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An all-fiber laser oscillating directly at single TE01 mode through ring-core fibersNov 10 2018Cylindrical vector beams (CVBs) have a wide range of applications owing to their particular polarization characteristics and optical field distributions. For the first time, an azimuthally polarized fiber laser without any polarization controller is proposed ... More

On unbiased performance evaluation for protein inferenceNov 29 2012This letter is a response to the comments of Serang (2012) on Huang and He (2012) in Bioinformatics. Serang (2012) claimed that the parameters for the Fido algorithm should be specified using the grid search method in Serang et al. (2010) so as to generate ... More

Passively Q-switching cylindrical vector beam fiber laser operating in high-order modeSep 12 2018We experimentally demonstrate a linear-cavity all-fiber passively Q-switching cylindrical vector beam (CVB) laser operating in high-order mode. This CVB fiber laser operates without any mode converter which always leads to high insertion loss, and it ... More

Protein Inference and Protein Quantification: Two Sides of the Same CoinOct 09 2012Motivation: In mass spectrometry-based shotgun proteomics, protein quantification and protein identification are two major computational problems. To quantify the protein abundance, a list of proteins must be firstly inferred from the sample. Then the ... More

Half-width of local spectral density of states given by width of nonperturbative parts of eigenfunctions: The Wigner-band-matrix modelDec 09 2015It is shown that, for a Hamiltonian with a band structure, the half width of local spectral density of states, or strength function, is closely related to the width of the nonperturbative (NPT) parts of energy eigenfunctions. In the Wigner-band random-matrix ... More

Capillary-driven binding of thin triangular prisms at fluid interfacesFeb 08 2018We observe capillary-driven binding between thin, equilateral triangular prisms at a flat air-water interface. The edge length of the equilateral triangle face is 120 $\mu m$, and the thickness of the prism is varied between 2 and 20 $\mu m$. For thickness ... More

Mode-locked fiber laser with offset splicing between two multimode fibers as a saturable absorberJul 03 2018A novel mode-locked fiber laser based on offset splicing technology between two kinds of graded index multimode fibers is proposed and experimentally demonstrated. The offset splice spot structure acts as a saturable absorber via nonlinear multimodal ... More

DLIMD: Dictionary Learning based Image-domain Material Decomposition for spectral CTMay 06 2019The potential huge advantage of spectral computed tomography (CT) is its capability to provide accuracy material identification and quantitative tissue information. This can benefit clinical applications, such as brain angiography, early tumor recognition, ... More

A new ignition hohlraum design for indirect-drive inertial confinement fusionJun 02 2016In this paper, a six-cylinder-port hohlraum is proposed to provide high symmetry flux on capsule. It is designed to ignite a capsule with 1.2 mm radius in indirect-drive inertial confinement fusion (ICF) . Flux symmetry and laser energy are calculated ... More

DLIMD: Dictionary Learning based Image-domain Material Decomposition for spectral CTMay 06 2019May 24 2019The potential huge advantage of spectral computed tomography (CT) is its capability to provide accuracy material identification and quantitative tissue information. This can benefit clinical applications, such as brain angiography, early tumor recognition, ... More

A Fast Solver for the Elastic Scattering of Multiple ParticlesDec 13 2018Consider the elastic scattering of a time-harmonic wave by multiple well separated rigid particles in two dimensions. To avoid using the complex Green's tensor of the elastic wave equation, we utilize the Helmholtz decomposition to convert the boundary ... More

Increasing stability for the inverse source scattering problem with multi-frequenciesJul 23 2016Consider the scattering of the two- or three-dimensional Helmholtz equation where the source of the electric current density is assumed to be compactly supported in a ball. This paper concerns the stability analysis of the inverse source scattering problem ... More

Yb-doped all fiber picosecond laser based on grade-index multimode fiber with microcavitySep 13 2018Sep 25 2018We demonstrate an all-fiber mode-locked laser at all-normal dispersion with a saturable absorber, which is based on a section of grade-index multimode fiber with inner microcavity embedded in the splice points. The absorption modulation depth of this ... More

Electromagnetic Scattering for Time-Domain Maxwell's Equations in an Unbounded StructureApr 26 2016The goal of this work is to study the electromagnetic scattering problem of time-domain Maxwell's equations in an unbounded structure. An exact transparent boundary condition is developed to reformulate the scattering problem into an initial-boundary ... More

Analysis of Time-Domain Scattering by Periodic StructuresApr 04 2016This paper is devoted to the mathematical analysis of a time-domain electromagnetic scattering by periodic structures which are known as diffraction gratings. The scattering problem is reduced equivalently into an initial-boundary value problem in a bounded ... More

Convergence of an adaptive finite element DtN method for the elastic wave scattering problemMar 08 2019Consider the scattering of an elastic plane wave by a rigid obstacle, which is immersed in a homogeneous and isotropic elastic medium in two dimensions. Based on a Dirichlet-to-Neumann (DtN) operator, an exact transparent boundary condition is introduced ... More

Convergence of an adaptive finite element DtN method for the elastic wave scattering by periodic structuresMay 09 2019Consider the scattering of a time-harmonic elastic plane wave by a periodic rigid surface. The elastic wave propagation is governed by the two-dimensional Navier equation. Based on a Dirichlet-to-Neumann (DtN) map, a transparent boundary condition (TBC) ... More

Inverse Electromagnetic Diffraction by Biperiodic Dielectric GratingsDec 08 2016Consider the incidence of a time-harmonic electromagnetic plane wave onto a biperiodic dielectric grating, where the surface is assumed to be a small and smooth perturbation of a plane. The diffraction is modeled as a transmission problem for Maxwell's ... More

Stability on the Inverse Random Source Scattering Problem for the One-Dimensional Helmholtz EquationJul 22 2016Consider the one-dimensional stochastic Helmholtz equation where the source is assumed to be driven by the white noise. This paper concerns the stability analysis of the inverse random source problem which is to reconstruct the statistical properties ... More

Low-dose spectral CT reconstruction using L0 image gradient and tensor dictionaryDec 13 2017Jul 24 2018Spectral computed tomography (CT) has a great superiority in lesion detection, tissue characterization and material decomposition. To further extend its potential clinical applications, in this work, we propose an improved tensor dictionary learning method ... More

Generation mode-locked square-wave pulse based on reverse saturable absorption effect in graded index multimode fiberApr 14 2019We firstly report mode-locked square-wave pulse in Yb-doped fiber laser based on graded index multimode fiber of reverse suturable absorption. By adjusting the pump power, the width of the square-wave can be tuned range from 350 ps to 52.6 ns with 3dB ... More

Analysis of Transient Acoustic-Elastic Interaction in an Unbounded StructureAug 19 2016Consider the wave propagation in a two-layered medium consisting of a homogeneous compressible air or fluid on top of a homogeneous isotropic elastic solid. The interface between the two layers is assumed to be an unbounded rough surface. This paper concerns ... More

Inverse elastic surface scattering with far-field dataDec 07 2017A rigorous mathematical model and an efficient computational method are proposed to solving the inverse elastic surface scattering problem which arises from the near-field imaging of periodic structures. We demonstrate how an enhanced resolution can be ... More

Flip-Rotate-Pooling Convolution and Split Dropout on Convolution Neural Networks for Image ClassificationJul 31 2015This paper presents a new version of Dropout called Split Dropout (sDropout) and rotational convolution techniques to improve CNNs' performance on image classification. The widely used standard Dropout has advantage of preventing deep neural networks ... More

Inverse obstacle scattering for Maxwell's equations in an unbounded structureNov 29 2018This paper is concerned with analysis of electromagnetic wave scattering by an obstacle which is embedded in a two-layered lossy medium separated by an unbounded rough surface. Given a dipole point source, the direct problem is to determine the electromagnetic ... More

Highly tunable ultra-narrow-resonances with optical nano-antenna phased arrays in the infraredNov 14 2014We report our recent development in pursuing high Quality-Factor (high-Q factor) plasmonic resonances, with vertically aligned two dimensional (2-D) periodic nanorod arrays. The 2-D vertically aligned nano-antenna array can have high-Q resonances varying ... More

Strong-Feller property for Navier-Stokes equations driven by space-time white noiseSep 27 2017Sep 29 2017In this paper we prove strong Feller property for the Markov semigroups associated to the two or three dimensional Navier-Stokes (N-S) equations driven by space-time white noise using the theory of regularity structures introduced by Martin Hairer in ... More

Lattice approximation to the dynamical $Φ_3^4$ modelAug 23 2015We study the lattice approximations to the dynamical $\Phi^4_3$ model by paracontrolled distributions proposed in [GIP13]. We prove that the solutions to the lattice systems converge to the solution to the dynamical $\Phi_3^4$ model in probability, locally ... More

Three-dimensional Navier-Stokes equations driven by space-time white noiseMay 31 2014Jan 04 2017In this paper we study 3D Navier-Stokes (NS) equation driven by space-time white noise by using regularity structure theory introduced in [Hai14] and paracontrolled distribution proposed in [GIP13]. We obtain local existence and uniqueness of solutions ... More

A Wong-Zakai theorem for $Φ^4_3$ modelApr 16 2015We prove a version of the Wong-Zakai theorem for the dynamical $\Phi_3^4$ model driven by space-time white noise on $\mathbb{T}^3$. For the $\Phi^4_3$ model it is proved in [Hai14] that a renormalisation has to be performed in order to define the nonlinear ... More

Dimension reduction-based significance testing in nonparametric regressionOct 13 2015A dimension reduction-based adaptive-to-model test is proposed for significance of a subset of covariates in the context of a nonparametric regression model. Unlike existing local smoothing significance tests, the new test behaves like a local smoothing ... More

Inverse Random Source Scattering for Elastic WavesAug 09 2016This paper is concerned with the direct and inverse random source scattering problems for elastic waves where the source is assumed to be driven by an additive white noise. Given the source, the direct problem is to determine the displacement of the random ... More

An all-dielectric bowtie waveguide with deep subwavelength mode confinementJun 21 2017Jun 30 2017To fulfil both size and power requirements for future photonic integrated circuits, an effective approach is to miniaturize photonic components. Surface plasmon polariton (SPP) is one of the most promising candidates for subwavelength mode confinement, ... More

A primal-dual fixed point algorithm for multi-block convex minimizationFeb 01 2016We extend a primal-dual fixed point algorithm (PDFP) proposed in [5] to solve two kinds of separable multi-block minimization problems, arising in signal processing and imaging science. This work shows the flexibility of applying PDFP algorithm to multi-block ... More

A primal-dual fixed-point algorithm for minimization of the sum of three convex separable functionsDec 31 2015Many problems arising in image processing and signal recovery with multi-regularization can be formulated as minimization of a sum of three convex separable functions. Typically, the objective function involves a smooth function with Lipschitz continuous ... More

Distributed Control and Stabilization for Discrete-time Large Scale Systems With Imposed ConstraintsJan 02 2018This paper is concerned with the distributed control and stabilization problems for linear discrete-time large scale systems with imposed constraints. The main contributions of this paper are: Firstly, by using the maximum principle (necessary condition) ... More

Inverse obstacle scattering problem for elastic waves with phased or phaseless far-field dataNov 30 2018This paper concerns an inverse elastic scattering problem which is to determine the location and the shape of a rigid obstacle from the phased or phaseless far-field data for a single incident plane wave. By introducing the Helmholtz decomposition, the ... More

Computation of Transmission Eigenvalues for Elastic WavesFeb 11 2018The goal of this paper is to develop numerical methods computing a few smallest elasticity transmission eigenvalues, which are of practical importance in inverse scattering theory. The problem is challenging since it is nonlinear, non-self-adjoint, and ... More

Approximating three-dimensional Navier-Stokes equations driven by space-time white noiseSep 17 2014In this paper we study approximations to 3D Navier-Stokes (NS) equation driven by space-time white noise by paracontrolled distribution proposed in [GIP13]. A solution theory for this equation has been developed recently in [ZZ14] based on regularity ... More

Accreting Circumplanetary Disks: Observational SignaturesAug 27 2014Oct 06 2014I calculate the spectral energy distributions (SEDs) of accreting circumplanetary disks using atmospheric radiative transfer models. Circumplanetary disks only accreting at $10^{-10} M_{\odot} yr^{-1}$ around a 1 M$_{J}$ planet can be brighter than the ... More

Translation invariance of Fock spacesJan 21 2011We show that there is only one Hilbert space of entire functions that is invariant under the action of naturally defined weighted translations.

Computing log-likelihood and its derivatives for restricted maximum likelihood methodsAug 25 2016Recent large scale genome wide association analysis involves large scale linear mixed models. Quantifying (co)-variance parameters in the mixed models with a restricted maximum likelihood method results in a score function which is the first derivative ... More

Eigenvalue resolution of self-adjoint matricesApr 28 2015Oct 10 2016Resolution of a compact group action in the sense described by Albin and Melrose is applied to the conjugation action by the unitary group on self-adjoint matrices. It is shown that the eigenvalues are smooth on the resolved space and that the trivial ... More

A simple proof of the strong integrality for full colored HOMFLYPT invariantsMar 13 2016By using the HOMFLY skein theory. We prove a strong integrality theorem for the reduced colored HOMFLYPT invariants defined by a basis in the full HOMFLY skein of the annulus.

Max-Margin Nonparametric Latent Feature Models for Link PredictionJun 18 2012We present a max-margin nonparametric latent feature model, which unites the ideas of max-margin learning and Bayesian nonparametrics to discover discriminative latent features for link prediction and automatically infer the unknown latent social dimension. ... More

Doubling property and vanishing order of Steklov eigenfunctionsJul 06 2014The paper is concerned with the doubling estimates and vanishing order of the Steklov eigenfunction on the boundary of a smooth boundary domain $\mathbb R^n$. The eigenfunction is given by a Dirichlet-to-Neumann map. We improve the doubling property shown ... More

Interior nodal sets of Steklov eigenfunctions on surfacesJul 02 2015Oct 20 2015We investigate the interior nodal sets $\mathcal{N}_\lambda$ of Steklov eigenfunctions on connected and compact surfaces with boundary. The optimal vanishing order of Steklov eigenfunctions is shown be $C\lambda$. The singular sets $\mathcal{S}_\lambda$ ... More

Higher Codimensional Alpha Invariants and Characterization of Projective SpacesMay 18 2018We generalize the definition of alpha invariant to arbitrary codimension. We also give a lower bound of these alpha invariants for K-semistable Q-Fano varieties and show that we can characterize projective spaces among all K-semistable Fano manifolds ... More

Rigidity of Area-Minimizing $2$-Spheres in $n$-Manifolds with Positive Scalar CurvatureMar 14 2019We prove that the least area of the non-contractible immersed spheres is no more than $4\pi$ in any oriented compact manifold with dimension $n+2\leq 7$ which satisfies $R\geq 2$ and admits a map to $\mathbf S^2\times T^n$ with nonzero degree. We also ... More

Statistical inference for autoregressive models under heteroscedasticity of unknown formApr 06 2018Aug 09 2018This paper provides an entire inference procedure for the autoregressive model under (conditional) heteroscedasticity of unknown form with a finite variance. We first establish the asymptotic normality of the weighted least absolute deviations estimator ... More

Hyperspectral Unmixing: Ground Truth Labeling, Datasets, Benchmark Performances and SurveyAug 17 2017Oct 11 2017Hyperspectral unmixing (HU) is a very useful and increasingly popular preprocessing step for a wide range of hyperspectral applications. However, the HU research has been constrained a lot by three factors: (a) the number of hyperspectral images (especially ... More

Loss Rate Estimators and the Properties for the Tree TopologyAug 05 2015A large number of explicit estimators are proposed in this paper for loss rate estimation in a network of the tree topology. All of the estimators are proved to be unbiased and consistent instead of asymptotic unbiased as that obtained in [1] for a specific ... More

Explicit Estimators for Loss TomographyMay 29 2012Aug 13 2013Full likelihood has been widely used in loss tomography because most believe it can produce accurate estimates although the full likelihood estimators proposed so far are complex in structure and expensive in execution. We in this paper advocate a different ... More

A new approach to parton recombination in a QCD evolution equationSep 15 1998Parton recombination is reconsidered in perturbation theory without using the AGK cutting rules in the leading order of the recombination. We use time-ordered perturbation theory to sum the cut diagrams, which are neglected in the GLR evolution equation. ... More

Sharp well-posedness and ill-posedness for the 3-D micropolar fluid system in Fourier-Besov spacesMay 08 2018We study the Cauchy problem of the incompressible micropolar fluid system in $\mathbb{R}^{3}$. In a recent work of the first author and Jihong Zhao \cite{ZhuZ18}, it is proved that the Cauchy problem of the incompressible micropolar fluid system is locally ... More

Statistical Properties of Loss Rate Estimators in Tree Topology (2)Jul 01 2017Four types of explicit estimators are proposed here to estimate the loss rates of the links in a network with the tree topology and all of them are derived by the maximum likelihood principle. One of the four is developed from an estimator that was used ... More

"Charged" Particle's Tunneling from Rotating Black HolesJan 24 2011The behavior of a scalar field theory near the event horizon in a rotating black hole background can be effectively described by a two dimensional field theory in a gauge field background. Based on this fact, we proposal that the quantum tunneling from ... More

Quantitative uniqueness of solutions to parabolic equationsAug 06 2017We investigate the quantitative uniqueness of solutions to parabolic equations with lower order terms on compact smooth manifolds. Quantitative uniqueness is a quantitative form of strong unique continuation property. We characterize quantitative uniqueness ... More

Nodal sets of Robin and Neumann eigenfunctionsOct 30 2018We investigate the measure of nodal sets for Robin and Neumann eigenfunctions in the domain and on the boundary of the domain. A polynomial upper bound for the interior nodal sets is obtained for the Robin eigenfunctions in the smooth domain. For the ... More

Doubling inequality and nodal sets for solutions of bi-Laplace equationsFeb 16 2018Dec 19 2018We investigate the doubling inequality and nodal sets for the solutions of bi-Laplace equations. A polynomial upper bound for the nodal sets of solutions and their gradient is obtained based on the recent development of nodal sets for Laplace eigenfunctions ... More

The power operation structure on Morava E-theory of height 2 at the prime 3Oct 13 2012We give explicit calculations of the algebraic theory of power operations for a specific Morava E-theory spectrum and its K(1)-localization. These power operations arise from the universal degree-3 isogeny of elliptic curves associated to the E-theory. ... More

Control of Three Dimensional Water WavesDec 17 2017We study the exact controllability for spatially periodic water waves with surface tension, by localized exterior pressures applied to free surfaces. We prove that in any dimension, the exact controllability holds within arbitrarily short time, for sufficiently ... More

Mutually unbiased bases as minimal Clifford covariant 2-designsMay 05 2015Jul 06 2015Mutually unbiased bases (MUB) are interesting for various reasons. The most attractive example of (a complete set of) MUB is the one constructed by Ivanovi\'c as well as Wootters and Fields, which is referred to as the canonical MUB. Nevertheless, little ... More

Tomographic and Lie algebraic significance of generalized symmetric informationally complete measurementsAug 04 2014Generalized symmetric informationally complete (SIC) measurements are SIC measurements that are not necessarily rank one. They are interesting originally because of their connection with rank-one SICs. Here we reveal several merits of generalized SICs ... More

SIC~POVMs and Clifford groups in prime dimensionsMar 18 2010Jun 30 2010We show that in prime dimensions not equal to three, each group covariant symmetric informationally complete positive operator valued measure (SIC~POVM) is covariant with respect to a unique Heisenberg--Weyl (HW) group. Moreover, the symmetry group of ... More

On Vector ARMA Models Consistent with a Finite Matrix Covariance SequenceAug 15 2017Aug 28 2017We formulate the so called "VARMA covariance matching problem" and demonstrate the existence of a solution using the degree theory from differential topology.

Regularity of solutions to a model for solid-solid phase transitions driven by configurational forcesFeb 04 2011In a previous work, we prove the existence of weak solutions to an initial-boundary value problem, with $H^1(\Omega)$ initial data, for a system of partial differential equations, which consists of the equations of linear elasticity and a nonlinear, degenerate ... More

Bredon Cohomology of Polyhedral ProductsNov 17 2018A polyhedral product is a natural subspace of a Cartesian product, which is specified by a simplicial complex K. The automorphism group Aut(K) of K induces a group action on the polyhedral product. In this paper we study this group action and give a formula ... More

Cyber InsuranceSep 30 2018This chapter will first present a principal-agent game-theoretic model to capture the interactions between one insurer and one user. The insurer is deemed as the principal who does not have incomplete information about user's security policies. The user, ... More

A momentum conserving $N$-body scheme with individual timestepsDec 29 2017$N$-body simulations study the dynamics of $N$ particles under the influence of mutual long-distant forces such as gravity. In practice, $N$-body codes will violate Newton's third law if they use either an approximate Poisson solver or individual timesteps. ... More

On the critical branching random walk III: the critical dimensionJan 31 2017In this paper, we study the critical branching random walk in the critical dimension, $Z^4$. We provide the asymptotics of the probability of visiting a fixed finite subset and the range of the critical branching random walk conditioned on the total number ... More

Relativistic corrections to the form factors of $B_c$ into $P$-wave orbitally excited charmoniumOct 19 2017May 14 2018We investigated the form factors of the $B_{c}$ meson into $P$-wave orbitally excited charmonium using the nonrelativistic QCD effective theory. Through the analytic computation, the next-to-leading order relativistic corrections to the form factors were ... More

Development in the Scattering Matrix Theory: From Spin-Orbit-Coupling Affected Shot Noise to Quantum PumpingNov 16 2010The review chapter starts by a pedagogical introduction to the general concept of the scattering theory: from the fundamental wave-function picture to the second-quantization language, with the aim to clear possible ambiguity in conventional textbooks. ... More

Determining All Maximum Uniquely Restricted Matching in Bipartite GraphsSep 28 2010The approach mapping from a matching of bipartite graphs to digraphs has been successfully used for forcing set problem, in this paper, it is extended to uniquely restricted matching problem. We show to determine a uniquely restricted matching in a bipartite ... More

Note on "Hydrodynamic Phase Locking of Swimming Microorganisms"Aug 29 2009We make remarks on Elfring and Lauga's [{\it Phys. Rev. Lett.} {\bf 103}, 088101 (2009)] paper. The energy dissipation or viscous dissipation plays an important role in the phase-locked state.

The Hecke algebra action on Morava E-theory of height 2May 23 2015Given a one-dimensional formal group of height 2, let E be the Morava E-theory spectrum associated to its universal deformation over the Lubin-Tate ring. By computing with moduli spaces of elliptic curves, we give an explicitation for an algebra of Hecke ... More

Analysis on Metric Space QJul 21 2006Jul 26 2006In this paper, we show that the metric space Q is a positively-curved space (PC-space) in the sense of Alexandrov. We also discuss some issues like metric tangent cone and exponential map of Q. Then we give a stratification of this metric space according ... More

Propagation of Singularities for Gravity-Capillary Water WavesOct 22 2018We generalize the wavefront set of H\"ormander and the homogeneous wavefront set of Nakamura to the quasi-homogeneous wavefront set, which enables us to obtain the propagation of singularities for gravity-capillary water waves of finite depth. Consequences ... More

A Fast Algorithm to Calculate Power Sum of Natural NumbersMay 26 2018Permutations can be represented as linear combinations of natural numbers with different powers. In this paper, its coefficient matrix and inverse matrix is derived, and the results show the coefficient matrix is a lower triangular matrix while the inverse ... More

Projective dimension and regularity of path ideals of cyclesOct 11 2016In this paper, we give a formula to compute all the top degree graded Betti numbers of the path ideals of a cycle. As a consequence we can give a formula to compute its projective dimension and regularity.

Semistable models for modular curves and power operations for Morava E-theories of height 2Aug 13 2015Dec 29 2018We construct an integral model for Lubin-Tate curves as moduli of finite subgroups of formal deformations over complete Noetherian local rings. They are p-adic completions of the modular curves X_0(p) at a mod-p supersingular point. Our model is semistable ... More

Process-Level Large Deviations for Nonlinear Hawkes Point ProcessesAug 11 2011Oct 14 2014In this paper, we prove a process-level, also known as level-3 large deviation principle for a very general class of simple point processes, i.e. nonlinear Hawkes process, with a rate function given by the process-level entropy, which has an explicit ... More

Analysis of a multigrid preconditioner for Crouzeix-Raviart discretization of elliptic PDE with jump coefficientOct 24 2011In this paper, we present a multigrid $V$-cycle preconditioner for the linear system arising from piecewise linear nonconforming Crouzeix-Raviart discretization of second order elliptic problems with jump coefficients. The preconditioner uses standard ... More

Cluster-tilted algebras and their intermediate coveringsAug 18 2008Apr 30 2010We construct the intermediate coverings of cluster-tilted algebras by defining the generalized cluster categories. These generalized cluster categories are Calabi-Yau triangulated categories with fraction CY-dimension and have also cluster tilting objects ... More

On Theorem 6 in "Relative Entropy and the Multivariable Multidimensional Moment Problem" [Mar 2006 1052-1066]May 30 2018Jun 06 2018Matrix-valued covariance extension and multivariate spectral estimation are formulated as generalized moment problems in the "THREE" approach and its extensions. Under this context, we discuss Theorem 6 in \cite{Georgiou-06} concerning the bijectivity ... More

An adaptive finite element PML method for the elastic wave scattering problem in periodic structuresMay 27 2016An adaptive finite element method is presented for the elastic scattering of a time-harmonic plane wave by a periodic surface. First, the unbounded physical domain is truncated into a bounded computational domain by introducing the perfectly matched layer ... More

A fast direct imaging method for the inverse obstacle scattering problem with nonlinear point scatterersJun 21 2017Consider the scattering of a time-harmonic plane wave by heterogeneous media consisting of linear or nonlinear point scatterers and extended obstacles. A generalized Foldy-Lax formulation is developed to take fully into account of the multiple scattering ... More

A Generalization of the Kodaira Vanishing and Embedding TheoremFeb 02 1995We give several generalizations of the Kodaira vanishing and embedding theorems for K\"ahler manifolds to the case where the relevent line bundle has a small region of negative curvature. To prove the vanishing theorems we adapt techniques of Elworthy-Rosenberg ... More

Spectra and elliptic flow of (multi-)strange hadrons at RHIC and LHC within viscous hydrodynamics+hadron cascade hybrid modelJul 14 2016Aug 15 2016Using the (2+1)-dimensional ultrarelativistic viscous hydrodynamics+hadron cascade, VISHNU, hybrid model, we study the $p_{\rm T}$-spectra and elliptic flow of $\Lambda$, $\Xi$, and $\Omega$ in Au+Au collisions at $\sqrt{s_{NN}}$=200 GeV and in Pb+Pb ... More

Log rationally connected surfacesDec 08 2014Jul 02 2015In this paper, combining the works of Miyanishi-Tsunoda and Keel-McKernan, we prove the log Castelnuovo's rationality criterion for smooth quasiprojective surfaces over complex numbers.

Exotic Charmonium-like States at BESIIIMay 18 2015The recent measurement results of exotic charmonium-like states, the so called XYZ particles, at BESIII have been presented. I mainly discussed the charged Zc(3900) state, its neutral partner, and possible excited states.

Charmonium and Light Meson SpectroscopyDec 10 2012This talk reviews recent experimental results on selected topics in the spectroscopy of charmonia, charmonium-like states and light mesons.

Inclined Massive Planets in a Protoplanetary Disc: Gap Opening, Disc Breaking, and Observational SignaturesDec 04 2018We carry out three-dimensional hydrodynamical simulations to study planet-disc interactions for inclined high mass planets, focusing on the disc's secular evolution induced by the planet. We find that, when the planet is massive enough and the induced ... More

Rigidity of Area-Minimizing $2$-Spheres in $n$-Manifolds with Positive Scalar CurvatureMar 14 2019Mar 15 2019We prove that the least area of the non-contractible immersed spheres is no more than $4\pi$ in any oriented compact manifold with dimension $n+2\leq 7$ which satisfies $R\geq 2$ and admits a map to $\mathbf S^2\times T^n$ with nonzero degree. We also ... More

Global classical solutions of 3D compressible viscoelastic system near equilibriumSep 12 2018In this paper, we prove the global existence of general small solutions to compressible viscoelastic system. We remove the "initial state" assumption ($\tilde \rho_0 \det F_0 =1$) and the "div-curl" structure assumption compared with previous works. It ... More

Statistical Physics and Information Theory Perspectives on Linear Inverse ProblemsMay 15 2017Jul 12 2017Many real-world problems in machine learning, signal processing, and communications assume that an unknown vector $x$ is measured by a matrix A, resulting in a vector $y=Ax+z$, where $z$ denotes the noise; we call this a single measurement vector (SMV) ... More

Strongly Unitary Equivalence and Approximately Unitary Equivalence of Normal Compact Operators over Topological SpacesSep 01 2017Let $A$ and $B$ be compact operators over a topological space $X$ and suppose that these operators are normal and have same distinct eigenvalues at each point. By obstruction theory, we establish a necessary and sufficient condition for $A$ and $B$ to ... More

Explicit Maximum Likelihood Loss Estimator in Multicast TomographyApr 27 2010For the tree topology, previous studies show the maximum likelihood estimate (MLE) of a link/path takes a polynomial form with a degree that is one less than the number of descendants connected to the link/path. Since then, the main concern is focused ... More

A geometrizing higher twist effect on nuclear targetAug 30 2004Feb 13 2005The higher twist effects in deep inelastic scattering on the nuclear target are studied using time ordered perturbation theory. We showed that the collinear rescattering of the outgoing quark on the extra nucleons via the contacting gluon-pair is dominant ... More

Towards a dictionary for the Bargmann transformJun 21 2015There is a canonical unitary transformation from $L^2(\R)$ onto the Fock space $F^2$, called the Bargmann transform. The purpose of this article is to translate some important results and operators from the context of $L^2(\R)$ to that of $F^2$. Examples ... More