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Unsupervised Cross-spectral Stereo Matching by Learning to SynthesizeMar 04 2019Unsupervised cross-spectral stereo matching aims at recovering disparity given cross-spectral image pairs without any supervision in the form of ground truth disparity or depth. The estimated depth provides additional information complementary to individual ... More

Transient supersolid properties in an array of dipolar quantum dropletsJan 23 2019Mar 08 2019We study theoretically and experimentally the emergence of supersolid properties in a dipolar Bose-Einstein condensate. The theory reveals a ground state phase diagram with three distinct regimes - a regular Bose-Einstein condensate, incoherent and coherent ... More

High Resolution Molecular Spectroscopy for Producing Ultracold Absolute Ground-State $^{23}$Na$^{87}$Rb MoleculesOct 13 2017We report a detailed molecular spectroscopy study on the lowest excited electronic states of $^{23}\rm{Na}^{87}\rm{Rb}$ for producing ultracold $^{23}\rm{Na}^{87}\rm{Rb}$ molecules in the electronic, rovibrational and hyperfine ground state. Starting ... More

Exploring Few-Body Processes with an Ultracold Light-Heavy Bose-Bose MixtureNov 10 2016We report the observation of several few-body processes with an ultracold Bose-Bose mixture consisting of sodium and rubidium atoms and weakly-bound NaRb Feshbach dimers. Preparing a pure dimer sample and tuning the scattering length between Na and Rb ... More

High-resolution Internal State Control of Ultracold $^{23}$Na$^{87}$Rb MoleculesDec 30 2017We report the full control over the internal states of ultracold $^{23}$Na$^{87}$Rb molecules, including vibrational, rotational and hyperfine degrees of freedom. Starting from a sample of weakly bound Feshbach molecules, we realize the creation of molecules ... More

Observation of resonant scattering between ultracold heteronuclear Feshbach moleculesNov 10 2016Aug 15 2019We report the observation of a dimer-dimer inelastic collision resonance for ultracold Feshbach molecules made of bosonic sodium and rubidium atoms. This resonance, which we attribute to the crossing of the dimer-dimer threshold with a heteronuclear tetramer ... More

FreeSense:Indoor Human Identification with WiFi SignalsAug 11 2016Human identification plays an important role in human-computer interaction. There have been numerous methods proposed for human identification (e.g., face recognition, gait recognition, fingerprint identification, etc.). While these methods could be very ... More

Measurement of accelerator neutron radiation field spectrum by Extended Range Neutron Multisphere Spectrometers and unfolding programNov 10 2015This paper described a measurement of accelerator neutron radiation field at a transport beam line of Beijing-TBF. The experiment place was be selected around a Faraday Cup with a graphite target impacted by electron beam at 2.5GeV. First of all, we simulated ... More

Dipolar Collisions of Ultracold Ground-state Bosonic MoleculesDec 01 2018The dipolar collision between ultracold polar molecules is an important topic both by its own right from the fundamental point of view and for the successful exploration of many-body physics with strong and long-range dipolar interactions. Here, we report ... More

Transient supersolid properties in an array of dipolar quantum dropletsJan 23 2019We study theoretically and experimentally the emergence of supersolid properties in a dipolar Bose-Einstein condensate. The theory reveals a ground state phase diagram with three distinct regimes - a regular Bose-Einstein condensate, incoherent and coherent ... More

Collisions of ultracold ^{23}Na^{87}Rb molecules with controlled chemical reactivitiesJan 27 2018The collision of molecules at ultracold temperatures is of great importance for understanding the chemical interactions at the quantum regime. While much theoretical work has been devoted to this, experimental data are only available sparsely mainly due ... More

The Fate of the Higgs Mode in a Trapped Dipolar SupersolidJul 22 2019We theoretically investigate the spectrum of elementary excitations of a trapped dipolar quantum gas across the BEC-supersolid phase transition. Our calculations reveal the existence of distinct Higgs and Nambu-Goldstone modes that emerge from the softening ... More

View Inter-Prediction GAN: Unsupervised Representation Learning for 3D Shapes by Learning Global Shape Memories to Support Local View PredictionsNov 07 2018In this paper we present a novel unsupervised representation learning approach for 3D shapes, which is an important research challenge as it avoids the manual effort required for collecting supervised data. Our method trains an RNN-based neural network ... More

Seq-SG2SL: Inferring Semantic Layout from Scene Graph Through Sequence to Sequence LearningAug 19 2019Generating semantic layout from scene graph is a crucial intermediate task connecting text to image. We present a conceptually simple, flexible and general framework using sequence to sequence (seq-to-seq) learning for this task. The framework, called ... More

Studying Cultural Differences in Emoji Usage across the East and the WestApr 04 2019Global acceptance of Emojis suggests a cross-cultural, normative use of Emojis. Meanwhile, nuances in Emoji use across cultures may also exist due to linguistic differences in expressing emotions and diversity in conceptualizing topics. Indeed, literature ... More

Distant IE by Bootstrapping Using Lists and Document StructureJan 04 2016Distant labeling for information extraction (IE) suffers from noisy training data. We describe a way of reducing the noise associated with distant IE by identifying coupling constraints between potential instance labels. As one example of coupling, items ... More

Coherent heteronuclear spin dynamics in an ultracold spin-1 mixtureFeb 13 2015We report the observation of coherent heteronuclear spin dynamics driven by inter-species spin-spin interaction in an ultracold spinor mixture, which manifests as periodical and well correlated spin oscillations between two atomic species. In particular, ... More

Long-range states of the NaRb molecule near the Na($3^2S_{1/2}$)+Rb($5^2P_{3/2}$) asymptoteJan 09 2016We report a high-resolution spectroscopic investigation of the long-range states of the $^{23}$Na$^{87}$Rb molecule near its Na($3^2S_{1/2}$)+Rb($5^2P_{3/2}$) asymptote. This study was performed with weakly bound ultracold molecules produced via magneto-association ... More

The low-energy Goldstone mode in a trapped dipolar supersolidJun 11 2019A supersolid is a counter-intuitive state of matter that combines the frictionless flow of a superfluid with the crystal-like periodic density modulation of a solid. Since the first prediction in the 1950s, experimental efforts to realize this state have ... More

Y^2Seq2Seq: Cross-Modal Representation Learning for 3D Shape and Text by Joint Reconstruction and Prediction of View and Word SequencesNov 07 2018A recent method employs 3D voxels to represent 3D shapes, but this limits the approach to low resolutions due to the computational cost caused by the cubic complexity of 3D voxels. Hence the method suffers from a lack of detailed geometry. To resolve ... More

Creation of an ultracold gas of ground-state $^{23}\rm{Na}^{87}\rm{Rb}$ moleculesFeb 12 2016May 19 2016We report the successful production of an ultracold sample of absolute ground-state $^{23}$Na$^{87}$Rb molecules. Starting from weakly-bound Feshbach molecules formed via magneto-association, the lowest rovibrational and hyperfine level of the electronic ... More

Quantum correlations in dilute dipolar quantum droplets beyond the extended Gross-Pitaevskii equationApr 23 2019Dipolar quantum droplets are exotic quantum objects that are self-bound due to the subtle balance of attraction, repulsion and quantum correlations. Here we present a systematic study of the critical atom number of these self-bound droplets, comparing ... More

Entanglement in resonant photon scatteringSep 01 2005Sep 03 2005Single--photon which is initially uncorrelated with atom, will evolve to be entangled with the atom on their continuous kinetic variables in the process of resonant scattering. We find the relations between the entanglement and their physical control ... More

MIMS: Towards a Message Interface based Memory SystemJan 01 2013Memory system is often the main bottleneck in chipmultiprocessor (CMP) systems in terms of latency, bandwidth and efficiency, and recently additionally facing capacity and power problems in an era of big data. A lot of research works have been done to ... More

Application of canonical Hamiltonian formulation to nonlinear light-envelope propagationsJan 04 2014We first point out it is conditional to apply the variational approach to the nonlocal nonlinear Schr\"{o}dinger equation (NNLSE), that is, the response function must be an even function. Different from the variational approach, the canonical Hamiltonian ... More

Control momentum entanglement with atomic spontaneously generated coherenceJan 05 2007Feb 28 2007With atomic spontaneously generated coherence (SGC), we propose a novel scheme to coherently control the atom--photon momentum entanglement through atomic internal coherence. A novel phenomena of ``phase entanglement in momentum'' is proposed, and we ... More

EE-AE: An Exclusivity Enhanced Unsupervised Feature Learning ApproachMar 30 2019Unsupervised learning is becoming more and more important recently. As one of its key components, the autoencoder (AE) aims to learn a latent feature representation of data which is more robust and discriminative. However, most AE based methods only focus ... More

AMS-SFE: Towards an Alignment of Manifold Structures via Semantic Feature Expansion for Zero-shot LearningApr 12 2019Zero-shot learning (ZSL) aims at recognizing unseen classes with knowledge transferred from seen classes. This is typically achieved by exploiting a semantic feature space (FS) shared by both seen and unseen classes, i.e., attributes or word vectors, ... More

Adaptive Adjustment with Semantic Feature Space for Zero-Shot RecognitionMar 30 2019In most recent years, zero-shot recognition (ZSR) has gained increasing attention in machine learning and image processing fields. It aims at recognizing unseen class instances with knowledge transferred from seen classes. This is typically achieved by ... More

A Two-Layer Local Constrained Sparse Coding Method for Fine-Grained Visual CategorizationMay 11 2015Fine-grained categories are more difficulty distinguished than generic categories due to the similarity of inter-class and the diversity of intra-class. Therefore, the fine-grained visual categorization (FGVC) is considered as one of challenge problems ... More

Quantum data hiding with spontaneous parameter down-conversionJan 17 2003Aug 20 2003Here we analyze the practical implication of the existing quantum data hiding protocol with Bell states produced with optical downconverter. We show that the uncertainty for the producing of the Bell states with spontaneous parameter down-conversion should ... More

Quantum secret sharing without entanglementDec 10 2002After analysing the main quantum secret sharing protocol based on the entanglement states, we propose an idea to directly encode the qubit of quantum key distributions, and then present a quantum secret sharing scheme where only product states are employed. ... More

Preparation of multi-party entanglement of individual photons and atomic ensemblesAug 12 2002Nov 01 2003An experimental feasible scheme is proposed to generate Greenberger-Horne-Zeilinger (GHZ) type of maximal entanglement. Distinguishing from the previous schemes, this entanglement can be chosen between either atomic ensembles (stationary qubit) or individual ... More

Semidefinite programming relaxations for linear semi-infinite polynomial programmingSep 21 2015Oct 14 2015This paper studies a class of so-called linear semi-infinite polynomial programming (LSIPP) problems. It is a subclass of linear semi-infinite programming problems whose constraint functions are polynomials in parameters and index sets are basic semialgebraic ... More

High rate locally correctable codes via liftingApr 03 2013Feb 05 2014We present a general framework for constructing high rate error correcting codes that are locally correctable (and hence locally decodable if linear) with a sublinear number of queries, based on lifting codes with respect to functions on the coordinates. ... More

Transverse momentum broadening due to the multiple scatteringAug 12 1998Using the Drell-Yan process in hadron-nucleus collisions and deeply inelastic lepton-nucleus scattering (DIS) as examples, I show that the transverse momentum broadening can be expressed in terms of four-parton correlation functions. I argue that jet ... More

Nuclear Dependence in Transverse Momentum Distribution for Drell-Yan PairJan 30 1998In terms of multiple scattering picture, I compute the nuclear dependence in Drell-Yan transverse momentum distribution, $d\sigma / dQ^2 dq_T^2$, in hadron-nucleus collisions. I present the results for large $q_T$ region and discuss the possible suppression ... More

Nuclear Dependence in Drell-Yan Transverse Momentum DistributionNov 24 1997Nov 28 1997We calculate the nuclear enhancement in Drell-Yan transverse momentum distribution in hadron-nucleus collisions. In terms of multiple scattering picture, we compute the contributions from double scattering. Applying the generalized factorization theorem, ... More

The Discord-like Correlation of Bipartite CoherenceNov 01 2016Quantum discord is a measure of quantum correlation by the the mutual information difference between the state and the output state after the local von Neumann measurement, where the mutual information contained in a bipartite state is defined as the ... More

Coupled-channel scattering in 1+1 dimensional lattice modelApr 29 2013Based on the Lippmann-Schwinger equation approach, a generalized L\"uscher's formula in 1+1 dimensions for two particles scattering in both the elastic and coupled-channel cases in moving frames is derived. A 2D coupled-channel scattering lattice model ... More

Strict entanglement monotonicity under local operations and classical communicationApr 02 2019Entanglement monotone is defined as a convex measure of entanglement that does not increase on average under local operations and classical communication (LOCC). Here we call an entanglement monotone a strict entanglement monotone (SEM) if it decreases ... More

Latent Variable Algorithms for Multimodal Learning and Sensor FusionApr 23 2019Multimodal learning has been lacking principled ways of combining information from different modalities and learning a low-dimensional manifold of meaningful representations. We study multimodal learning and sensor fusion from a latent variable perspective. ... More

The Shape of X-ray Cavities in Galaxy Clusters: Probing Jet Properties and ViscosityAug 21 2014Mar 13 2015X-ray observations of galaxy clusters have detected numerous X-ray cavities, evolved from the interaction of AGN jets with the intracluster medium (ICM) and providing compelling evidence for the importance of jet-mode AGN feedback. Here we argue for the ... More

SDPTools: High Precision SDP Solver in MapleDec 21 2011Semidefinite programs are an important class of convex optimization problems. It can be solved efficiently by SDP solvers in Matlab, such as SeDuMi, SDPT3, DSDP. However, since we are running fixed precision SDP solvers in Matlab, for some applications, ... More

Oscillatory integrals related to Carleson's theorem: fractional monomialsMar 15 2015Stein and Wainger proved the $L^p$ bounds of the polynomial Carleson operator for all integer-power polynomials without linear term. In the present paper, we partially generalise this result to all fractional monomials in dimension one. Moreover, the ... More

On the U-module Structure of the Unipotent Specht Modules of Finite General Linear GroupsApr 16 2013Apr 17 2013Let $q$ be a prime power, $G=GL_n(q)$ and let $U\leqslant G$ be the subgroup of (lower) unitriangular matrices in $G$. For a partition $\lambda$ of $n$ denote the corresponding unipotent Specht module over the complex field $\C$ for $G$ by $S^\lambda$. ... More

Invariant foliations for stochastic partial differential equations with dynamic boundary conditionsNov 19 2013Invariant foliations are complicated random sets useful for describing and understanding the qualitative behaviors of nonlinear dynamical systems. We will consider invariant foliations for stochastic partial differential equation with dynamical boundary ... More

Spherically averaged maximal function and scattering for the 2D cubic derivative Schrödinger equationJul 02 2014Jan 21 2016We prove scattering for the 2D cubic derivative Schr\"odinger equation with small data in the critical Besov space with one degree angular regularity. The main new ingredient is that we prove a spherically averaged maximal function estimate for the 2D ... More

On the limiting velocity of random walks in mixing random environmentJun 27 2011Sep 10 2012We consider random walks in strong-mixing random Gibbsian environments in $\mathbb{Z}^d, d\ge 2$. Based on regeneration arguments, we will first provide an alternative proof of Rassoul-Agha's conditional law of large numbers (CLLN) for mixing environment ... More

Liouville theorems for stationary flows of shear thickening fluids in 2DJun 23 2012In this paper we consider the entire weak solutions $u$ of the equations for stationary flows of shear thickening fluids in the plane and prove Liouville theorems under the conditions on the finiteness of energy and under the integrability condition of ... More

A stability result on optimal Skorokhod embeddingJan 27 2017Motivated by the model- independent pricing of derivatives calibrated to the real market, we consider an optimization problem similar to the optimal Skorokhod embedding problem, where the embedded Brownian motion needs only to reproduce a finite number ... More

Combinatorial Yamabe flow on hyperbolic surfaces with boundaryMar 20 2010This paper studies the combinatorial Yamabe flow on hyperbolic surfaces with boundary. It is proved by applying a variational principle that the length of boundary components is uniquely determined by the combinatorial conformal factor. The combinatorial ... More

Local rigidity of inversive distance circle packingMar 08 2009Apr 02 2009A Euclidean (or hyperbolic) circle packing on a closed triangulated surface with prescribed inversive distance is locally determined by its cone angles. We prove this by applying a variational principle.

Operated semigroups, Motzkin paths and rooted treesOct 02 2007Combinatorial objects such as rooted trees that carry a recursive structure have found important applications recently in both mathematics and physics. We put such structures in an algebraic framework of operated semigroups. This framework provides the ... More

Quotient Problem For Entire Functions with Moving TargetsFeb 21 2019As an analogue of the Hadamard quotient problem in number theory, the quotient problem (in the sense of complex entire functions) for two sequences $F(n)=a_0+a_1f_1^n+\cdots+a_lf_l^n$ and $ G(n)=b_0+b_1g_1^n+\cdots+b_mg_m^n$, has been solved, where the ... More

An IRT-based Model for Omitted and Not-reached ItemsApr 07 2019Missingness is a common occurrence in educational assessment and psychological measurement. It could not be casually ignored as it may threaten the validity of the test if not handled properly. Considering the difference between omitted and not-reached ... More

Entanglement of individual photon and atomic ensemblesJun 07 2002Oct 27 2003Here we present an experimentally feasible scheme to entangle flying qubit (individual photon with polarization modes) and stationary qubit (atomic ensembles with long-lived collective excitations). This entanglement integrate two different species can ... More

Building Task-Oriented Visual Dialog Systems Through Alternative Optimization Between Dialog Policy and Language GenerationSep 06 2019Reinforcement learning (RL) is an effective approach to learn an optimal dialog policy for task-oriented visual dialog systems. A common practice is to apply RL on a neural sequence-to-sequence (seq2seq) framework with the action space being the output ... More

On the 1D Cubic NLS in an Almost Critical SpaceNov 03 2014We obtain the local well-posedness of the one dimensional cubic nonlinear Schr\"odinger Equation for initial data in the modulation space $M_{2, p}$ for all $2\le p<\infty$, which covers all the subcritical cases from the viewpoint of scaling. Moreover, ... More

The Discord-like Correlation of Bipartite CoherenceNov 01 2016Nov 08 2016Quantum discord is a measure of quantum correlation by the the mutual information difference between the state and the output state after the local von Neumann measurement, where the mutual information contained in a bipartite state is defined as the ... More

Visual Data Deblocking using Structural Layer PriorsJul 06 2015The blocking artifact frequently appears in compressed real-world images or video sequences, especially coded at low bit rates, which is visually annoying and likely hurts the performance of many computer vision algorithms. A compressed frame can be viewed ... More

Leading soft gluon production in high energy nuclear collisionsFeb 23 1999The leading soft gluon p_T distribution in heavy ion collisions was obtained by Kovner, McLerran, and Weigert after solving classical Yang-Mills equations. I show explicitly this result can be understood in terms of conventional QCD perturbation theory. ... More

LIME: A Method for Low-light IMage EnhancementMay 17 2016Jul 24 2016When one captures images in low-light conditions, the images often suffer from low visibility. This poor quality may significantly degrade the performance of many computer vision and multimedia algorithms that are primarily designed for high-quality inputs. ... More

Gluon mini-jet production in nuclear collisions at high energiesDec 04 1998We show explicitly that the leading soft gluon $p_T$ distribution, predicted by Kovner, McLerran, and Weigert after solving classical Yang-Mills equations, can be understood in terms of conventional QCD perturbation theory. We also demonstrate that the ... More

A coupled-channel formalism for three-body final state interactionMay 29 2015Jul 15 2016From dispersion relation approach, a formalism that describes final state interaction among three particles in a coupled-channel system is presented in this work. Different representations of coupled-channel three-body formalism with only spinless particles ... More

A VEST of the Pseudoinverse Learning AlgorithmMay 20 2018Aug 16 2018In this paper, we briefly review the basic scheme of the pseudoinverse learning (PIL) algorithm and present some discussions on the PIL, as well as its variants. The PIL algorithm, first presented in 1995, is a non-gradient descent and non-iterative learning ... More

Index of Equivariant Callias-Type Operators and Invariant Metrics of Positive Scalar CurvatureMar 15 2018Oct 17 2018For a Lie group G acting properly and isometrically on a Riemannian manifold M, we define G-Callias-type operators and show they have an index in the K-theory of the maximal group C*-algebra. The construction pairs a Dirac operator with an element of ... More

Semidefinite programming relaxations for linear semi-infinite polynomial programmingSep 21 2015Nov 14 2017This paper studies a class of so-called linear semi-infinite polynomial programming (LSIPP) problems. It is a subclass of linear semi-infinite programming problems whose constraint functions are polynomials in parameters and index sets are basic semialgebraic ... More

Cloud-based or On-device: An Empirical Study of Mobile Deep InferenceJul 14 2017Apr 15 2018Modern mobile applications are benefiting significantly from the advancement in deep learning, e.g., implementing real-time image recognition and conversational system. Given a trained deep learning model, applications usually need to perform a series ... More

Baxter Algebras and Umbral CalculusJul 09 2004We apply recent constructions of free Baxter algebras to the study of the umbral calculus. We give a characterization of the umbral calculus in terms of Baxter algebra. This characterization leads to a natural generalization of the umbral calculus that ... More

Single annulus estimates for the variation-norm Hilbert transforms along Lipschitz vector fieldsOct 17 2016Let v be a planar Lipschitz vector field. We prove that the r-th variation-norm Hilbert transform along v, composed with a standard Littlewood-Paley projection operator P_k, is bounded from L^2 to L^{2, \infty}, and from L^p to itself for all p>2. Here ... More

On a binary system of Prendiville: The cubic caseJan 24 2017Sep 23 2018We prove sharp decoupling inequalities for a class of two dimensional non-degenerate surfaces in R^5, introduced by Prendiville. As a consequence, we obtain sharp bounds on the number of integer solutions of the Diophantine systems associated with these ... More

Remarks on the maximal operator and Hilbert transform along variable parabolasMay 01 2015We prove the boundedness of the maximal operator and Hilbert transform along certain variable parabolas in $L^p$ for $p>p_0$ with some $p_0\in (1, 2)$. Connections with the Hilbert transform along vector fields and the polynomial Carleson's maximal operator ... More

The Broken Engine of SzilardOct 29 2014A crucial step in the operation of the Szilard engine is the isothermal expansion of a single particle system. This expansion, seemingly a natural consequence, is unable to proceed when the piston is considered appropriately to be a thermal system subject ... More

Information and Estimation over Binomial and Negative Binomial ModelsJul 31 2012In recent years, a number of results have been developed which connect information measures and estimation measures under various models, including, predominently, Gaussian and Poisson models. More recent results due to Taborda and Perez-Cruz relate the ... More

Exploring the capability and limits of the feedback mechanismMay 01 2003Feedback is a most important concept in control systems, its main purpose is to deal with internal and/or external uncertainties in dynamical systems, by using the on-line observed information. Thus, a fundamental problem in control theory is to understand ... More

Mappings of finite distortion of polynomial typeJan 18 2012Feb 01 2012Suppose that $f: \bR^n\to\bR^n$ is a mapping of $K$-bounded $p$-mean distortion for some $p>n-1$. We prove the equivalence of the following properties of $f$: doubling condition for $J(x,f)$ over big balls centered at origin, boundedness of multiplicity ... More

Local Well-posedness for dispersion generalized Benjamin-Ono equations in Sobolev spacesDec 10 2008Dec 21 2008We prove that the Cauchy problem for the dispersion generalized Benjamin-Ono equation \[\partial_t u+|\partial_x|^{1+\alpha}\partial_x u+uu_x=0,\ u(x,0)=u_0(x),\] is locally well-posed in the Sobolev spaces $H^s$ for $s>1-\alpha$ if $0\leq \alpha \leq ... More

Global Well-posedness of Korteweg-de Vries equation in $H^{-3/4}(\R)$Oct 20 2008Apr 20 2009We prove that the Korteweg-de Vries initial-value problem is globally well-posed in $H^{-3/4}(\R)$ and the modified Korteweg-de Vries initial-value problem is globally well-posed in $H^{1/4}(\R)$. The new ingredient is that we use directly the contraction ... More

Uniqueness in Calderón Problem with Partial Data for Less Smooth ConductivitiesJun 23 2012In this paper we study the inverse conductivity problem with partial data. Moreover, we show that, in dimension $n\geq 3$ the uniqueness of the Calder\'{o}n problem holds for the $C^{1}\bigcap H^{3/2, 2}$ conductivities.

A modified large-scale structure-preserving doubling algorithm for a large-scale Riccati equation from transport theoryJul 09 2014We consider the large scale nonsymmetric algebraic Riccati equation arising in transport theory, where the $n\times n$ coefficient matrices $B, C$ are symmetric and low-ranked and $A, E$ are rank one updates of nonsingular diagonal matrices. By introducing ... More

Spectral bound for separations in Eulerian digraphsNov 10 2015The spectra of digraphs, unlike those of graphs, is a relatively unexplored territory. In a digraph, a separation is a pair of sets of vertices X and Y such that there are no arcs from X and Y . For a subclass of eulerian digraphs, we give an bound on ... More

Asymptotic Spreading Fastened by Inter-Specific Coupled Nonlinearities: a Cooperative SystemAug 26 2010Jan 05 2012This paper is concerned with the asymptotic spreading of a Lotka-Volterra cooperative system. By using the theory of asymptotic spreading of nonautonomous equations, the asymptotic speeds of spreading of unknown functions formulated by a coupled system ... More

Mappings of finite distortion: Formation of exponential cuspMay 17 2010We consider a quasi-convex planar domain \Omega with a rectifiable boundary containing an exponential cusp and show that there is no homeomorphism f: \bR^2\to\bR^2 of finite distortion with \exp(\lambda K)\in L_{loc}^{1}(\bR^2) for some \lambda>0 such ... More

Information Measure as Time ComplexityMay 28 2016Jan 24 2017The concept of Shannon entropy of random variables was generalized to measurable functions in general, and to simple functions with finite values in particular. It is shown that the information measure of a function is related to the time complexity of ... More

Constructing UMEB from maximally entangled basisSep 13 2016Sep 15 2016A new way of constructing unextendible maximally entangled basis (UMEB) from maximally entangled basis (MEB) is proposed. Consequently, it is shown that if there is an $N$-member UMEB in $\mathbb{C}^d\otimes \mathbb{C}^d$, then there exists a $(qd)^2-q(d^2-N)$-member ... More

The 90/10 phenomenon in directed signed social networksApr 14 2016We empirical study the signs' property in the directed signed social networks of Slashdot and Epinions by using an reshuffled approach. Through calculating the entropy $S_{out}$ and the giant component $G$, we find an interesting 90/10 phenomenon: each ... More

Gluon Propagator and Heavy Quark Potential in an Anisotropic QCD PlasmaSep 23 2008The hard-loop resummed propagator in an anisotropic QCD plasma in general linear gauges are computed. We get the explicit expressions of the gluon propagator in covariant gauge, Coulomb gauge and temporal axial gauge. Considering one gluon exchange, the ... More

Information Measure as Time ComplexityMay 28 2016Oct 21 2016The concept of Shannon entropy of random variables was generalized to measurable functions in general, and to simple functions with finite values in particular. It is shown that the information measure of a function is related to the time complexity of ... More

Quantified-Self 2.0: Using Context-Aware Services for Promoting Gradual Behaviour ChangeOct 03 2016The recent development of smartphone and wearable sensor technologies enable general public to carry self-tracking tasks more easily. Much work has been devoted to life data collection and visualisation to help people with better self-understanding. We ... More

Exclusivity Regularized MachineMar 28 2016May 16 2016It has been recognized that the diversity of base learners is of utmost importance to a good ensemble. This paper defines a novel measurement of diversity, termed as exclusivity. With the designed exclusivity, we further propose an ensemble model, namely ... More

One spatial dimensional finite volume three-body interaction for a short-range potentialJul 11 2016In this work, we use McGuire's model to describe scattering of three spinless identical particles in one spatial dimension, we first present analytic solutions of Faddeev's equation for scattering of three spinless particles in free space. The three particles ... More

Quantum Sheaf Cohomology and Duality of Flag ManifoldsAug 02 2018We study the quantum sheaf cohomology of flag manifold with deformation of the tangent bundle and use the ring structure to derive how the deformation transforms under the biholomorphic duality of flag manifolds. Realized as the OPE ring of A/2-twisted ... More

A sparse grid discontinuous Galerkin method for the high-dimensional Helmholtz equation with variable coefficientsMay 22 2019The simulation of high-dimensional problems with manageable computational resource represents a long-standing challenge. In a series of our recent work [25, 17, 18, 24], a class of sparse grid DG methods has been formulated for solving various types of ... More

Nonscattering solutions to the $L^{2}$-supercritical NLS EquationsJan 12 2011Jan 20 2011We investigate the nonlinear Schr\"{o}dinger equation $iu_{t}+\Delta u+|u|^{p-1}u=0$ with $1+\frac{4}{N}<p<1+\frac{4}{N-2}$ (when $N=1, 2$, $1+\frac{4}{N}<p<\infty$) in energy space $H^1$ and study the divergent property of infinite-variance and nonradial ... More

Traveling Wave Solutions for Integro-Difference SystemsMay 17 2013Feb 18 2014This paper is concerned with the traveling wave solutions for integro-difference systems of higher order. By using Schauder fixed point theorem, the existence of traveling wave solutions is reduced to the existence of generalized upper and lower solutions. ... More

Surface Crouzeix-Raviart element for the Laplace-Beltrami equationDec 17 2018This paper is concerned with the nonconforming finite element discretization of geometric partial differential equations. In specific, we construct a surface Crouzeix-Raviart element on the linear approximated surface, analogous to a flat surface. The ... More

Properties of Free Baxter AlgebrasJul 09 2004The study of free Baxter algebras was started by Rota and Cartier thirty years ago. We continue this study by applying two recent constructions of free Baxter algebras. We investigate the basic structure of a free Baxter algebra, and characterize in detail ... More

Sharp spherically averaged Strichartz estimates for the Schrödinger equationJun 10 2014We prove generalized Strichartz estimates with weaker angular integrability for the Schr\"odinger equation. Our estimates are sharp except some endpoints. Then we apply these new estimates to prove the scattering for the 3D Zakharov system with small ... More

Matrix Models for Deconfinement and Their Perturbative CorrectionsSep 23 2014Nov 27 2014Matrix models for the deconfining phase transition in $SU(N)$ gauge theories have been developed in recent years. With a few parameters, these models are able to reproduce the lattice results of the thermodynamic quantities in the semi-quark gluon plasma(QGP) ... More