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Adaptive generalized multiscale finite element methods for H(curl)-elliptic problems with heterogeneous coefficientsFeb 08 2018In this paper, we construct an adaptive multiscale method for solving H(curl)-elliptic problems in highly heterogeneous media. Our method is based on the generalized multiscale finite element method. We will first construct a suitable snapshot space, ... More

Jordan Derivations and Lie derivations on Path AlgebrasMar 22 2012Without the faithful assumption, we prove that every Jordan derivation on a class of path algebras of quivers without oriented cycles is a derivation and that every Lie derivation on such kinds of algebras is of the standard form.

Lie Derivations of Dual Extension AlgebrasMar 02 2013Let $K$ be a field and $\Gamma$ a finite quiver without oriented cycles. Let $\Lambda$ be the path algebra $K(\Gamma, \rho)$ and let $\mathscr{D}(\Lambda)$ be the dual extension of $\Lambda$. In this paper, we prove that each Lie derivation of $\mathscr{D}(\Lambda)$ ... More

K-Commuting Mappings of Generalized Matrix AlgebrasNov 27 2011Motivated by the intensive and powerful works of Beidar and Bresar, we will study k-commuting mappings of generalized matrix algebras in this article. The general form of arbitrary k-commuting mapping of a generalized matrix algebra is determined. It ... More

Projective cell modules of Frobenius cellular algebrasApr 15 2013For a finite dimensional Frobenius cellular algebra, a sufficient and necessary condition for a simple cell module to be projective is given. A special case that dual bases of the cellular basis satisfying a certain condition is also considered. The result ... More

Jordan Derivations of some extension algebrasMar 02 2013In this paper, we mainly study Jordan derivations of dual extension algebras and those of generalized one-point extension algebras. It is shown that every Jordan derivation of dual extension algebras is a derivation. As applications, we obtain that every ... More

Fusion procedure for Degenerate cyclotomic Hecke algebrasDec 13 2013The primitive idempotents of the generic degenerate cycloctomic Hecke algebras are derived by consecutive evaluations of a certain rational function. This rational function depends only on the Specht modules and the normalization factors are the weights ... More

Metal artifact reduction based on the combined prior imageAug 22 2014Sep 04 2014Metallic implants introduce severe artifacts in CT images, which degrades the image quality. It is an effective method to reduce metal artifacts by replacing the metal affected projection with the forward projection of a prior image. How to find a good ... More

Asymptotically Optimal Sampling-based Kinodynamic PlanningJul 10 2014Feb 05 2016Sampling-based algorithms are viewed as practical solutions for high-dimensional motion planning. Recent progress has taken advantage of random geometric graph theory to show how asymptotic optimality can also be achieved with these methods. Achieving ... More

Jordan Derivations and Antiderivations of Generalized Matrix AlgebrasFeb 12 2012Let $\mathcal{G}=[A & M N & B]$ be a generalized matrix algebra defined by the Morita context $(A, B,_AM_B,_BN_A, \Phi_{MN}, \Psi_{NM})$. In this article we mainly study the question of whether there exist proper Jordan derivations for the generalized ... More

Quantum entropy-typical subspace and universal data compressionOct 21 2014The quantum entropy-typical subspace theory is specified. It is shown that any mixed state with von Neumann entropy less than h can be preserved approximately by the entropy-typical subspace with entropy= h. This result implies an universal compression ... More

Centimeter-deep tissue fluorescence microscopic imaging with high signal-to-noise ratio and picomole sensitivityOct 07 2015Fluorescence microscopic imaging in centimeter-deep tissue has been highly sought-after for many years because much interesting in vivo micro-information, such as microcirculation, tumor angiogenesis, and metastasis, may deeply locate in tissue. In this ... More

A Bayesian Nonparametic Approach for Estimating Individualized Treatment-Response CurvesAug 18 2016We study the problem of estimating the continuous response over time of interventions from observational time series---a retrospective dataset where the policy by which the data are generated are unknown to the learner. We are motivated by applications ... More

Degree heterogeneity in spatial networks with total cost constraintDec 01 2011Recently, In [Phys. Rev. Lett. 104, 018701 (2010)] the authors studied a spatial network which is constructed from a regular lattice by adding long-range edges (shortcuts) with probability $P_{ij}\sim r_{ij}^{-\alpha}$, where $r_{ij}$ is the Manhattan ... More

Network error correction with limited feedback capacityDec 13 2013Feb 01 2014We consider the problem of characterizing network capacity in the presence of adversarial errors on network links,focusing in particular on the effect of low-capacity feedback links cross network cuts.

Temporal effects in trend prediction: identifying the most popular nodes in the futureDec 21 2014Prediction is an important problem in different science domains. In this paper, we focus on trend prediction in complex networks, i.e. to identify the most popular nodes in the future. Due to the preferential attachment mechanism in real systems, nodes' ... More

Power Efficiency for Device-to-Device CommunicationsJul 18 2013The concept of device-to-Device (D2D) communication as an underlay coexistence with cellular networks gains many advantages of improving system performance. In this paper, we model such a two-layer heterogenous network based on stochastic geometry approach. ... More

A robust ranking algorithm to spammingDec 17 2010Ranking problem of web-based rating system has attracted many attentions. A good ranking algorithm should be robust against spammer attack. Here we proposed a correlation based reputation algorithm to solve the ranking problem of such rating systems where ... More

Kinetics of Muller's Ratchet from Adaptive Landscape ViewpointSep 19 2011Sep 21 2011Background: The accumulation of deleterious mutations of a population directly contributes to the fate as to how long the population would exist. Muller's ratchet provides a quantitative framework to study the effect of accumulation. Adaptive landscape ... More

Single-scan scatter correction in CBCT by using projection correlation based view interpolation (PC-VI) and a stationary ring-shaped beam stop array (BSA)Oct 30 2014In the scatter correction for x-ray Cone Beam (CB) CT, the single-scan scheme with moving Beam Stop Array (BSA) offers reliable scatter measurement with low dose, and by using Projection Correlation based View Interpolation (PC-VI), the primary fluence ... More

Self-Paced Learning: an Implicit Regularization PerspectiveJun 01 2016Sep 18 2016Self-paced learning (SPL) mimics the cognitive mechanism of humans and animals that gradually learns from easy to hard samples. One key issue in SPL is to obtain better weighting strategy that is determined by minimizer function. Existing methods usually ... More

Hyperscaling Violating Solutions in Generalised EMD TheoryAug 10 2016Sep 01 2016This short note is devoted to deriving scaling but hyperscaling violating solutions in a generalised Einstein-Maxwell-Dilaton theory with an arbitrary number of scalars and vectors. We obtain analytic solutions in some special case and discuss the physical ... More

Wonderful compactification of an arrangement of subvarietiesNov 14 2006Jan 01 2009We define the wonderful compactification of an arrangement of subvarieties. Given a complex nonsingular algebraic variety $Y$ and certain collection $\mathcal{G}$ of subvarieties of $Y$, the wonderful compactification $Y_\mathcal{G}$ can be constructed ... More

Phase transition for accessibility percolation on hypercubesFeb 26 2015In this paper, we consider accessibility percolation on hypercubes, i.e., we place i.i.d.\ uniform random variables on vertices of a hypercube, and study whether there is a path (possibly with back steps) connecting two vertices such that the values of ... More

Chow Motive of Fulton-MacPherson configuration spaces and wonderful compactificationsNov 15 2006Jan 01 2009We study the Chow groups and the Chow motives of the wonderful compactifications $Y_{\mathcal{G}}$ of arrangements of subvarieties. We prove a natural decomposition of the Chow motive of $Y_\mathcal{G}$, in particular of the Fulton-MacPherson configuration ... More

Benchmarking Quantum Hardware for Training of Fully Visible Boltzmann MachinesNov 14 2016Quantum annealing (QA) is a hardware-based heuristic optimization and sampling method applicable to discrete undirected graphical models. While similar to simulated annealing, QA relies on quantum, rather than thermal, effects to explore complex search ... More

Kazhdan-Lusztig polynomials and drift configurationsJun 09 2010Oct 04 2010The coefficients of the Kazhdan-Lusztig polynomials $P_{v,w}(q)$ are nonnegative integers that are upper semicontinuous on Bruhat order. Conjecturally, the same properties hold for $h$-polynomials $H_{v,w}(q)$ of local rings of Schubert varieties. This ... More

The Primary Design of the RidgetronMay 27 2016The ridgetron is used to accelerate the intense beam for the electron irradiation. According to the electromagnetic field simulation, the extend electrode should be cancelled to increase the shunt impedence. The method of parameter sweeping with constraint ... More

Bijection between Conjugacy Classes and Irreducible Representations of Finite Inverse SemigroupsAug 28 2012In this paper we show that the irreducible representations of a finite inverse semigroup $S$ over an algebraically closed field $F$ are in bijection with the conjugacy classes of $S$ if the characteristic of $F$ is zero or a prime number that does not ... More

Method for classifying multiqubit states via the rank of the coefficient matrix and its application to four-qubit statesJan 11 2012Oct 26 2012We construct coefficient matrices of size 2^l by 2^{n-l} associated with pure n-qubit states and prove the invariance of the ranks of the coefficient matrices under stochastic local operations and classical communication (SLOCC). The ranks give rise to ... More

The Isospin Distribution of Fragments in Reactions 96Ru+96Ru, 96Ru+96Zr, 96Zr+96Ru, and 96Zr+96Zr at Beam Energy 400 AMeVNov 21 2002The isospin distribution of particles and fragments in collisions 96Ru+96Ru, 96Ru+96Zr, 96Zr+96Ru, and 96Zr+96Zr at beam energy 400 AMeV is studied with isospin dependent QMD model. We find that the rapidity distribution of differential neutron-proton ... More

On the B-twisted topological sigma model and Calabi-Yau geometryFeb 27 2014We provide a rigorous perturbative quantization of the B-twisted topological sigma model via a first order quantum field theory on derived mapping space in the formal neighborhood of constant maps. We prove that the first Chern class of the target manifold ... More

The isospin dependent nucleon-nucleon inelastic cross section in the nuclear mediumOct 04 2016A theoretical calculation on the energy-, density-, and isospin-dependent nucleon-nucleon (NN) inelastic cross section $\sigma^*_{NN\rightarrow N\Delta}$, based on the self-consistent relativistic Boltzmann-Uehling-Uhlenbeck microscopic transport theory, ... More

Electrodynamics on Cosmological ScalesAug 26 2015Feb 29 2016Maxwell's equations cannot describe a homogeneous and isotropic universe with a uniformly distributed net charge, because the electromagnetic field tensor in such a universe must be vanishing everywhere. For a closed universe with a nonzero net charge, ... More

Effects of non-WKB Alfven waves on a multicomponent solar wind with differential ion flowApr 10 2008We present multicomponent solar wind models self-consistently incorporating the contribution from dissipationless, monochromatic, finite-wavelength (non-WKB), hydromagnetic, toroidal Alfv\'en waves, which are coupled to the flow only through the ponderomotive ... More

Propagation of non-WKB Alfven waves in a multicomponent solar wind with differential ion flowFeb 14 2007Mar 27 2007The propagation of dissipationless, hydromagnetic, non-WKB, purely toroidal Alfv\'en waves in a realistic background three-fluid solar wind with axial symmetry and differential proton-alpha flow is investigated. The wave equations are derived from standard ... More

Finite time blowup of generalized Euler ODE in matrix geometryFeb 11 2015In this paper, we study the finite time blowup of the generalized Euler ODE in the matrix geometry. We can extend Sullivan's result which is about the finite time blowup result of initial invertible linear operators to singular linear operators. we can ... More

Uniform regularity for linear kinetic equations with random input based on hypocoercivityDec 05 2016In this paper we study the effect of randomness in kinetic equations that preserve mass. The analysis is carried out in a general setting, with the regularity result not depending on the specific form of the collision term, the probability distribution ... More

Some degenerations of Kazhdan-Lusztig ideals and multiplicities of Schubert varietiesJan 20 2010We study Hilbert-Samuel multiplicity for points of Schubert varieties in the complete flag variety, by Groebner degenerations of the Kazhdan-Lusztig ideal. In the covexillary case, we give a positive combinatorial rule for multiplicity by establishing ... More

Hardness results on generalized connectivityMay 04 2010Let $G$ be a nontrivial connected graph of order $n$ and let $k$ be an integer with $2\leq k\leq n$. For a set $S$ of $k$ vertices of $G$, let $\kappa (S)$ denote the maximum number $\ell$ of edge-disjoint trees $T_1,T_2,...,T_\ell$ in $G$ such that $V(T_i)\cap ... More

The asymptotic number of occurrences of a subtree in trees with bounded maximum degree and an application to the Estrada indexMay 07 2010Let $\mathcal {T}^{\Delta}_n$ denote the set of trees of order $n$, in which the degree of each vertex is bounded by some integer $\Delta$. Suppose that every tree in $\mathcal {T}^{\Delta}_n$ is equally likely. For any given subtree $H$, we show that ... More

The asymptotic value of Randic index for treesMar 25 2010Let $\mathcal{T}_n$ denote the set of all unrooted and unlabeled trees with $n$ vertices, and $(i,j)$ a double-star. By assuming that every tree of $\mathcal{T}_n$ is equally likely, we show that the limiting distribution of the number of occurrences ... More

Further results on Liouville type theorems for some conformally invariant fully nonlinear equationsJan 22 2003We present some further results on Liouville type theorems for some conformally invariant fully nonlinear equations.

The asymptotic values of the general Zagreb and Randić indices of trees with bounded maximum degreeApr 11 2010Let $\mathcal {T}^{\Delta}_n$ denote the set of trees of order $n$, in which the degree of each vertex is bounded by some integer $\Delta$. Suppose that every tree in $\mathcal {T}^{\Delta}_n$ is equally likely. We show that the number of vertices of ... More

Notes on a minimal set of generators for the radical ideal defining the diagonal locus of $(\C^2)^n$Jan 09 2009Sep 09 2009We develop several techniques for the study of the radical ideal $I$ defining the diagonal locus of $(\C^2)^n$. Using these techniques, we give combinatorial construction of generators for $I$ of certain bi-degrees.

One-way information reconciliation schemes of quantum key distributionJan 05 2012May 14 2012Information reconciliation(IR) is a basic step of quantum key distribution (QKD). Classical message interaction is necessary in a practical IR scheme, and the communication complexity has become a bottleneck of QKD's development. Here we propose a concatenated ... More

Probing equilibration with respect to isospin degree of freedom in intermediate energy heavy ion collisionsSep 26 2001We have studied equilibration with respect to isospin degree of freedom in four 96 mass systems $^{96}Ru+^{96}Ru$, $^{96}Ru+^{96}Zr$, $^{96}Zr+^{96}Ru$, $^{96}Zr+^{96}Zr$ at 100 AMeV and 400 AMeV with isospin dependent QMD. We propose that the neutron-proton ... More

Lawson homology, morphic cohomology and Chow motivesNov 04 2007In this paper, the Lawson homology and morphic cohomology are defined on the Chow motives. We also define the rational coefficient Lawson homology and morphic cohomology of the Chow motives of finite quotient projective varieties. As a consequence, we ... More

On focal submanifolds of isoparametric hypersurfaces and Simons formulaJan 28 2015The focal submanifolds of isoparametric hypersurfaces in spheres are all minimal Willmore submanifolds, mostly being $\mathcal{A}$-manifolds in the sense of A.Gray but rarely Ricci-parallel (\cite{QTY},\cite{LY},\cite{TY3}). In this paper we study the ... More

Dirichlet problems of a quasi-linear elliptic systemNov 20 2003We discuss the Dirichlet problem of the quasi-linear elliptic system \begin{eqnarray*} -e^{-f(U)}div(e^{f(U)}\bigtriangledown U)+&{1/2}f'(U)|\bigtriangledown U|^2&=0, {in $\Omega$}, & U|_{\partial\Omega}&=\phi. \end{eqnarray*} Here $\Omega$ a smooth bounded ... More

A Novel Feature-based Bayesian Model for Query Focused Multi-document SummarizationDec 10 2012Dec 27 2013Both supervised learning methods and LDA based topic model have been successfully applied in the field of query focused multi-document summarization. In this paper, we propose a novel supervised approach that can incorporate rich sentence features into ... More

Edge-grafting theorems on permanents of the Laplacian matrices of graphs and their applicationsJun 20 2012The trees, respectively unicyclic graphs, on $n$ vertices with the smallest Laplacian permanent are studied. In this paper, by edge-grafting transformations, the $n$-vertex trees of given bipartition having the second and third smallest Laplacian permanent ... More

Thermal conductivity of one-dimensional lattices with self-consistent heat baths: a heuristic derivationFeb 04 2009We derive the thermal conductivities of one-dimensional harmonic and anharmonic lattices with self-consistent heat baths (BRV lattice) from the Single-Mode Relaxation Time (SMRT) approximation. For harmonic lattice, we obtain the same result as previous ... More

Angular momentum transport in a multicomponent solar wind with differentially flowing, thermally anisotropic ionsDec 09 2008The Helios measurements of the angular momentum flux $L$ for the fast solar wind show that the individual ion contributions, $L_p$ and $L_\alpha$, tend to be negative (i.e., in the sense of counter-rotation with the Sun). However, the opposite holds for ... More

Unconditionally Secure Quantum Bit Commitment Protocols Based on Correlation Immune Boolean FunctionJul 14 2006Aug 10 2006A class of quantum protocols of bit commitment is constructed based on the nonorthogonal states coding and the correlation immunity of some Boolean functions. The binding condition of these protocols is guaranteed mainly by the law of causality and the ... More

Engineering two-mode squeezed states of cold atomic clouds with a superconducting stripline resonatorSep 16 2010A scheme is proposed for engineering two-mode squeezed states of two separated cold atomic clouds positioned near the surface of a superconducting stripline resonator. Based on the coherent magnetic coupling between the atomic spins and a stripline resonator ... More

Optomechanical photon shuttling between photonic cavitiesSep 03 2014Mechanical motion of photonic devices driven by optical forces provides a profound means of coupling between optical fields. The current focus of these optomechanical effects has been on cavity optomechanics systems in which co-localized optical and mechanical ... More

Existence and exponential stability of positive almost periodic solution for Nicholson's blowflies models on time scalesAug 05 2015Nov 12 2015In this paper, we first give a new definition of almost periodic time scales, two new definitions of almost periodic functions on time scales and investigate some basic properties of them. Then, as an application, by using the fixed point theorem in Banach ... More

On some conformally invariant fully nonlinear equations, Part II: Liouville, Harnack and YamabeMar 25 2004The Yamabe problem concerns finding a conformal metric on a given closed Riemannian manifold so that it has constant scalar curvature. This paper concerns mainly a fully nonlinear version of the Yamabe problem and the corresponding Liouville type problem. ... More

Polynomial invariants of degree 4 for even-$n$ qubits and their applications in entanglement classificationAug 11 2013We develop a simple method for constructing polynomial invariants of degree 4 for even-$n$ qubits and give explicit expressions for these polynomial invariants. We demonstrate the invariance of the polynomials under stochastic local operations and classical ... More

Gradient Estimates for Parabolic Systems from Composite MaterialMay 07 2011Jul 05 2012In this paper we derive $W^{1,\infty}$ and piecewise $C^{1,\alpha}$ estimates for solutions, and their $t-$derivatives, of divergence form parabolic systems with coefficients piecewise H\"older continuous in space variables $x$ and smooth in $t$. This ... More

MB-tensors and MB0-tensorsNov 24 2014Dec 01 2014The class of MB(MB0)-tensors, which is a generation of B(B0)-tensors and quasi-double B(B0)-tensors, is proposed. And we prove that an even order symmetric MB(MB0)-tensor is positive (semi-)definite. This provides a positive answer for the conjecture ... More

Double B-tensor and quasi-double B-tensorAug 11 2014In this paper, we propose two new classes of tensors: double B-tensors and quasi-double B-tensors, give some properties of double B-tensors and quasi-double B-tensors, discuss their relationships with B-tensors and positive definite tensors and show that ... More

Implicit Asymptotic Preserving Method for Linear Transport EquationsFeb 01 2016The computation of the radiative transfer equation is expensive mainly due to two stiff terms: the transport term and the collision operator. The stiffness in the former comes from the fact that particles (such as photons) travels at the speed of light, ... More

Towards Label Imbalance in Multi-label Classification with Many LabelsApr 05 2016In multi-label classification, an instance may be associated with a set of labels simultaneously. Recently, the research on multi-label classification has largely shifted its focus to the other end of the spectrum where the number of labels is assumed ... More

A New Unified Theory of Electromagnetic and Gravitational InteractionsNov 04 2015Mar 30 2016In this paper we present a new unified theory of electromagnetic and gravitational interactions. By considering a four-dimensional spacetime as a hypersurface embedded in a five-dimensional bulk spacetime, we derive the complete set of field equations ... More

Quantum Criticality and DBI Magneto-resistanceAug 08 2016Sep 01 2016We use the DBI action from string theory and holography to study the magneto-resistance at quantum criticality with hyperscaling violation. We find and analyze a rich class of scaling behaviors for the magneto-resistance. A special case describes the ... More

Network analysis of the state space of chaotic map in digital domainOct 28 2014Nov 04 2014Complex dynamics of chaotic maps under an infinite-precision mathematical framework have been well known. The case in a finite-precision computer remains to be further explored. Previous work treated a digital chaotic map as a black box and gave different ... More

Uniqueness of positive bound states to Schrodinger systems with critical exponentsAug 02 2007We prove the uniqueness for the positive solutions of the following elliptic systems: \begin{eqnarray*} \left\{\begin{array}{ll} - \lap (u(x)) = u(x)^{\alpha}v(x)^{\beta} - \lap (v(x)) = u(x)^{\beta} v(x)^{\alpha} \end{array} \right. \end{eqnarray*} Here ... More

Novel Algorithm for Sparse Solutions to Linear Inverse Problems with Multiple MeasurementsMay 20 2009In this report, a novel efficient algorithm for recovery of jointly sparse signals (sparse matrix) from multiple incomplete measurements has been presented, in particular, the NESTA-based MMV optimization method. In a nutshell, the jointly sparse recovery ... More

Beat the Rayleigh limit: OAM based super-resolution diffraction tomographyJun 27 2013This letter is the first to report that a super-resolution imaging beyond the Rayleigh limit can be achieved by using classical diffraction tomography (DT) extended with orbital angular momentum (OAM), termed as OAM based diffraction tomography (OAM-DT). ... More

The neighbor-scattering number can be computed in polynomial time for interval graphsMar 17 2006Neighbor-scattering number is a useful measure for graph vulnerability. For some special kinds of graphs, explicit formulas are given for this number. However, for general graphs it is shown that to compute this number is NP-complete. In this paper, we ... More

Characters and patterns of communities in networksJan 14 2013In this paper, we propose some new notions to characterize and analyze the communities. The new notions are general characters of the communities or local structures of networks. At first, we introduce the notions of internal dominating set and external ... More

Chemical distances for percolation of planar Gaussian free fields and critical random walk loop soupsMay 14 2016Aug 29 2016We initiate the study on chemical distances of percolation clusters for level sets of two-dimensional discrete Gaussian free fields as well as loop clusters generated by two-dimensional random walk loop soups. One of our results states that the chemical ... More

Asymmetric optical amplifier based on PT-symmetryNov 19 2012We design and optimize a waveguide structure consisted of three segments of PT-symmetric coupler. It can amplify the difference mode with the attenuation of the sum mode, so performs an asymmetric optical amplifier. Also, the dependence of the amplification ... More

The generalized connectivity of complete bipartite graphsDec 28 2010Let $G$ be a nontrivial connected graph of order $n$, and $k$ an integer with $2\leq k\leq n$. For a set $S$ of $k$ vertices of $G$, let $\kappa (S)$ denote the maximum number $\ell$ of edge-disjoint trees $T_1,T_2,...,T_\ell$ in $G$ such that $V(T_i)\cap ... More

Homogeneous solutions of stationary Navier-Stokes equations with isolated singularities on the unit sphere. I. One singularitySep 26 2016We classify all $(-1)-$homogeneous axisymmetric no swirl solutions of incompressible stationary Navier-Stokes equations in three dimension which are smooth on the unit sphere minus the south pole, parameterize them as a two dimensional surface with boundary, ... More

Controlled generation of field squeezing with cold atomic clouds coupled to a superconducting transmission line resonatorFeb 26 2010We propose an efficient method for controlled generation of field squeezing with cold atomic clouds trapped close to a superconducting transmission line resonator. It is shown that, based on the coherent strong magnetic coupling between the collective ... More

Model-Checking of Linear-Time Properties Based on Possibility MeasureMar 10 2012Sep 25 2016We study the LTL model-checking in possibilistic Kripke structure using possibility measure. First, the notion of possibilistic Kripke structure and the related possibility measure are introduced, then model-checking of reachability and repeated reachability ... More

Classification of general n-qubit states under stochastic local operations and classical communication in terms of the rank of coefficient matrixJun 30 2011May 04 2012We solve the entanglement classification under stochastic local operations and classical communication (SLOCC) for general n-qubit states. For two arbitrary pure n-qubit states connected via local operations, we establish an equation between the two coefficient ... More

Rank-based SLOCC classification for odd n qubitsJun 21 2011We study the entanglement classification under stochastic local operations and classical communication (SLOCC) for odd n-qubit pure states. For this purpose, we introduce the rank with respect to qubit i for an odd n-qubit state. The ranks with respect ... More

SLOCC determinant invariants of order 2^{n/2} for even n qubitsJun 17 2011Feb 02 2012In this paper, we study SLOCC determinant invariants of order 2^{n/2} for any even n qubits which satisfy the SLOCC determinant equations. The determinant invariants can be constructed by a simple method and the set of all these determinant invariants ... More

Higher cohomology of the pluricanonical bundle is not deformation invariantDec 01 2006Jan 16 2008In this paper, we compute the dimensions of the 1st and 2nd cohomology groups of all the pluricanonical bundles for Hirzebruch surfaces, and the dimensions of the 1st and 2nd cohomology groups of the second pluricanonical bundles for a blow-up of a projective ... More

$q,t$-Catalan numbers and generators for the radical ideal defining the diagonal locus of $(\C^2)^n$Sep 09 2009Let $I$ be the ideal generated by alternating polynomials in two sets of $n$ variables. Haiman proved that the $q,t$-Catalan number is the Hilbert series of the graded vector space $M(=\bigoplus_{d_1,d_2}M_{d_1,d_2})$ spanned by a minimal set of generators ... More

Production and rescattering of strange baryons at SPS energies in a transport model with hadron potentialsOct 13 2010A mean-field potential version of the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) model is used to investigate the production of strange baryons, especially the $\Lambda$s and $\overline{\Lambda}$s, from heavy ion collisions at SPS energies. ... More

On the Lagrangian angle and the Kähler angle of immersed surfaces in the complex plane $\bbc^2$Nov 09 2015In this paper, we discuss the Lagrangian angle and the K\"ahler angle of immersed surfaces in $\mathbb C^2$. Firstly, we provide an extension of Lagrangian angle, Maslov form and Maslov class to more general surfaces in $\mathbb C^2$ than Lagrangian surfaces, ... More

Constraints and Soliton Solutions for the KdV Hierarchy and AKNS HierarchyNov 26 2010It is well-known that the finite-gap solutions of the KdV equation can be generated by its recursion operator.We generalize the result to a special form of Lax pair, from which a method to constrain the integrable system to a lower-dimensional or fewer ... More

The Lawson homology and Deligne-Beilinson cohomology for Fulton-MacPherson configuration spacesSep 28 2006In this paper, we compute the Lawson homology groups and Deligne-Beilinson cohomology groups for Fulton-MacPherson configuration spaces. The explicit formulas are given.

Query-focused Multi-document Summarization: Combining a Novel Topic Model with Graph-based Semi-supervised LearningDec 10 2012Dec 31 2013Graph-based semi-supervised learning has proven to be an effective approach for query-focused multi-document summarization. The problem of previous semi-supervised learning is that sentences are ranked without considering the higher level information ... More

Electromagnetic Force on a BraneSep 29 2016A fundamental assumption in the theory of brane world is that all matter and radiation are confined on the four-dimensional brane and only gravitons can propagate in the five-dimensional bulk spacetime. The brane world theory did not provide an explanation ... More

Nonlinear differentiation equation and analytic function spacesOct 09 2015In this paper we consider the nonlinear complex differential equation $$(f^{(k)})^{n_{k}}+A_{k-1}(z)(f^{(k-1)})^{n_{k-1}}+\cdot\cdot\cdot+A_{1}(z)(f')^{n_{1}}+A_{0}(z)f^{n_{0}}=0, $$where $ A_{j}(z)$, $ j=0, \cdots, k-1 $, are analytic in the unit disk ... More

Note on two results on the rainbow connection number of graphsOct 23 2011An edge-colored graph $G$, where adjacent edges may be colored the same, is rainbow connected if any two vertices of $G$ are connected by a path whose edges have distinct colors. The rainbow connection number $rc(G)$ of a connected graph $G$ is the smallest ... More

Temperature dependence of thermal conductivity in 1D nonlinear latticesMar 22 2007We examine the temperature dependence of thermal conductivity of one dimensional nonlinear (anharmonic) lattices with and without on-site potential. It is found from computer simulation that the heat conductivity depends on temperature via the strength ... More

Some Numerical Results For Ito EquationJan 21 2013By the method of invariant manifold, we investigate the Ito equation numerically with high precision. By the numerical results, we can completely determine the form of analytic soliton solutions for the Ito equation. In fact, by the numerical data we ... More

A Novel Algorithm for Compressive Sensing: Iteratively Reweighed Operator Algorithm (IROA)Mar 28 2009Compressive sensing claims that the sparse signals can be reconstructed exactly from many fewer measurements than traditionally believed necessary. One of issues ensuring the successful compressive sensing is to deal with the sparsity-constraint optimization. ... More

Solutions for Toda systems on Riemann surfacesApr 19 2005Aug 26 2005In this paper, we study the solutions of Toda systems on Riemann surface in the critical case, we prove a sufficient condition for the existence of solutions of Toda systems.

Structure of Hochschild cohomology of path algebras and differential formulation of Euler's polyhedron formulaOct 11 2010Jun 24 2012This article studies the Lie algebra $Diff(K\Gamma)$ of derivations on the path algebra $K\Gamma$ of a quiver $\Gamma$ and the Lie algebra on the first Hochschild cohomology group $H^1(K\Gamma)$. We relate these Lie algebras to the algebraic and combinatorial ... More

A general Liouville type theorem for some conformally invariant fully nonlinear equationsJan 21 2003We establish a general Liouville type theorem for conformally invariant fully nonlinear equations.

Fluctuation limits of the super-Brownian motion with a single point catalystNov 02 2009Oct 20 2014We prove a fluctuating limit theorem of a sequence of super-Brownian motions over $\mbb{R}$ with a single point catalyst. The weak convergence of the processes on the space of Schwarz distributions is established. The limiting process is an Ornstein-Uhlenbeck ... More

Primary visual cortex as a saliency map: parameter-free prediction of behavior from V1 physiologyNov 02 2014It has been hypothesized that neural activities in the primary visual cortex (V1) represent a saliency map of the visual field to exogenously guide attention. This hypothesis has so far provided only qualitative predictions and their confirmations. We ... More