal function associated to intrinsic norms of Chern-Levine-Nirenberg and Bedford-Taylor. We prove a conjecture of Chern-Levine-Nirenberg ... More

Superconducting transition of FeSe/SrTiO3 induced by adsorption of semiconducting organic moleculesMar 22 2017We prepared superconducting and non-superconducting FeSe films on SrTiO3(001) substrates (FeSe/STO) and investigated the superconducting transition induced by charge transfer between organic molecules and FeSe layers by low temperature scanning tunneling ... More

On long time dynamics of perturbed KdV equationsOct 21 2013Dec 06 2013Consider perturbed KdV equations: \[u_t+u_{xxx}-6uu_x=\epsilon f(u(\cdot)),\quad x\in\mathbb{T}=\mathbb{R}/\mathbb{Z},\;\int_{\mathbb{T}}u(x,t)dx=0,\] where the nonlinearity defines analytic operators $u(\cdot)\mapsto f(u(\cdot))$ in sufficiently smooth ... More

Brill's equations as a GL(V)-moduleAug 10 2015Apr 17 2016The Chow variety of polynomials that decompose as a product of linear forms has been studied for more than 100 years. Brill, Gordon and others obtained set-theoretical equations for the Chow variety. In this article, I compute Brill's equations as a GL(V)-module. ... More

Generalized Floquet Exponent, Attractiveness Portrait and Structure Hidden in an AttractorMar 06 2014The generalized Floquet exponent and the attractiveness portrait (or A-portrait for short) of the attractor and of the smallest invariant closed set are suggested to be used for the study of dynamical systems. Based on the A-portrait, some simple structures ... More

Solitary Wave Solutions for the Nonlinear Dirac EquationsDec 12 2008In this paper we prove the existence and local uniqueness of stationary states for the nonlinear Dirac equation \[ i \sum_{j=0}^{3} \ga^j \pd_j \psi - m\psi + F(\bar{\psi}\psi)\psi =0 \] where $ m >0$ and $ F(s) = |s|^{\theta}$ for $ 1\leq \theta < 2.$ ... More

DeepCas: an End-to-end Predictor of Information CascadesNov 16 2016Information cascades, effectively facilitated by most social network platforms, are recognized as a major factor in almost every social success and disaster in these networks. Can cascades be predicted? While many believe that they are inherently unpredictable, ... More

Projective dimension and regularity of powers of edge ideals of vertex-weighted rooted forestsApr 04 2019In this paper we provide some exact formulas for projective dimension and the regularity of powers of edge ideals of vertex-weighted rooted forests. These formulas are functions of the weight of the vertices and the number of edges. We also give some ... More

Effects of Home Resources and School Environment on Eighth-Grade Mathematics Achievement in TaiwanDec 31 2017Over the past decades, researchers have explored the relationship among home resources, school environment, and students' mathematics achievement in a large amount of studies. Many of them suggested that rich home resources for learning were related to ... More

Regularity of powers of edge ideals of vertex-weighted oriented unicyclic graphsApr 04 2019In this paper we provide some exact formulas for the regularity of powers of edge ideals of vertex-weighted oriented cycles and vertex-weighted unicyclic graphs. These formulas are functions of the weight of vertices and the number of edges. We also give ... More

Rasch Analysis of the Mathematics Self Concept QuestionnaireDec 31 2017TIMSS & PIRLS International Study Center is a research center at Boston College that conducts a series of assessments in a number of countries to measure trends in mathematics and science achievement at the fourth and eighth grades. In general, TIMSS ... More

Base Station Switch-off with Mutual Repulsion in 5G Massive MIMO NetworksJun 07 2018When small cells are densely deployed in the fifth generation (5G) cellular networks, switching off a part of base stations (BSs) is a practical approach for saving energy consumption considering the variation of traffic load. The small cell network with ... More

Vehicles to Pedestrians Signal Transmissions Based on Cloud ComputingDec 31 2018Collisions between vehicles and pedestrians usually result in the fatality to the vulnerable road users (VRUs). Thus, new technologies are needed to be developed for protecting the VRUs. Based on the high density of pedestrians and limited computing capability ... More

Global Well-posedness and soliton resolution for the Derivative Nonlinear Schrödinger equationJun 20 2017We study the Derivative Nonlinear Schr\"odinger equation for general initial conditions in weighted Sobolev spaces that can support bright solitons (but excluding spectral singularities). We prove global well-posedness and give a full description of the ... More

Soliton Resolution for the Derivative Nonlinear Schrödinger EquationOct 10 2017Feb 17 2018We study the Derivative Nonlinear Schr\"odinger equation for generic initial data in a weighted Sobolev space that can support bright solitons (but exclude spectral singularities). Drawing on previous well-posedness results, we give a full description ... More

Pseudometrically Constrained Centroidal Voronoi Tessellations: Generating uniform antipodally symmetric points on the unit sphere with a novel acceleration strategy and its applications to Diffusion and 3D radial MRINov 30 2012Purpose: The purpose of this work is to investigate the hypothesis that uniform sampling measurements that are endowed with antipodal symmetry play an important role when the raw data and image data are related through the Fourier relationship as in q-space ... More

Spin structure of harmonically trapped one-dimensional atoms with spin-orbit couplingAug 04 2015We introduce a theoretical approach to determine the spin structure of harmonically trapped atoms with two-body zero-range interactions subject to an equal mixture of Rashba and Dresselhaus spin-orbit coupling created through Raman coupling of atomic ... More

A Microscopic Convexity Principle for Nonlinear Partial Differential EquationsMay 06 2008We establish a microscopic convexity principle for nonlinear elliptic and parabolic partial differential equations in general form.

A fully nonlinear conformal flow on locally conformally flat manifoldsDec 22 2001We study a fully nonlinear flow for conformal metrics. The long-time existence and the sequential convergence of flow are established for locally conformally flat manifolds. As an application, we solve the $\sk$-Yamabe problem for locally conformal flat ... More

The Dirichlet Problem for a Complex Monge-Ampere Type Equation on Hermitian ManifoldsOct 19 2012Jun 28 2013We are concerned with fully nonlinear elliptic equations on complex manifolds and search for technical tools to overcome difficulties in deriving a priori estimates which arise due to the nontrivial torsion and curvature, as well as the general (non-pseudoconvex) ... More

Conformal deformations of the smallest eigenvalue of the Ricci tensorMay 05 2005We consider deformations of metrics in a given conformal class such that the smallest eigenvalue of the Ricci tensor to be a constant. It is related to the notion of minimal volumes in comparison geometry. Such a metric with the smallest eigenvalue of ... More

Interior C2 regularity of convex solutions to prescribing scalar curvature equationsNov 02 2017We establish interior $C^2$ estimates for convex solutions of scalar curvature equation and $\sigma_2$-Hessian equation. We also prove interior curvature estimate for isometrically immersed hypersurfaces $(M^n,g)\subset \mathbb R^{n+1}$ with positive ... More

Weighted badly approximable vectors and gamesSep 27 2015Jan 11 2017We prove that the set of (r_1,r_2,..,r_{d})-badly approximable vectors is a winning set if r_1=r_2=...=r_{d-1}\geq r_{d}.

Super-Tonks-Girardeau gas of spin-1/2 interacting fermionsMay 04 2010Oct 20 2010Fermi gases confined in tight one-dimensional waveguides form two-particle bound states of atoms in the presence of a strongly attractive interaction. Based on the exact solution of the one-dimensional spin-1/2 interacting Fermi gas, we demonstrate that ... More

Hausdorff dimension of divergent trajectories on homogeneous spaceMay 18 2018For one parameter subgroup action on a finite volume homogeneous space, we consider the set of points admitting divergent on average trajectories. We show that the Hausdorff dimension of this set is strictly less than the manifold dimension of the homogeneous ... More

Projective dimension and regularity of edge ideals of some vertex-weighted oriented $m$-partite graphsApr 08 2019In this paper we provide some exact formulas for the projective dimension and the regularity of edge ideals associated to three special types of vertex-weighted oriented $m$-partite graphs. These formulas are functions of the weight and number of vertices. ... More

Global Well-Posesedness for the Derivative Nonlinear Schrodinger EquationOct 10 2017We study the Derivative Nonlinear Schr\"odinger (DNLS). equation for general initial conditions in weighted Sobolev spaces that can support bright solitons (but exclude spectral singularities corresponding to algebraic solitons). We show that the set ... More

Nonexistence of decreasing equisingular approximations with logarithmic polesJun 15 2015Jun 21 2015In this article, we present that for any complex manifold whose dimension is bigger than one, there exists a multiplier ideal sheaf such that there don't exist equisingular weights with logarithmic poles, which are not smaller than the orginal weight. ... More

Small World MCMC with Tempering: Ergodicity and Spectral GapNov 20 2012When sampling a multi-modal distribution $\pi(x)$, $x\in \rr^d$, a Markov chain with local proposals is often slowly mixing; while a Small-World sampler \citep{guankrone} -- a Markov chain that uses a mixture of local and long-range proposals -- is fast ... More

A Computationally Efficient Projection-Based Approach for Spatial Generalized Linear Mixed ModelsSep 08 2016Inference for spatial generalized linear mixed models (SGLMMs) for high-dimensional non-Gaussian spatial data is computationally intensive. The computational challenge is due to the high-dimensional random effects and because Markov chain Monte Carlo ... More

Numerical Analysis of Electroconvection Phenomena in Cross-flowDec 28 2018Jan 04 2019Electroconvective phenomena in the presence of cross-flow between two parallel electrodes is investigated in a numerical study. The two-relaxation-time Lattice Boltzmann Method with fast Poisson solver solves for the spatiotemporal distribution of flow ... More

Nonparametric Multiple Change Point Detection for Non-Stationary Times SeriesJan 10 2019Jan 11 2019This article considers a nonparametric method for detecting change points in non-stationary time series. The proposed method will divide the time series into several segments so that between two adjacent segments, the normalized spectral density functions ... More

Coupling geometry on binary bipartite networks: hypotheses testing on pattern geometry and nestednessJan 31 2018Upon a matrix representation of a binary bipartite network, via the permutation invariance, a coupling geometry is computed to approximate the minimum energy macrostate of a network's system. Such a macrostate is supposed to constitute the intrinsic structures ... More

Curvature estimates for immersed hypersurfaces in Riemannian manifoldsApr 21 2016Aug 22 2016We establish mean curvature estimate for immersed hypersurface with nonnegative extrinsic scalar curvature in Riemannian manifold $(N^{n+1}, \bar g)$ through regularity study of a degenerate fully nonlinear curvature equation in general Riemannian manifold. ... More

The structure of restricted Leibniz algebrasMar 31 2014The paper studies the structure of restricted Leibniz algebras. More specifically speaking, we first give the equivalent definition of restricted Leibniz algebras, which is by far more tractable than that of a restricted Leibniz algebras in [6]. Second, ... More

Dynamic interfacial polaron enhanced superconductivity of FeSe/SrTiO3Dec 08 2018The observation of substantially enhanced superconductivity of single-layer FeSe films on SrTiO3 has stimulated intensive research interest. At present, conclusive experimental data on the corresponding electron-boson interaction is still missing. Here ... More

The Role of SrTiO3 Phonon Penetrating into thin FeSe Films in the Enhancement of SuperconductivityMay 23 2016Aug 10 2016The significant role of interfacial coupling on the superconductivity enhancement in FeSe films on SrTiO3 has been widely recognized. But the explicit origination of this coupling is yet to be identified. Here by surface phonon measurements using high ... More

Multiplier ideal sheaves, complex singularity exponents, and restriction formulaOct 13 2015Oct 25 2015In this article, we obtain two sharp equality conditions in the restriction formula on complex singularity exponents: an equality between the codimension of the zero variety of related multiplier ideal sheaves and the relative codimension of the restriction ... More

Regularization Parameter Selection Method for Sign LMS with Reweighted L1-Norm Constriant AlgorithmMar 12 2015Apr 28 2015Broadband frequency-selective fading channels usually have the inherent sparse nature. By exploiting the sparsity, adaptive sparse channel estimation (ASCE) algorithms, e.g., least mean square with reweighted L1-norm constraint (LMS-RL1) algorithm, could ... More

A mean curvature type flow in space formsSep 19 2013In this article, we introduce a new type of mean curvature flow for bounded star-shaped domains in space forms and prove its longtime existence, exponential convergence without any curvature assumption. Along this flow, the enclosed volume is a constant ... More

Simple, Fast, and Scalable Reachability OracleMay 02 2013Jul 01 2013A reachability oracle (or hop labeling) assigns each vertex v two sets of vertices: Lout(v) and Lin(v), such that u reaches v iff Lout(u) \cap Lin(v) \neq \emptyset. Despite their simplicity and elegance, reachability oracles have failed to achieve efficiency ... More

KdV equation under periodic boundary conditions and its perturbationsSep 06 2013Oct 23 2013In this paper we discuss properties of the KdV equation under periodic boundary conditions, especially those which are important to study perturbations of the equation. Next we review what is known now about long-time behaviour of solutions for perturbed ... More

A Polyhedral Study of the Integrated Minimum-Up/-Down Time and Ramping PolytopeApr 07 2016In this paper, we study the polyhedral structure of an integrated minimum-up/-down time and ramping polytope, which has broad applications in variant industries. The polytope we studied includes minimum-up/-down time, generation ramp-up/-down rate, logical, ... More

Two Relaxation Time Lattice Boltzmann Method Coupled to Fast Fourier Transform Poisson Solver: Application to Electroconvective FlowDec 11 2018Dec 22 2018Electroconvective flow between two infinitely long parallel electrodes is investigated via a multiphysics computational model. The model solves for spatiotemporal flow properties using two-relaxation-time Lattice Boltzmann Method for fluid and charge ... More

On the deformations and derivations of $n$-ary multiplicative Hom-Nambu-Lie superalgebrasJan 03 2014In this paper, we introduce the relevant concepts of $n$-ary multiplicative Hom-Nambu-Lie superalgebras and construct three classes of $n$-ary multiplicative Hom-Nambu-Lie superalgebras. As a generalization of the notion of derivations for $n$-ary multiplicative ... More

Embedding 5-planar graphs in three pagesJan 22 2018A \emph{book-embedding} of a graph $G$ is an embedding of vertices of $G$ along the spine of a book, and edges of $G$ on the pages so that no two edges on the same page intersect. the minimum number of pages in which a graph can be embedded is called ... More

Quench Dynamics of the Gaudin-Yang ModelMar 11 2018We study the quench dynamics of one dimensional bosons or fermion quantum gases with either attractive or repulsive contact interactions. Such systems are well described by the Gaudin-Yang model which turns out to be quantum integrable. We use a contour ... More

Period-doubling cascades of a Silnikov equationDec 07 2013Dec 15 2013Based on numerical results of a Silnikov equation, three period-doubling cascades, corresponding respectively to three different characters of the rotation number of a limit closed orbit, are studied, and the Feigenbaum constant is used successfully in ... More

Distributing points uniformly on the unit sphere under a mirror reflection symmetry constraintMar 15 2014Apr 15 2014Uniformly distributed point sets on the unit sphere with and without symmetry constraints have been found useful in many scientific and engineering applications. Here, a novel variant of the Thomson problem is proposed and formulated as an unconstrained ... More

Post model-fitting exploration via a "Next-Door" analysisJun 04 2018We propose a simple method for evaluating the model that has been chosen by an adaptive regression procedure, our main focus being the lasso. This procedure deletes each chosen predictor and refits the lasso to get a set of models that are "close" to ... More

Improved Channel Estimation with Partial Sparse Constraint for AF Cooperative Communication SystemsJul 30 2012Accurate channel state information (CSI) is necessary for coherent detection in amplify and forward (AF) broadband cooperative communication systems. Based on the assumption of ordinary sparse channel, efficient sparse channel estimation methods have ... More

Polaron, molecule and pairing in one-dimensional spin-1/2 Fermi gas with an attractive Delta-function interactionFeb 14 2012Using solutions of the discrete Bethe ansatz equations, we study in detail the quantum impurity problem of a spin-down fermion immersed into a fully ploarized spin-up Fermi sea with weak attraction. We prove that this impurity fermion in the one-dimensional ... More

Algebraic Bethe ansatz for the one-dimensional Hubbard model with open boundariesAug 03 1999The one-dimensional Hubbard model with open boundary conditions is exactly solved by means of algebraic Bethe ansatz. The eigenvalue of the transfer matrix, the energy spectrum as well as the Bethe ansatz equations are obtained.

Complete break-up of the helium atom by proton and antiproton impactJun 10 2009We present a fully {\it ab initio}, non-perturbative, time-dependent approach to describe single and double ionization of helium by proton and antiproton impact. A flexible and accurate finite-element discrete-variable-representation is applied to discretize ... More

Electric-field induced helium-helium resonancesMar 20 2019The tunability of the helium-helium interaction through an external electric field is investigated. For a static external field, electric-field induced resonances and associated electric-field induced bound states are calculated for the $^4$He-$^4$He, ... More

Regularity of the geodesic equation in the space of Sasakian metricsJun 30 2009Jul 29 2009This paper is devoted to the regularity analysis of a geodesic equation in the space of Sasakian metrics. Firstly, we reduce the geodesic equation in the space of Sasakian metrics to a Dirichlet problem of degenerate complex Monge-Amp\'ere type eqution ... More

Hypersurfaces of Constant Curvature in Hyperbolic Space IIOct 09 2008Dec 14 2008We find complete hypersurfaces of constant curvature in hyperbolic space with a prescribed asymptotic boundary at infinity for a general class of (elliptic) curvature functions which includes the higher order mean curvatures and their curvature quotients. ... More

Bounded orbits of certain diagonalizable flows on $SL_{n}(\mathbb{R})/SL_{n}(\mathbb{Z})$May 27 2016We prove that the set of points that have bounded orbits under certain diagonalizable flows is a hyperplane absolute winning subset of $SL_{n}(\mathbb{R})/SL_{n}(\mathbb{Z})$.

A Monge-Ampere Type Fully Nonlinear Equation on Hermitian ManifoldsOct 19 2012We study a fully nonlinear equation of complex Monge-Ampere type on Hermitian manifolds. We establish the a priori estimates for solutions of the equation up to the second order derivatives with the help of a subsolution.

Scattering framework for two particles with isotropic spin-orbit coupling applicable to all energiesAug 19 2016Previous work developed a K-matrix formalism applicable to positive energies for the scattering between two $s$-wave interacting particles with two internal states, isotropic spin-orbit coupling and vanishing center-of-mass momentum [H. Duan, L. You and ... More

Badly approximable vectors in higher dimensionSep 27 2015We prove that the set of (r_1,r_2,..,r_{d})-badly approximable vectors is a winning set if r_1=r_2=...=r_{d-1}\geq r_{d}.

Improvement of a Theorem of George Gunther Lorentz (1963) and its Generalization to the Multivariate CaseSep 27 2016In this short note we have proved an enhanced version of a theorem of G. G. Lorentz [1] and its generalization to the multivariate case which gives a non- uniform estimate of degree of approximation by a polynomial with positive coefficients. The performance ... More

Geometric inequalities on locally conformally flat manifoldsFeb 27 2003Oct 02 2003Through the study of some elliptic and parabolic fully nonlinear PDEs, we establish conformal versions of quermassintegral inequality, the Sobolev inequality and the Moser-Trudinger inequality for the geometric quantities associated to the Schouten tensor ... More

Affine Combination of Two Adaptive Sparse Filters for Estimating Large Scale MIMO ChannelsJul 23 2014Large scale multiple-input multiple-output (MIMO) system is considered one of promising technologies for realizing next-generation wireless communication system (5G) to increasing the degrees of freedom in space and enhancing the link reliability while ... More

Convexity estimates for level sets of quasiconcave solutions to fully nonlinear elliptic equationsApr 07 2010Oct 10 2010We establish a geometric lower bound for the principal curvature of the level surfaces of solutions to $F(D^2u, Du, u, x)=0$ in convex ring domains, under a refined structural condition introduced by Bianchini-Longinetti-Salani in \cite{BLS}. We also ... More

Entropy and a convergence theorem for Gauss curvature flow in high dimensionJun 04 2013In this paper we prove uniform regularity estimates for the normalized Gauss curvature flow in higher dimensions. The convergence of solutions in $C^\infty$-topology to a smooth strictly convex soliton as $t$ approaches to infinity is obtained as a consequence ... More

Continuity in Information AlgebrasJan 02 2012In this paper, the continuity and strong continuity in domain-free information algebras and labeled information algebras are introduced respectively. A more general concept of continuous function which is defined between two domain-free continuous information ... More

Clarkson-Erdös-Schwartz Theorem on a SectorSep 08 2011We prove a Clarkson-Erd\"os-Schwartz type theorem for the case of a closed sector in the plane. Concretely, we get some sufficient conditions for the incompleteness and minimality of a M\"untz system $E(\Lambda)={z^{\lambda_n}:n=0,1,...}$ in the space ... More

Many-body properties of quasi-one dimensional Boson gas across a narrow CIROct 09 2012Feb 05 2013We study strong interaction effects in a one-dimensional (1D) Boson gas across a narrow confinement induced resonance (CIR). In contrast to the zero range potential, the 1D two-body interaction in the narrow CIR can be written as a polynomial of derivative ... More

The quermassintegral inequalities for starshaped domainsOct 23 2007Oct 17 2008We give a simple proof of the insoperimetric inequality for quermassintegrals of non-convex starshaped domains, using a reslut of Gerhardt \cite{G} and Urbas \cite{U} on an expanding geometric curvature flow.