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Efficient quantum repeater in perspectives of both entanglement concentration rate and LOCC complexityOct 08 2017Quantum entanglement is an indispensable resource for many significant quantum information processing tasks. However, because of the noise in quantum channels, it is difficult to distribute quantum entanglement over a long distance in practice. A solution ... More

Decomposition of Quantum Markov Chains and Its ApplicationsAug 22 2016Feb 14 2018Markov chains have been widely employed as a fundamental model in the studies of probabilistic and stochastic communicating and concurrent systems. It is well-understood that decomposition techniques play a key role in reachability analysis and model-checking ... More

The Structure of Decoherence-free SubsystemsFeb 14 2018Decoherence-free subsystems have been successfully developed as a tool to preserve fragile quantum information against noises. In this letter, we develop a structure theory for decoherence-free subsystems. Based on it, we present an effective algorithm ... More

Super-activating Quantum Memory with EntanglementAug 02 2017Nov 21 2018Noiseless subsystems were proved to be an efficient and faithful approach to preserve fragile information against decoherence in quantum information processing and quantum computation. They were employed to design a general (hybrid) quantum memory cell ... More

From independent sets and vertex colorings to isotropic spaces and isotropic decompositionsApr 08 2019In the 1970's, Lov\'asz built a bridge between graphs and alternating matrix spaces, in the context of perfect matchings (FCT 1979). A similar connection between bipartite graphs and matrix spaces plays a key role in the recent resolutions of the non-commutative ... More

A Product Line Systems Engineering Process for Variability Identification and ReductionJun 12 2018Software Product Line Engineering has attracted attention in the last two decades due to its promising capabilities to reduce costs and time to market through reuse of requirements and components. In practice, developing system level product lines in ... More

Barrier tunneling of the Loop-Nodal Semimetal in the Hyperhoneycomb latticeJan 09 2018We theoretically investigate the barrier tunneling in the three-dimensional model of the hyperhoneycomb lattice, which is a nodal-line semimetal with a Dirac loop at zero energy. In the presence of a rectangular potential, the scattering amplitudes for ... More

A Nonlinear Pairwise Swapping Dynamics to Model the Selfish Rerouting Evolutionary GameMay 22 2013Mar 11 2015In this paper, a nonlinear revision protocol is proposed and embedded into the traffic evolution equation of the classical proportional-switch adjustment process (PAP), developing the present nonlinear pairwise swapping dynamics (NPSD) to describe the ... More

Hey, you, keep away from my device: remotely implanting a virus expeller to defeat Mirai on IoT devicesJun 19 2017Mirai is botnet which targets out-of-date Internet-of-Things (IoT) devices. The disruptive Distributed Denial of Service (DDoS) attack last year has hit major Internet companies, causing intermittent service for millions of Internet users. Since the affected ... More

Zero and Few Shot Learning with Semantic Feature Synthesis and Competitive LearningOct 19 2018Zero-shot learning (ZSL) is made possible by learning a projection function between a feature space and a semantic space (e.g.,~an attribute space). Key to ZSL is thus to learn a projection that is robust against the often large domain gap between the ... More

Transferrable Feature and Projection Learning with Class Hierarchy for Zero-Shot LearningOct 19 2018Zero-shot learning (ZSL) aims to transfer knowledge from seen classes to unseen ones so that the latter can be recognised without any training samples. This is made possible by learning a projection function between a feature space and a semantic space ... More

Zero-Shot Learning with Sparse Attribute PropagationDec 11 2018Mar 18 2019Zero-shot learning (ZSL) aims to recognize a set of unseen classes without any training images. The standard approach to ZSL requires a set of training images annotated with seen class labels and a semantic descriptor for seen/unseen classes (attribute ... More

$Q|SI\rangle$: A Quantum Programming EnvironmentOct 26 2017This paper describes a quantum programming environment, named $Q|SI\rangle$. It is a platform embedded in the .Net language that supports quantum programming using a quantum extension of the $\mathbf{while}$-language. The framework of the platform includes ... More

Decomposition of Quantum Markov Chains and Zero-error CapacityAug 22 2016Markov chains have been widely applied in information theory and various areas of its applications. Quantum Markov chains are a natural quantum extension of Markov chains. This paper studies irreducibility and periodicity of (discrete time) quantum Markov ... More

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

The Dirichlet problem for fully nonlinear elliptic equations on Riemannian manifoldsMar 10 2014Aug 29 2018We solve the Dirichlet problem for fully nonlinear elliptic equations on Riemannian manifolds under essentially optimal structure conditions, especially with no restrictions to the curvature of the underlying manifold and the second fundamental form of ... More

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

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

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

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

Second Order Estimates and Regularity for Fully Nonlinear Elliptic Equations on Riemannian ManifoldsNov 01 2012We derive a priori second order estimates for solutions of a class of fully nonlinear elliptic equations on Riemannian manifolds under some very general structure conditions. We treat both equations on closed manifolds, and the Dirichlet problem on manifolds ... More

Model Checking Applied to Quantum PhysicsFeb 08 2019Model checking has been successfully applied to verification of computer hardware and software, communication systems and even biological systems. In this paper, we further push the boundary of its applications and show that it can be adapted for applications ... More

Visualizing the elongated vortices in $γ$-Ga nanostripsJan 21 2015Apr 03 2016We study the magnetic response of superconducting $\gamma$-Ga via low temperature scanning tunneling microscopy and spectroscopy. The magnetic vortex cores rely substantially on the Ga geometry, and exhibit an unexpectedly-large axial elongation with ... More

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

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

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

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

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

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

On estimates for fully nonlinear elliptic equations with Neumann boundary conditions on Riemannian ManifoldsNov 29 2018We derive gradient and second order {\em a priori} estimates for solutions of the Neumann problem for a general class of fully nonlinear elliptic equations on compact Riemannian manifolds with boundary. These estimates yield regularity and existence results. ... More

Restricted hom-Lie algebrasOct 06 2015The paper studies the structure of restricted hom-Lie algebras. More specifically speaking, we first give the equivalent definition of restricted hom-Lie algebras. Second, we obtain some properties of $p$-mappings and restrictable hom-Lie algebras. Finally, ... More

Hypersurfaces of constant curvature in Hyperbolic spaceOct 19 2010We show that for a very general and natural class of curvature functions, the problem of finding a complete strictly convex hypersurface satisfying f({\kappa}) = {\sigma} over (0,1) with a prescribed asymptotic boundary {\Gamma} at infinity has at least ... More

A Class of Extended Ishikawa Iterative Processes in Banach Spaces for Nonexpansive MappingsJun 29 2011A class of extended Ishikowa Iterative processes is proposed and studied, which involves many kinds of Mann and Ishikawa iterative processes. The main conclusion of the present work extends and generalizes some recent results of this research line.

Bernstein Polynomial Model for Nonparametric Multivariate DensityJan 22 2019In this paper, we study the Bernstein polynomial model for estimating the multivariate distribution functions and densities with bounded support. As a mixture model of multivariate beta distributions, the maximum (approximate) likelihood estimate can ... More

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

On a class of fully nonlinear elliptic equations on Hermitian manifoldsJan 24 2013We derive a priori $C^2$ estimates for a class of complex Monge-Ampere type equations on Hermitian manifolds. As an application we solve the Dirichlet problem for these equations under the assumption of existence of a subsolution; the existence result, ... More

Complex Monge-Ampere equations and totally real submanifoldsOct 09 2009We study the Dirichlet problem for complex Monge-Ampere equations in Hermitian manifolds with general (non-pseudoconvex) boundary. Our main result extends the classical theorem of Caffarelli, Kohn, Nirenberg and Spruck in the flat case. We also consider ... More

Complex Monge-Ampere equations on Hermitian manifoldsJun 18 2009We study complex Monge-Ampere equations on Hermitian manifolds, extending classical existence results of Yau and Aubin in the Kahler case, and those of Caffarelli, Kohn, Nirenberg and Spruck for the Dirichlet problem in $C^n$. As an application we generalize ... More

Fast model-fitting of Bayesian variable selection regression using the iterative complex factorization algorithmJun 29 2017Jul 30 2018Bayesian variable selection regression (BVSR) is able to jointly analyze genome-wide genetic datasets, but the slow computation via Markov chain Monte Carlo (MCMC) hampered its wide-spread usage. Here we present a novel iterative method to solve a special ... More

biggy: An Implementation of Unified Framework for Big Data Management SystemOct 22 2018Various tools, softwares and systems are proposed and implemented to tackle the challenges in big data on different emphases, e.g., data analysis, data transaction, data query, data storage, data visualization, data privacy. In this paper, we propose ... More

Comment on "Does Gluons Carry Half of the Nucleon Momentum?" by X. S. Chen et. al. (PRL103, 062001 (2009))Oct 27 2009The authors claim to have found a "proper", "gauge-invariant" definition of a charged-particle's momentum in gauge theory, which is more "superior" than the textbook version. I show that their result arises from a misunderstanding of gauge symmetry by ... More

Purely-Nonperturbative Composite Operators and Parton DistributionsMay 14 1997A class of purely-nonperturbative (PNP) composite operators is defined in Quantum Chromodynamics, which is perturbative scheme and scale independent and are useful to describe the internal structure of a strong interacting system. The operator product ... More

Off-Forward Parton DistributionsJul 13 1998Recently, there have been some interesting developments involving off-forward parton distributions of the nucleon, deeply virtual Compton scattering, and hard diffractive vector-meson production. These developments are triggered by the realization that ... More

BREAKUP OF HADRON MASSES AND ENERGY-MOMENTUM TENSOR OF QCDFeb 01 1995Hadron masses are shown to be separable in QCD into contributions of quark and gluon kinetic and potential energies, quark masses, and the trace anomaly. The separation is based on a study of the structure of the QCD energy-momentum tensor and its matrix ... More

Energy Dependence of Moments of Net-Proton, Net-Kaon, and Net-Charge Multiplicity Distributions at STARNov 22 2016One of the main goals of the RHIC Beam Energy Scan (BES) program is to study the QCD phase structure, which includes the search for the QCD critical point, over a wide range of chemical potential. Theoretical calculations predict that fluctuations of ... More

Proton Tomography Through Deeply Virtual Compton ScatteringMay 03 2016In this prize talk, I recall some of the history surrounding the discovery of deeply virtual Compton scattering, and explain why it is an exciting experimental tool to obtain novel tomographic pictures of the nucleons at Jefferson Lab 12 GeV facility ... More

Comment on "Spin and Orbital Angular Momentum in Gauge Theories" by X. S. Chen et. al. (PRL100, 232002 (2008))Oct 27 2008The individual parts of the total angular momentum operator in interacting theories cannot satisfy the canonical angular momentum commutation rule, including those proposed in the above paper. Furthermore, the operators in the new proposal a) are non-local ... More

Generalized Parton Distributions and the Spin Structure of the NucleonNov 09 2002Generalized parton distributions are a new type of hadronic observables which has recently stimulated great interest among theorists and experimentalists alike. Introduced to delineate the spin structure of the nucleon, the orbital angular momentum of ... More

Deeply Virtual Compton ScatteringSep 17 1996Apr 10 1997We study in QCD the physics of deeply-virtual Compton scattering (DVCS)---the virtual Compton process in the large s and small t kinematic region. We show that DVCS can probe a new type of off-forward parton distributions. We derive an Altarelli-Parisi ... More

HADRON SUBSTRUCTURE PROBED WITH HADRON BEAMSFeb 09 1995In this talk, I focus on the quark-gluon structure of hadrons probed using high-energy hadron beams. I start with a brief review on recent major achievements in measuring parton distributions of the nucleon, pion, and kaon, with hadron facilities at CERN ... More

Parton Physics on Euclidean LatticeMay 07 2013I show that the parton physics related to correlations of quarks and gluons on the light-cone can be studied through the matrix elements of frame-dependent, equal-time correlators in the large momentum limit. This observation allows practical calculations ... More

Viewing the Proton Through "Color"-FiltersApr 04 2003Jun 18 2003While the form factors and parton distributions provide separately the shape of the proton in coordinate and momentum spaces, a more powerful imaging of the proton structure can be obtained through phase-space distributions. Here we introduce the Wigner-type ... More

Gauge-Invariant Decomposition of Nucleon Spin and Its Spin-OffMar 08 1996I introduce a gauge invariant decomposition of the nucleon spin into quark helicity, quark orbital, and gluon contributions. The total quark (and hence the quark orbital) contribution is shown to be measurable through virtual Compton scattering in a special ... More

Interpolating the Nucleon's Spin-Dependent Sum Rules at High and Low EnergiesJul 20 1993I discuss a few interpolating sum rules for spin structure functions of the nucleon. Using the concept of duality, I argue that the $G_1$ sum rule, including the elastic contribution, is useful for learning higher twist matrix elements of the nucleon. ... More

Chiral-Odd and Spin-Dependent Quark Fragmentation Functions and their ApplicationsJul 08 1993We define a number of quark fragmentation functions for spin-0, -1/2 and -1 hadrons, and classify them according to their twist, spin and chirality. As an example of their applications, we use them to analyze semi-inclusive deep-inelastic scattering on ... More

Uncertainty Principle in Control Theory, Part I: Analysis of Performance LimitationsFeb 22 2014This paper investigates performance limitations and tradeoffs in the control design for linear time-invariant systems. It is shown that control specifications in time domain and in frequency domain are always mutually exclusive determined by uncertainty ... More

Higher Moments of Net-Kaon Multiplicity Distributions at STARNov 22 2016Fluctuations of conserved quantities such as baryon number (B), electric charge number (Q), and strangeness number (S), are sensitive to the correlation length and can be used to probe non-gaussian fluctuations near the critical point. Experimentally, ... More

Prime Graphs and Exponential Composition of SpeciesMay 01 2007Nov 10 2009In this paper, we enumerate prime graphs with respect to the Cartesian multiplication of graphs. We use the unique factorization of a connected graph into the product of prime graphs given by Sabidussi to find explicit formulas for labeled and unlabeled ... More

On Credit-based Incentive Mechanisms of Voluntary User Comment Reviewing in Social NetworksAug 14 2016With the recent advance of micro-blogs and social networks, people can view and post comments on the websites in a very convenient way. However, it is also a big concern that the malicious users keep polluting the cyber environment by scamming, spamming ... More

Dual method for continuous-time Markowitz's Problems with nonlinear wealth equationsJun 30 2008Continuous-time mean-variance portfolio selection model with nonlinear wealth equations and bankruptcy prohibition is investigated by the dual method. A necessary and sufficient condition which the optimal terminal wealth satisfies is obtained through ... More

On the cumulative Parisian ruin of multi-dimensional Brownian motion modelsNov 25 2018Consider a multi-dimensional Brownian motion which models different lines of business of an insurance company. Our main result gives an approximation for the cumulative Parisian ruin probability as the initial capital becomes large. An approximation for ... More

Complete invariant geodesic metrics on outer spaces and Jacobian varieties of tropical curvesNov 08 2012Let $\mathrm{Out}(F_n)$ be the outer automorphism group of the free group $F_n$. It acts properly on the outer space $X_n$ of marked metric graphs, which is a finite-dimensional infinite simplicial complex with some simplicial faces missing. In this paper, ... More

A Symplectic Multi-Particle Tracking Model for Self-Consistent Space-Charge SimulationOct 15 2016Symplectic tracking is important in accelerator beam dynamics simulation. So far, to the best of our knowledge, there is no self-consistent symplectic space-charge tracking model available in the accelerator community. In this paper, we present a two-dimensional ... More

HG-Caffe: Mobile and Embedded Neural Network GPU (OpenCL) Inference Engine with FP16 SupportingJan 03 2019Breakthroughs in the fields of deep learning and mobile system-on-chips are radically changing the way we use our smartphones. However, deep neural networks inference is still a challenging task for edge AI devices due to the computational overhead on ... More

Compression of Quantum Multi-Prover Interactive ProofsOct 10 2016We present a protocol that transforms any quantum multi-prover interactive proof into a nonlocal game in which questions consist of logarithmic number of bits and answers of constant number of bits. As a corollary, this proves that the promise problem ... More

Remarks on Entropy Formulae for Linear Heat EquationMay 02 2017May 17 2017In this note, we prove some new entropy formulae for linear heat equation on static Riemannian manifold with nonnegative Ricci curvature. The results are simpler versions of Cao and Hamilton's entropies for Ricci flow coupled with heat-type equations. ... More

Modified Ringel-Hall algebras, naive lattice algebras and lattice algebrasAug 13 2018For a given hereditary abelian category satisfying some finiteness conditions, in certain twisted cases it is shown that the modified Ringel-Hall algebra is isomorphic to the naive lattice algebra and there exists an epimorphism from the modified Ringel-Hall ... 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

A maximum rank problem for degenerate elliptic fully nonlinear equationsSep 21 2010Oct 10 2010The solutions to the Dirichlet problem for two degenerate elliptic fully nonlinear equations in $n+1$ dimensions, namely the real Monge-Amp\`ere equation and the Donaldson equation, are shown to have maximum rank in the space variables when $n \leq 2$. ... More

Partial Legendre transforms of non-linear equationsOct 11 2010The partial Legendre transform of a non-linear elliptic differential equation is shown to be another non-linear elliptic differential equation. In particular, the partial Legendre transform of the Monge-Amp\`ere equation is another equation of Monge-Amp\`ere ... More

The Asymptotic Dirichlet Problems on manifolds with unbounded negative curvatureJan 10 2014Elton P. Hsu used probabilistic method to show that the asymptotic Dirichlet problem is uniquely solvable under the curvature conditions $-C e^{2-\eta}r(x) \leq K_M(x)\leq -1$ with $\eta>0$. We give an analytical proof of the same statement. In addition, ... More

Sentence Correction Based on Large-scale Language ModellingSep 22 2017Nov 02 2017With the further development of informatization, more and more data is stored in the form of text. There are some loss of text during their generation and transmission. The paper aims to establish a language model based on the large-scale corpus to complete ... More

Simulation-Based Analytics for Fabrication Quality-Associated Decision SupportMar 18 2019Automated, data-driven quality management systems, which facilitate the transformation of data into useable information, are desired to enhance decision-making processes. Integration of accurate, reliable, and straightforward approaches that measure uncertainty ... More

High Order Numerical Integrators for Relativistic Charged Particle TrackingFeb 15 2017In this paper, we extend several time reversible numerical integrators to solve the Lorentz force equations from second order accuracy to higher order accuracy for relativistic charged particle tracking in electromagnetic fields. A fourth order algorithm ... More

A symplectic particle-in-cell model for space-charge beam dynamics simulationJan 12 2018Space-charge effects play an important role in high intensity particle accelerators and were studied using a variety of macroparticle tracking models. In this paper, we propose a symplectic particle-in-cell (PIC) model and compare this model with a recently ... More

On the Correctness of Inverted Index Based Public-Key Searchable Encryption Scheme for Multi-time SearchAug 24 2016In this short note we argue that the state-of-art inverted index based public key searchable encryption scheme proposed by Wang et al may not be completely correct by giving a counterexample.

Well-rounded equivariant deformation retracts of Teichmüller spacesFeb 04 2013Jan 22 2014In this paper, we construct spines, i.e., $\Mod_g$-equivariant deformation retracts, of the Teichm\"uller space $\T_g$ of compact Riemann surfaces of genus $g$. Specifically, we define a $\Mod_g$-stable subspace $S$ of positive codimension and construct ... More

Individual departure time decision considering departure scheduling utilityApr 24 2013Mar 09 2015The scheduling utility plays a fundamental role in addressing the commuting travel behaviours. In this paper, a new scheduling utility, termed as DMRD-SU, was suggested based on some recent research findings in behavioural economics. DMRD-SU admitted ... More

Localization Trajectory and Chern-Simons axion coupling for Bilayer Quantum Anomalous Hall SystemsDec 07 2018Quantum anomalous Hall (QAH) multilayers provide a platform of topological materials with high Chern numbers. We investigate the localization routes of bilayer QAH systems with Chern number C = 2 under strong disorder, by numerical simulations on their ... More

Localization Trajectory and Chern-Simons axion coupling for Bilayer Quantum Anomalous Hall SystemsDec 07 2018Mar 12 2019Quantum anomalous Hall (QAH) multilayers provide a platform of topological materials with high Chern numbers. We investigate the localization routes of bilayer QAH systems with Chern number C = 2 under strong disorder, by numerical simulations on their ... More

Detection of a superconducting phase in a two-atom layer of hexagonal Ga film grown on semiconducting GaN(0001)Mar 24 2014Jan 17 2015The recent observation of superconducting state at atomic scale has motivated the pursuit of exotic condensed phases in two-dimensional (2D) systems. Here we report on a superconducting phase in two-monolayer crystalline Ga films epitaxially grown on ... More

Analytic adjoint ideal sheaves associated to plurisubharmonic functionsApr 25 2016In this article, we will present that the analytic adjoint ideal sheaves associated to plurisubharmonic functions are not coherent.

Strong openness conjecture for plurisubharmonic functionsNov 15 2013In this article, we give a proof of the strong openness conjecture for plurisubharmonic functions posed by Demailly.

Strong openness conjecture and related problems for plurisubharmonic functionsJan 28 2014In this article, we solve the strong openness conjecture on the multiplier ideal sheaves for the plurisubharmonic functions posed by Demailly. We prove two conjectures about the growth of the volumes of the sublevel sets of plurisubharmonic functions ... More

Quantum Criticality of 1D Attractive Fermi GasOct 06 2010Aug 10 2011We obtain an analytical equation of state for one-dimensional strongly attractive Fermi gas for all parameter regime in current experiments. From the equation of state we derive universal scaling functions that control whole thermodynamical properties ... More

Stabilizer Circuits, Quadratic Forms, and Computing Matrix RankMar 29 2019Apr 05 2019We show that a form of strong simulation for $n$-qubit quantum stabilizer circuits $C$ is computable in $O(s + n^\omega)$ time, where $\omega$ is the exponent of matrix multiplication. Solution counting for quadratic forms over $\mathbb{F}_2$ is also ... More

A unified approach to the thermodynamics and quantum scaling functions of one-dimensional strongly attractive $SU(w)$ Fermi GasesAug 26 2017In this letter we present a unified derivation of the pressure equation of states, thermodynamics and scaling functions for the one-dimensional (1D) strongly attractive Fermi gases with $SU(w)$ symmetry. These physical quantities provide a rigorous understanding ... More

Small-world MCMC and convergence to multi-modal distributions: From slow mixing to fast mixingMar 01 2007We compare convergence rates of Metropolis--Hastings chains to multi-modal target distributions when the proposal distributions can be of ``local'' and ``small world'' type. In particular, we show that by adding occasional long-range jumps to a given ... More

Zero-Shot Learning with Sparse Attribute PropagationDec 11 2018Zero-shot learning (ZSL) aims to recognize a set of unseen classes without any training images. The standard approach to ZSL requires a semantic descriptor for each class/instance, with attribute vector being the most widely used. Attribute annotation ... More

Domain-Invariant Projection Learning for Zero-Shot RecognitionOct 19 2018Zero-shot learning (ZSL) aims to recognize unseen object classes without any training samples, which can be regarded as a form of transfer learning from seen classes to unseen ones. This is made possible by learning a projection between a feature space ... More

Maximally symmetric subspace decomposition of the Schwarzschild black holeJun 28 2004The well-known Schwarzschild black hole was first obtained as a stationary, spherically symmetric solution of the Einstein's vacuum field equations. But until thirty years later, efforts were made for the analytic extension from the exterior area $(r>2GM)$ ... More

Cutoffs for product chainsJan 23 2017Feb 09 2017In this article, we consider products of ergodic Markov chains and discuss their cutoffs in the total variation. Through a new inequality relating the total variation and the Hellinger distance, we may identify the total variation cutoffs with cutoffs ... More

On the Variability Estimation of Lognormal Distribution Based on Sample Harmonic and Arithmetic MeansMar 11 2015For the lognormal distribution, an unbiased estimator of the squared coefficient of variation is derived from the relative ratio of sample arithmetic to harmonic means. Analytical proofs and simulation results are presented.

Estimation of weighted $L^2$ norm related to Demailly's Strong Openness ConjectureMar 18 2016In the present article, we obtain an estimation of the weighted $L^2$ norm near the singularities of plurisubharmonic weight related to Demailly's strong openness conjecture, which implies the convergence of the weighted $L^2$ norm.

On the periodicity of some Farhi arithmetical functionsMar 06 2009May 03 2009Let $k\in\mathbb{N}$. Let $f(x)\in \Bbb{Z}[x]$ be any polynomial such that $f(x)$ and $f(x+1)f(x+2)... f(x+k)$ are coprime in $\mathbb{Q}[x]$. We call $$g_{k,f}(n):=\frac{|f(n)f(n+1)... f(n+k)|}{\text{lcm}(f(n),f(n+1),...,f(n+k))}$$ a Farhi arithmetic ... More

Ground test of satellite constellation based quantum communicationNov 30 2016Satellite based quantum communication has been proven as a feasible way to achieve global scale quantum communication network. Very recently, a low-Earth-orbit (LEO) satellite has been launched for this purpose. However, with a single satellite, it takes ... More

Central limit theorem for linear spectral statistics of deformed Wigner matricesDec 04 2017Dec 11 2017We consider large-dimensional Hermitian random matrices of the form $W=M+\vartheta V$ where $M$ is a Wigner matrix and $V$ is a random or deterministic, real, diagonal matrix whose entries are independent of $M$. For a large class of diagonal matrices ... More

Planetesimal Accretion in Binary Systems: The Effects of Gas DissipationJun 25 2008Currently, one of major problems concerning planet formation theory in close binary systems is, the strong perturbation from the companion star can increase relative velocities ($\triangle V$) of planetesimals around the primary and thus hinder their ... More

CP violation in neutrino mixing with $δ= -π/2$ in $A_4$ Type-II seesaw modelMay 08 2015Nov 25 2015We study a class of models for neutrino mass matrix in Type-II seesaw with $A_4$ family symmetry. The resulting neutrino mass matrix can be naturally made to respect a $\mu-\tau$ exchange plus CP conjugate symmetry (GLS) with the CP violating phase $\delta$ ... More

Variable is Better Than Invariable: Stable Sparse VSS-NLMS Algorithms with Application to Estimating MIMO ChannelsNov 06 2013To estimate multiple-input multiple-output (MIMO) channels, invariable step-size normalized least mean square (ISSNLMS) algorithm was applied to adaptive channel estimation (ACE). Since the MIMO channel is often described by sparse channel model due to ... More