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Analytic Wavefunctions for Neutral Bulk Excitations in Fractional Quantum Hall FluidsJun 27 2013We show the model wavefunctions for the neutral collective modes in fractional quantum Hall (FQH) states have simple analytic forms obtained from judicially reducing the powers of selected pairs in the ground state Jastrow factor. This scheme of "pair ... More

Analytic Wavefunctions for Collective Modes in Fractional Quantum Hall FluidsMar 25 2013Apr 12 2013We show model wavefunctions for neutral collective modes in fractional quantum Hall (FQH) states have simple analytic forms obtained from judicially reducing the powers of selected pairs in the ground state Jastrow factor. This scheme of "pair excitations" ... More

On a problem of Yau regarding a higher dimensional generalization of the Cohn-Vossen inequalityApr 03 2011We show that a problem by Yau can not be true in general. The counterexamples are constructed based on the recent work of Wu and Zheng.

Emergent Commensurability from Hilbert Space Truncation in Fractional Quantum Hall FluidsDec 31 2018Jan 18 2019We show that model states of fractional quantum Hall fluids at all experimentally detected plateau can be uniquely determined by imposing translational invariance with a particular scheme of Hilbert space truncation motivated from physical local measurements. ... More

Dirac Cone Metric and the Origin of the Spin Connections in Monolayer GrapheneFeb 05 2014Jun 11 2015We show that the modulation of the hopping amplitudes in the honeycomb lattice of the monolayer graphene uniquely defines a metric which corresponds to the shape of the Dirac cone. The spin connection of this effective metric field can be obtained from ... More

Geometric Aspects and Neutral Excitations in the Fractional Quantum Hall EffectDec 10 2013In this thesis, I will present studies on the collective modes of the fractional quantum Hall states, which are bulk neutral excitations reflecting the incompressibility that defines the topological nature of these states. It was first pointed out by ... More

A characterization of Koiso's typed solitonsFeb 04 2008By extending Koiso's examples to the non-compact case, we construct complete gradient Kahler-Ricci solitons of various types on certain holomorphic line bundles over compact Kahler-Einstein manifolds. Moreover, a uniformization result on steady gradient ... More

Aspects of Three-body Interactions in Generic Fractional Quantum Hall Systems and Impact of Galilean Invariance BreakingJun 06 2018Nov 01 2018We derive full analytic expressions of three-body interactions from Landau level (LL) mixing in fractional quantum Hall (FQH) systems with Schrieffer-Wolff transformation. The formalism can be applied to any LL, and to very general systems without rotational ... More

Transformations between nonlocal and local integrable equationsApr 30 2017Recently, a number of nonlocal integrable equations, such as the PT-symmetric nonlinear Schrodinger (NLS) equation and PT-symmetric Davey-Stewartson equations, were proposed and studied. Here we show that many of such nonlocal integrable equations can ... More

On general rogue waves in the parity-time-symmetric nonlinear Schrodinger equationMar 14 2019This article addresses the question of general rogue-wave solutions in the nonlocal parity-time-symmetric nonlinear Schrodinger equation. By generalizing the previous bilinear Kadomtsev-Petviashvili reduction method, large classes of rogue waves are derived ... More

General rogue waves in the nonlocal PT-symmetric nonlinear Schrodinger equationNov 16 2017Rogue waves in the nonlocal PT-symmetric nonlinear Schrodinger (NLS) equation are studied by Darboux transformation. Three types of rogue waves are derived, and their explicit expressions in terms of Schur polynomials are presented. These rogue waves ... More

On the existence of specified cycles in bipartite tournamentsJun 20 2017For two integers $n\geq 3$ and $2\leq p\leq n$, we denote $D(n,p)$ the digraph obtained from a directed $n$-cycle by changing the orientations of $p-1$ consecutive arcs. In this paper, we show that a family of $k$-regular $(k\geq 3)$ bipartite tournament ... More

Graph Bayesian Optimization: Algorithms, Evaluations and ApplicationsMay 03 2018Nov 06 2018Network structure optimization is a fundamental task in complex network analysis. However, almost all the research on Bayesian optimization is aimed at optimizing the objective functions with vectorial inputs. In this work, we first present a flexible ... More

Filament Eruption and Its Reformation Caused by Emerging Magnetic FluxMar 04 2019We present observations of the eruption and then reformation of a filament caused by its nearby emerging magnetic flux. Driven by the emerging magnetic flux, the emerged positive fluxes moved toward and cancelled with its nearby negative fluxes, where ... More

Dynamics of Taxi-like Logistics Systems: Theory and Microscopic SimulationsJul 10 2018In this paper we study the dynamics of a class of bi-agent logistics systems consisting of two types of agents interacting on an arbitrary complex network. By approximating the system with simple microscopic models and solving them analytically, we reveal ... More

General rogue waves and their dynamics in several reverse time integrable nonlocal nonlinear equationsDec 16 2017A study of general rogue waves in some integrable reverse time nonlocal nonlinear equations is presented. Specifically, the reverse time nonlocal nonlinear Schr\"odinger (NLS) and nonlocal Davey-Stewartson (DS) equations are investigated, which are nonlocal ... More

Classification and Unification of the Microscopic Deterministic Traffic Models with Identical DriversApr 09 2015Oct 03 2015We show that all existing deterministic microscopic traffic models with identical drivers (including both two-phase and three-phase models) can be understood as special cases from a master model by expansion around well-defined ground states. This allows ... More

An Effective Model for Traffic Dynamics and the Nature of the Congested PhaseDec 15 2014A simple algorithm for constructing an effective traffic model is presented. The algorithm uses statistically well-defined quantities extracted from the flow-density plot, and the resulting effective model naturally captures and predicts many quantitative ... More

Multiplex Structures: Patterns of Complexity in Real-World NetworksSep 10 2010Sep 14 2010Complex network theory aims to model and analyze complex systems that consist of multiple and interdependent components. Among all studies on complex networks, topological structure analysis is of the most fundamental importance, as it represents a natural ... More

A Unified Framework for Pricing Credit and Equity DerivativesDec 21 2007Sep 20 2008We propose a model which can be jointly calibrated to the corporate bond term structure and equity option volatility surface of the same company. Our purpose is to obtain explicit bond and equity option pricing formulas that can be calibrated to find ... More

Generalized McKay Quivers, Root System and Kac-Moody AlgebrasFeb 19 2011Let $Q$ be a finite quiver and $G\subseteq\Aut(\mathbbm{k}Q)$ a finite abelian group. Assume that $\hat{Q}$ and $\Gamma$ is the generalized Mckay quiver and the valued graph corresponding to $(Q, G)$ respectively. In this paper we discuss the relationship ... More

Efficient Intersection Control for Minimally Guided Vehicles: A Self-Organised and Decentralized ApproachAug 15 2017An important question for the practical applicability of the highly efficient traffic intersection control is about the minimal level of intelligence the vehicles need to have so as to move beyond the traffic light control. We propose an efficient intersection ... More

Second-order cosmological perturbations. I. Produced by scalar-scalar coupling in synchronous gaugeOct 18 2017Feb 03 2019We present a systematic study of the 2nd order scalar, vector and tensor metric perturbations in the Einstein-de Sitter Universe in synchronous coordinates. For the scalar-scalar coupling between 1st order perturbations, we decompose the 2nd order perturbed ... More

On compact Hermitian manifolds with flat Gauduchon connectionsSep 08 2017Given a Hermitian manifold $(M^n,g)$, the Gauduchon connections are the one parameter family of Hermitian connections joining the Chern connection and the Bismut connection. We will call $\nabla^s = (1-\frac{s}{2})\nabla^c + \frac{s}{2}\nabla^b$ the $s$-Gauduchon ... More

Hirzebruch manifolds and positive holomorphic sectional curvatureNov 20 2016Dec 13 2016This paper is the first step in a systematic project to study examples of K\"ahler manifolds with positive holomorphic sectional curvature ($H > 0$). Previously Hitchin proved that any compact K\"ahler surface with $H>0$ must be rational and he constructed ... More

A Lattice Story of Proton SpinApr 08 2019In this contribution, I summarized the recent Lattice QCD consensuses on the quark helicity, plus the investigations on the gluon helicity and orbital angular momenta. The preliminary non-perturbative normalized and renormalized Ji quark and gluon angular ... More

Dynamics of high-order solitons in the nonlocal nonlinear Schrödinger equationsFeb 15 2018A study of high-order solitons in three nonlocal nonlinear Schr\"{o}dinger equations is presented, which includes the \PT-symmetric, reverse-time, and reverse-space-time nonlocal nonlinear Schr\"{o}dinger equations. General high-order solitons in three ... More

Unitarity Method with Spurious PoleJun 25 2008Dec 13 2008In unitarity cut method, compact input of on-shell tree level amplitudes is crucial to simplify calculations. Although BCFW on-shell recursion relation gives very compact tree level amplitudes, they usually contain spurious poles. In this paper, we present ... More

Dynamics of Rogue Waves in the Partially PT-symmetric Nonlocal Davey-Stewartson SystemsOct 19 2017In this work, we study the dynamics of rogue waves in the partially $\cal{PT}$-symmetric nonlocal Davey-Stewartson(DS) systems. Using the Darboux transformation method, general rogue waves in the partially $\cal{PT}$-symmetric nonlocal DS equations are ... More

Both necessary and sufficient conditions for Bayesian exponential consistencyDec 05 2008The last decade has seen a remarkable development in the theory of asymptotics of Bayesian nonparametric procedures. Exponential consistency has played an important role in this area. It is known that the condition of $f_0$ being in the Kullback-Leibler ... More

Artificial Intelligence in Intelligent Tutoring Robots: A Systematic Review and Design GuidelinesFeb 26 2019This study provides a systematic review of the recent advances in designing the intelligent tutoring robot (ITR), and summarises the status quo of applying artificial intelligence (AI) techniques. We first analyse the environment of the ITR and propose ... More

Skew group algebras of deformed preprojective algebrasMar 09 2010Mar 21 2010Suppose that $Q$ is a finite quiver and $G\subseteq \Aut(Q)$ is a finite group, $k$ is an algebraic closed field whose characteristic does not divide the order of $G$. For any algebra $\Lambda=kQ/{\mathcal {I}}$, $\mathcal {I}$ is an arbitrary ideal of ... More

A note on the almost one half holomorphic pinchingSep 08 2017Motivated by a previous work of Zheng and the second named author, we study pinching constants of compact K\"ahler manifolds with positive holomorphic sectional curvature. In particular we prove a gap theorem following the work of Petersen and Tao on ... More

Post-Keplerian motion in Reissner-Nordström spacetimeFeb 27 2019We present the analytical post-Newtonian solutions for the test particle's motion in the Reissner-Nordstr\"{o}m spacetime. The solutions are formulated in the Wagoner-Will representation, the Epstein-Haugan representation, the Brumberg representation, ... More

Composite Behavioral Modeling for Identity Theft Detection in Online Social NetworksJan 21 2018In this work, we aim at building a bridge from poor behavioral data to an effective, quick-response, and robust behavior model for online identity theft detection. We concentrate on this issue in online social networks (OSNs) where users usually have ... More

Second-order cosmological perturbations IV. Produced by scalar-tensor and tensor-tensor couplings during the radiation dominated stageMay 08 2019We continue to study the 2nd-order cosmological perturbations in synchronous coordinates in the framework of the general relativity (GR) during the radiation dominated (RD) stage, and focus on the scalar-tensor and tensor-tensor couplings. The 1st-order ... More

On Curvature Tensors of Hermitian ManifoldsFeb 03 2016Jul 29 2018In this article, we examine the behavior of the Riemannian and Hermitian curvature tensors of a Hermitian metric, when one of the curvature tensors obeys all the symmetry conditions of the curvature tensor of a K\"ahler metric. We will call such metrics ... More

Pair Distribution Function of One-dimensional "Hard Sphere" Fermi and Bose SystemsJan 13 2009The pair distributions of one-dimensional "hard sphere" fermion and boson systems are exactly evaluated by introducing gap variables.

Wave Function and Pair Distribution Function of a Dilute Bose GasJul 14 2008The wave function of a dilute hard sphere Bose gas at low temperatures is discussed, emphasizing the formation of pairs. The pair distribution function is calculated for two values of $\sqrt{\rho a^3}$.

Seiberg Duality in Matrix Models IINov 24 2002Apr 16 2003In this paper we continue the investigation, within the context of the Dijkgraaf-Vafa Programme, of Seiberg duality in matrix models as initiated in hep-th/0211202, by allowing degenerate mass deformations. In this case, there are some massless fields ... More

An Observation on Finite Groups and WZW Modular InvariantsSep 11 2000In this short note, inspired by much recent activity centered around attempts to formulate various correspondences between the classification of affine SU(k) WZW modular-invariant partition functions and that of discrete finite subgroups of SU(k), we ... More

All-optical controlled phase gate in quantum dot moleculesFeb 26 2014May 19 2015We propose a two-qubit optically controlled phase gate in quantum dot molecules via adiabatic passage and hole tunneling. Our proposal combines the merits of the current generation of vertically stacked self-assembled InAs quantum dots and adiabatic passage. ... More

Computationally Designed Zirconium Organometallic Catalyst for Direct Epoxidation of Alkenes without Allylic H Atoms: Aromatic Linkage Eliminates Formation of Inert Octahedral ComplexesDec 30 2015We used density functional theory to computationally design a Zr organometallic catalyst for selectively oxidizing substrates using molecular oxygen as oxidant without coreductant. Each selective oxidation cycle involves four general steps: (a) a peroxo ... More

DGCNN: Disordered Graph Convolutional Neural Network Based on the Gaussian Mixture ModelDec 10 2017Convolutional neural networks (CNNs) can be applied to graph similarity matching, in which case they are called graph CNNs. Graph CNNs are attracting increasing attention due to their effectiveness and efficiency. However, the existing convolution approaches ... More

Adiabatic Regularization and Green's Function Regularization of Scalar Field in de Sitter Space: Positive Spectral Energy Density and No Trace AnomalyMar 25 2019To remove the vacuum UV divergence of a quantum field in curved spacetime, the conventional adiabatic regularization proposes to subtract the $k$-mode of stress tensor by its 4th-order subtraction term. For a massive scalar field in the vacuum in de Sitter ... More

The nondynamical r-matrix structure for the elliptic $A_{n-1}$ Calogero-Moser modelNov 14 1997In this paper, we construct a new Lax operator for the elliptic $A_{n-1}$ Calogero-Moser model with general $n(2\leq n$) from the classical dynamical twisting,in which the corresponding r-matrix is purely numeric (nondynamical one). The nondynamical r-matrix ... More

D^0-D^0bar mixing in Υ(1S) \to D^0 D^0bar decay at Super-BOct 06 2006Nov 13 2006$\Dz-\Dzb$ mixing and significant CP violation in the charm system may indicate the signature of new physics. In this study, we suggest that the coherent $\DzDzb$ events from the decay of $\Upsilon(1S) \to \Dz \Dzb$ can be used to measure both mixing ... More

The set of all orthogonal complex structures on the flat $6$-toriApr 19 2016In \cite{BSV}, Borisov, Salamon and Viaclovsky constructed non-standard orthogonal complex structures on flat tori $T^{2n}_{\mathbb R}$ for any $n\geq 3$. We will call these examples BSV-tori. In this note, we show that on a flat $6$-torus, all the orthogonal ... More

Weak Ricci curvature bounds for Ricci shrinkersApr 07 2011We show that for a complete Ricci shrinker there exists a sequence of points tending to infinity whose norms of the Ricci tensor grow at most linearly.

Standardization, Distance, Host Galaxy Extinction of Type Ia Supernova and Hubble Diagram from the Flux Ratio MethodOct 29 2009Jun 30 2010In this paper we generalize the flux ratio method Bailey et al. (2009) to the case of two luminosity indicators and search the optimal luminosity-flux ratio relations on a set of spectra whose phases are around not only the date of bright light but also ... More

Adsorption and dissociation of O$_{2}$ at Be(0001): First-principles prediction of an energy barrier on the adiabatic potential energy surfaceDec 08 2008The adsorption and dissociation of O$_{2}$ molecules at the Be(0001) surface is studied by using density-functional theory within the generalized gradient approximation and a supercell approach. The physi- and chemisorbed molecular precursor states are ... More

Development of Krylov and AMG linear solvers for large-scale sparse matrices on GPUsJun 02 2016This research introduce our work on developing Krylov subspace and AMG solvers on NVIDIA GPUs. As SpMV is a crucial part for these iterative methods, SpMV algorithms for single GPU and multiple GPUs are implemented. A HEC matrix format and a communication ... More

Credit derivatives pricing with default density term structure modelled by Lévy random fieldsDec 13 2011We model the term structure of the forward default intensity and the default density by using L\'evy random fields, which allow us to consider the credit derivatives with an after-default recovery payment. As applications, we study the pricing of a defaultable ... More

SilentSense: Silent User Identification via Dynamics of Touch and Movement Behavioral BiometricsAug 31 2013With the increased popularity of smartphones, various security threats and privacy leakages targeting them are discovered and investigated. In this work, we present \ourprotocoltight, a framework to authenticate users silently and transparently by exploiting ... More

Second-order cosmological perturbations. II. Produced by scalar-tensor and tensor-tensor couplingsOct 18 2017Feb 05 2019We study the second-order perturbations in the Einstein-de Sitter Universe in synchronous coordinate. We solve the second-order perturbed Einstein equation with scalar-tensor, and tensor-tensor couplings between 1st order perturbations, and obtain, for ... More

An inverse electromagnetic scattering problem for a bi-periodic inhomogeneous layer on a perfectly conducting plateMar 16 2010This paper is concerned with uniqueness for reconstructing a periodic inhomogeneous medium covered on a perfectly conducting plate. We deal with the problem in the frame of time-harmonic Maxwell systems without TE or TM polarization. An orthogonal relation ... More

Rare Semileptonic Decays of Heavy Mesons with Flavor SU(3) SymmetrySep 07 2007Dec 01 2008In this paper, we calculate the decay rates of $D^+ \to D^0 e^+ \nu$, $D^+_S \to D^0 e^+ \nu$, $B^0_S \to B^+ e^- \bar{\nu}$, $D^+_S \to D^+ e^- e^+$ and $B^0_S \to B^0 e^-e^+$ semileptonic decay processes, in which only the light quarks decay, while ... More

A $\hbar$-deformation of the $W_{N}$ algebra and its vertex operatorsJan 21 1997In this paper,we derive a $\hbar$-deformation of the $W_{N}$ algebra and its quantum Miura tranformation. The vertex operators for this $\hbar$-deformed $W_{N}$ algebra and its commutation relations are also obtained.

Understanding the Spatial and Temporal Activity Patterns of Subway Mobility FlowsFeb 05 2017Feb 19 2017In urban transportation systems, mobility flows in the subway system reflect the spatial and temporal dynamics of working days. To investigate the variability of mobility flows, we analyse the spatial community through a series of snapshots of subway ... More

Adiabatic Regularization and Green's Function Regularization of Scalar Field in de Sitter Space: Positive Spectral Energy Density and No Trace AnomalyMar 25 2019Apr 03 2019To remove the vacuum UV divergence of a quantum field in curved spacetime, the conventional adiabatic regularization proposes to subtract the $k$-mode of stress tensor by its 4th-order subtraction term. For a massive scalar field in the vacuum in de Sitter ... More

A Gradient Tree Boosting based Approach to Rumor Detecting on Sina WeiboJun 17 2018Rumor detecting on microblogging platforms such as Sina Weibo is a crucial issue. Most existing rumor detecting algorithms require a lot of propagation data for model training, thus they do not have good detecting accuracy at the early stage after a rumor ... More

The inverse electromagnetic scattering problem in a piecewise homogeneous mediumJan 18 2010This paper is concerned with the problem of scattering of time-harmonic electromagnetic waves from an impenetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is established, employing the integral equation method. ... More

On Bismut Flat ManifoldsMar 23 2016Jul 09 2016In this paper, we give a classification of all compact Hermitian manifolds with flat Bismut connection. We show that the torsion tensor of such a manifold must be parallel, thus the universal cover of such a manifold is a Lie group equipped with a bi-invariant ... More

Learning Optimal Data Augmentation Policies via Bayesian Optimization for Image Classification TasksMay 06 2019In recent years, deep learning has achieved remarkable achievements in many fields, including computer vision, natural language processing, speech recognition and others. Adequate training data is the key to ensure the effectiveness of the deep models. ... More

On the derivations of lattice Boltzmann evolution equationJun 21 2017A comparative analysis on the popular schemes for evaluating evolution equation in lattice Boltzmann method (LBM) is presented in this paper. It includes two classical characteristic-line schemes, Boesh-Karlin and He-Luo scheme, and a author-proposed ... More

Modelling the level of adoption of analytical tools; An implementation of multi-criteria evidential reasoningFeb 11 2016In the future, competitive advantages will be given to organisations that can extract valuable information from massive data and make better decisions. In most cases, this data comes from multiple sources. Therefore, the challenge is to aggregate them ... More

Zeeman Spectroscopy of the Star AlgebraMar 20 2002We solve the problem of finding all eigenvalues and eigenvectors of the Neumann matrix of the matter sector of open bosonic string field theory, including the zero modes, and switching on a background B-field. We give the discrete eigenvalues as roots ... More

The Spectrum of the Neumann Matrix with Zero ModesFeb 26 2002Mar 20 2002We calculate the spectrum of the matrix M' of Neumann coefficients of the Witten vertex, expressed in the oscillator basis including the zero-mode a_0. We find that in addition to the known continuous spectrum inside [-1/3,0) of the matrix M without the ... More

About Detecting CP-Violating Processes in $J/ψ\to \KzKzb $ DecayJul 25 2006Questions about detecting CP-violating decay process of $J/\psi\to K^0\bar{K}^0\to K_SK_S$ are discussed. Possible background and material regeneration effect are analyzed. The discussion can be directly extended to other vector quarkonium decays, like ... More

Derivation of lattice Boltzmann equation via analytical characteristic integralMar 17 2017Feb 13 2019A lattice Boltzmann (LB) theory, analytical characteristic integral (ACI) LB theory, is proposed in this paper. ACI LB theory takes Bhatnagar-Gross-Krook (BGK) Boltzmann equation as the exact kinetic equation behind Navier-Stokes continuum and momentum ... More

Dirac node lines in a two-dimensional bipartite square latticeDec 20 2016As a new type of quantum matter, Dirac node line (DNL) semimetals are currently attracting widespread interest in condensed matter physics and material science. The DNL featured by a closed line consisting of linear band crossings in the lattice momentum ... More

Learning From Hidden Traits: Joint Factor Analysis and Latent ClusteringMay 21 2016Dimensionality reduction techniques play an essential role in data analytics, signal processing and machine learning. Dimensionality reduction is usually performed in a preprocessing stage that is separate from subsequent data analysis, such as clustering ... More

Microscopic Statistical Characterisation of the Congested Traffic Flow and Some Salient Empirical FeaturesMar 14 2016We present large scale and detailed analysis of the microscopic empirical data of the traffic flow, focusing on the non-linear interactions between the vehicles when the traffic is congested. By implementing a "renormalisation" procedure that averages ... More

Reinforcement Learning with Perturbed RewardsOct 02 2018Oct 05 2018Recent studies have shown the vulnerability of reinforcement learning (RL) models in noisy settings. The sources of noises differ across scenarios. For instance, in practice, the observed reward channel is often subject to noise (e.g., when observed rewards ... More

D-Brane Gauge Theories from Toric Singularities and Toric DualityMar 13 2000May 13 2000Via partial resolution of Abelian orbifolds we present an algorithm for extracting a consistent set of gauge theory data for an arbitrary toric variety whose singularity a D-brane probes. As illustrative examples, we tabulate the matter content and superpotential ... More

Z-D Brane Box Models and Non-Chiral Dihedral QuiversSep 17 1999Generalising ideas of an earlier work \cite{Bo-Han}, we address the problem of constructing Brane Box Models of what we call the Z-D Type from a new point of view, so as to establish the complete correspondence between these brane setups and orbifold ... More

Nature of Quasielectrons and the Continuum of Neutral Bulk Excitations in the Laughlin Quantum Hall FluidsAug 22 2013Jan 17 2014We construct model wavefunctions for a family of single-quasielectron states supported by the $\nu=1/3$ fractional quantum Hall (FQH) fluid. The charge $e^*$ = $e/3$ quasielectron state is identified as a composite of a charge-$2e^*$ quasiparticle and ... More

A lower bound for the scalar curvature of certain steady gradient Ricci solitonsFeb 22 2011In this very short note we prove a lower bound for the scalar curvature of certain steady gradient Ricci solitons.

A necessary and sufficient condition for Ricci shrinkers to have positive AVRJan 18 2011In this short note we observe that a recent result of C.-W. Chen meshes well with earlier work of H.-D. Cao and D.-T. Zhou, O. Munteanu, J. Carrillo and L. Ni, and S.-J. Zhang to give a necessary and sufficient condition for complete noncompact shrinking ... More

On the spanning connectivity of tournamentsJun 15 2017Let $D$ be a digraph. A $k$-container of $D$ between $u$ and $v$, $C(u,v)$, is a set of $k$ internally disjoint paths between $u$ and $v$. A $k$-container $C(u,v)$ of $D$ is a strong (resp. weak) $k^{*}$-container if there is a set of $k$ internally disjoint ... More

A New Learning Paradigm for Random Vector Functional-Link Network: RVFL+Aug 28 2017Mar 17 2019In school, a teacher plays an important role in various classroom teaching patterns. Likewise to this human learning activity, the learning using privileged information (LUPI) paradigm provides additional information generated by the teacher to 'teach' ... More

Deep Neural Architecture Search with Deep Graph Bayesian OptimizationMay 14 2019Bayesian optimization (BO) is an effective method of finding the global optima of black-box functions. Recently BO has been applied to neural architecture search and shows better performance than pure evolutionary strategies. All these methods adopt Gaussian ... More

Post-Minkowskian solution for the small-deflection motion of test particles in Kerr-Newman spacetimeFeb 24 2019We derive the second-order post-Minkowskian solution for the small-deflection motion of test particles in the external field of the Kerr-Newman black hole via an iterative method. The analytical results are exhibited in the coordinate system constituted ... More

Testing the Uniqueness of the Open Bosonic String Field Theory VacuumMar 14 2001Apr 19 2001The operators K_n are generators of reparameterization symmetries of Witten's cubic open string field theory. One pertinent question is whether they can be utilised to generate deformations of the tachyon vacuum and thereby violate its uniqueness. We ... More

Robust Matrix Elastic Net based Canonical Correlation Analysis: An Effective Algorithm for Multi-View Unsupervised LearningNov 14 2017Nov 15 2017This paper presents a robust matrix elastic net based canonical correlation analysis (RMEN-CCA) for multiple view unsupervised learning problems, which emphasizes the combination of CCA and the robust matrix elastic net (RMEN) used as coupled feature ... More

The dynamical twisting and nondynamical r-matrix structure of elliptic Ruijsenaars-Schneider modelFeb 22 1998Sep 15 1999From the dynamical twisting of the classical r-matrix, we obtain a new Lax operator for the elliptic Ruijsenaars-Schneider model (cf. Ruijsenaars'). The corresponding r-matrix is shown to be the classical $Z_n$-symmetric elliptic r-matrix, which is the ... More

The nondynamical r-matrix structure of the elliptic Ruijsenaars-Schneider model with N=2Feb 22 1998We demonstrate that in a certain gauge the elliptic Ruijsenaars-Shneider model with N=2 admits a nondynamical r-matrix structure and the corresponding classical r-matrix is the same as that of its non-relativistic counterpart (Calogero-Moser model) in ... More

The nondynamical r-matrix structure of the elliptic Calogero-Moser modelNov 12 1997In this paper, we construct a new Lax operator for the elliptic Calogero-Moser model with N=2. The nondynamical r-matrix structure of this Lax operator is also studied . The relation between our Lax operator and the Lax operator given by Krichever is ... More

A $\hbar$-deformed Virasoro Algebra as Hidden Symmetry of the Restricted sine-Gordon ModelDec 26 1996Jan 21 1997As the Yangian double with center,which is deformed from affine algebra by the additive loop parameter $\hbar$ ,we get the commuting relation and the bosonization of quantum $\hbar$-deformed Virasoro algebra. The corresponding Miura transformation, associated ... More

Lie Groups with flat Gauduchon connectionsMay 12 2018Jul 29 2018We pursuit the research line proposed in \cite{YZ-Gflat} about the classification of Hermitian manifolds whose $s$-Gauduchon connection $\nabla^s =(1-\frac{s}{2})\nabla^c + \frac{s}{2}\nabla^b$ is flat, where $s \in \mathbb{R}$ and $\nabla^c$ and $\nabla^b$ ... More

A lower bound for the scalar curvature of noncompact nonflat Ricci shrinkersFeb 02 2011We show that recent work of Ni and Wilking yields the result that a noncompact nonflat Ricci shrinker has at most quadratic scalar curvature decay. The examples of noncompact K\"{a}hler--Ricci shrinkers by Feldman, Ilmanen, and Knopf exhibit that this ... More

Tensor and Its Tucker Core: the Invariance RelationshipsJan 07 2016Nov 06 2016In [13], Hillar and Lim famously demonstrated that "multilinear (tensor) analogues of many efficiently computable problems in numerical linear algebra are NP-hard". Despite many recent advancements, the state-of-the-art methods for computing such `tensor ... More

Polynomial Structures in One-Loop AmplitudesMar 21 2008Sep 17 2008A general one-loop scattering amplitude may be expanded in terms of master integrals. The coefficients of the master integrals can be obtained from tree-level input in a two-step process. First, use known formulas to write the coefficients of (4-2epsilon)-dimensional ... More

Parallel Triangular Solvers on GPUJun 02 2016In this paper, we investigate GPU based parallel triangular solvers systematically. The parallel triangular solvers are fundamental to incomplete LU factorization family preconditioners and algebraic multigrid solvers. We develop a new matrix format suitable ... More

Optimal Control of Complex Systems through Variational Inference with a Discrete Event Decision ProcessMay 07 2019Complex social systems are composed of interconnected individuals whose interactions result in group behaviors. Optimal control of a real-world complex system has many applications, including road traffic management, epidemic prevention, and information ... More

How Much Frequency Can Be Reused in 5G Cellular Networks---A Matrix Graph ModelJan 19 2014Apr 11 2014The 5th Generation cellular network may have the key feature of smaller cell size and denser resource employment, resulted from diminishing resource and increasing communication demands. However, small cell may result in high interference between cells. ... More

Non-cooperative game approach for task offloading in edge cloudsDec 19 2018Task offloading provides a promising way to enhance the capability of the mobile terminal (also called terminal user) that is distributed on network edge and communicates edge clouds with wireless. Generally, there are multiple edge cloud nodes with distinct ... More

On the favorite points of symmetric Lévy processesNov 12 2017Aug 08 2018This paper is concerned with asymptotic behavior (at zero and at infinity) of the favorite points of L\'evy processes. By exploring Molchan's idea for deriving lower tail probabilities of Gaussian processes with stationary increments, we extend the result ... More

Counting Gauge Invariants: the Plethystic ProgramJan 08 2007Mar 04 2007We propose a programme for systematically counting the single and multi-trace gauge invariant operators of a gauge theory. Key to this is the plethystic function. We expound in detail the power of this plethystic programme for world-volume quiver gauge ... More

On Correspondences Between Toric Singularities and (p,q)-websMar 12 2004We study four-dimensional N=1 gauge theories which arise from D3-brane probes of toric Calabi-Yau threefolds. There are some standing paradoxes in the literature regarding relations among (p,q)-webs, toric diagrams and various phases of the gauge theories, ... More