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A restriction estimate in $\mathbb{R}^3$ using broomsFeb 12 2018If $f$ is a function supported on the truncated paraboloid in $\mathbb{R}^3$ and $E$ is the corresponding extension operator, then we prove that for all $p> 3+ 3/13$, $\|Ef\|_{L^p(\mathbb{R}^3)}\leq C \|f\|_{L^{\infty}}$. The proof combines Wolff's two ... More

Symmetric Reduction and Hamilton-Jacobi Equation of Rigid Spacecraft with a RotorJul 05 2013Jan 01 2014In this paper, we consider the rigid spacecraft with an internal rotor as a regular point reducible regular controlled Hamiltonian (RCH) system. In the cases of coincident and non-coincident centers of buoyancy and gravity, we give explicitly the motion ... More

Hamilton-Jacobi Theorems for Regular Controlled Hamiltonian System and Its ReductionsMay 15 2013Aug 17 2013In this paper, we first prove a Hamilton-Jacobi theorem for regular controlled Hamiltonian (RCH) system on cotangent bundle of a configuration manifold, by using the symplectic form. This result is an extension of the geometric version of Hamilton-Jacobi ... More

The Geometrical Structure of Phase Space of the Controlled Hamiltonian System with SymmetryFeb 05 2018In this paper, from the viewpoint of completeness of Marsden-Weinstein reduction, we illustrate how to give the definitions of a controlled Hamiltonian (CH) system and a reducible controlled Hamiltonian system with symmetry; and how to describe the dynamics ... More

Regular Reduction of Controlled Magnetic Hamiltonian System with Symmetry of the Heisenberg GroupJun 11 2015Jul 08 2018A controlled magnetic Hamiltonian (CMH) system is a regular controlled Hamiltonian (RCH) system with magnetic symplectic form, it is an important special case of RCH system. Note that there is a magnetic term on the cotangent bundle of the Heisenberg ... More

Symmetric Reduction and Hamilton-Jacobi Equation of Underwater Vehicle with Internal RotorsOct 11 2013Aug 17 2014In this paper, we first give the regular point reduction by stages and Hamilton-Jacobi theorem of regular controlled Hamiltonian (RCH) system with symmetry on the generalization of a semidirect product Lie group. Next, as an application of the theoretical ... More

Criterion for the integrality of hypergeometric series with parameters from quadratic fieldsSep 29 2016For the hypergeometric series with parameters from the rational fields, there is an effective criterion due to Christol to decide whether the hypergeometric series is N-integral or not. Christol criterion is a basic and vital tool in the recent striking ... More

A Systemic Receptor Network Triggered by Human cytomegalovirus EntryAug 06 2010Virus entry is a multistep process that triggers a variety of cellular pathways interconnecting into a complex network, yet the molecular complexity of this network remains largely unsolved. Here, by employing systems biology approach, we reveal a systemic ... More

On The Stability of Video Detection and TrackingNov 20 2016Apr 04 2017In this paper, we study an important yet less explored aspect in video detection and tracking -- stability. Surprisingly, there is no prior work that tried to study it. As a result, we start our work by proposing a novel evaluation metric for video detection ... More

Wellposedness and regularity of steady-state two-sided variable-coefficient conservative space-fractional diffusion equationsJun 15 2016We study the Dirichlet boundary-value problem of steady-state two-sided variable-coefficient conservative space-fractional diffusion equations. We show that the Galerkin weak formulation, which was proved to be coercive and continuous for a constant-coefficient ... More

Frequency dependent admittance of a two-dimensional quantum wireAug 29 1996The frequency dependent conductance of a two-dimensional quantum wire is computed using a current conserving formalism. The correction to the dc-conductance due to a time-dependent potential is related to the local partial density of states which we compute ... More

Wellposedness of Neumann boundary-value problems of space-fractional differential equationsDec 07 2016Fractional differential equation (FDE) provides an accurate description of transport processes that exhibit anomalous diffusion but introduces new mathematical difficulties that have not been encountered in the context of integer-order differential equation. ... More

Anisotropic magnetotransport of superconducting and normal state in an electron-doped Nd_{1.85}Ce_{0.15}CuO_{4-δ} single crystalFeb 28 2011The anisotropic properties of an optimally doped Nd_{1.85}Ce_{0.15}CuO_{4-\delta} single crystal have been studied both below and above the critical temperature Tc via the resistivity measurement in magnetic field H up to 12 T. By scaling the conductivity ... More

Leveraging Social Signal to Improve Item Recommendation for Matrix FactorizationMay 17 2018Although Recommender Systems have been comprehensively studied in the past decade both in industry and academia, most of current recommender systems suffer from the following issues: 1) The data sparsity of the user-item matrix seriously affect the recommender ... More

Entropy Productions and Their Mathematical Representations: Clausius' vs. Kelvin's Views of the Second Law and IrreversibilityMay 24 2018We provide a stochastic mathematical theory for the nonequilibrium steady-state dissipation in a finite, compact driven system in terms of the non-stationary irreversibility in its external drive. A surjective map is rigorously established through a lift ... More

Intrinsic branching structure within random walk on $\mathbb{Z}$Dec 03 2010In this paper, we reveal the branching structure for a non-homogeneous random walk with bounded jumps. The ladder time $T_1,$ the first hitting time of $[1,\infty)$ by the walk starting from $0,$ could be expressed in terms of a non-homogeneous multitype ... More

Statistical Analysis of Magnetic Field SpectraOct 09 1998We have calculated and statistically analyzed the magnetic-field spectrum (the ``B-spectrum'') at fixed electron Fermi energy for two quantum dot systems with classically chaotic shape. This is a new problem which arises naturally in transport measurements ... More

Branching structure for an (L-1) random walk in random environment and its applicationsMar 19 2010By decomposing the random walk path, we construct a multitype branching process with immigration in random environment for corresponding random walk with bounded jumps in random environment. Then we give two applications of the branching structure. Firstly, ... More

Quantum Generic Attacks on Feistel SchemesOct 08 2010Feb 27 2017The Feistel scheme is an important structure in the block ciphers. The security of the Feistel scheme is related to distinguishability with a random permutation. In this paper, efficient quantum algorithms for distinguishing classical 3,4-round and unbalanced ... More

The secondary periodic element $β_{p^2/p^2-1}$ and its applicationsFeb 25 2014Jun 26 2014In this paper we prove that $\beta_{p^2/p^2-1}$ survives to $E_\infty$ in the Adams-Novikov spectral sequence for $p\geqslant 5$. As an easy consequence we prove that $\beta_{sp^2/j}$ are perminent cycles for all $s\geqslant 1$, $j\leqslant p^2-1$. From ... More

The elementary symmetric functions of reciprocals of the elements of arithmetic progressionsNov 06 2013Mar 24 2014Let $a$ and $b$ be positive integers. In 1946, Erd\H{o}s and Niven proved that there are only finitely many positive integers $n$ for which one or more of the elementary symmetric functions of $1/b, 1/(a+b),..., 1/(an-a+b)$ are integers. In this paper, ... More

Quantum Algorithms for Unit Group and principal ideal problemApr 08 2010Sep 01 2010Computing the unit group and solving the principal ideal problem for a number field are two of the main tasks in computational algebraic number theory. This paper proposes efficient quantum algorithms for these two problems when the number field has constant ... More

Decoupling and near-optimal restriction estimates for Cantor setsJul 28 2016For any $\alpha\in(0,d)$, we construct Cantor sets in $\mathbb{R}^d$ of Hausdorff dimension $\alpha$ such that the associated natural measure $\mu$ obeys the restriction estimate $\| \widehat{f d\mu} \|_{p} \leq C_p \| f \|_{L^2(\mu)}$ for all $p>2d/\alpha$. ... More

Modified equations for weak stochastic symplectic schemes via their generating functionsNov 09 2014In this paper, a systematic approach of constructing modified equations for weak stochastic symplectic methods of stochastic Hamiltonian systems is given via using the generating functions of the stochastic symplectic methods. This approach is valid for ... More

Two-grid economical algorithms for parabolic integro-differential equations with nonlinear memoryJun 13 2018Dec 31 2018In this paper, several two-grid finite element algorithms for solving parabolic integro-differential equations (PIDEs) with nonlinear memory are presented. Analysis of these algorithms is given assuming a fully implicit time discretization. It is shown ... More

Poisson Reduction of Controlled Hamiltonian System by Controllability DistributionDec 26 2013In this paper, we first study the Poisson reductions of controlled Hamiltonian (CH) system and symmetric CH system by controllability distributions. These reductions are the extension of Poisson reductions by distribution for Poisson manifolds to that ... More

Hamilton-Jacobi Theorems for Nonholonomic Reducible Hamiltonian Systems on a Cotangent BundleAug 30 2015Jul 31 2016Hamilton-Jacobi theorem reveals the deeply internal relationship between the generating function and the dynamical vector field of a Hamiltonian system. Because of the restriction given by constraints, in general, the dynamical vector field of nonholonomic ... More

Current partition: Nonequilibrium Green's function ApproachJul 22 1998We present a solution to the problem of AC current partition in a multi-probe mesoscopic conductor within the nonequilibrium Green's function formalism. This allows the derivation of dynamic conductance which is appropriate for nonequilibrium situations ... More

Perturbation: the Catastrophe Causer in Scale-Free NetworksJun 23 2004Jun 30 2004A new model about cascading occurrences caused by perturbation is established to search after the mechanism because of which catastrophes in networks occur. We investigate the avalanche dynamics of our model on 2-dimension Euclidean lattices and scale-free ... More

Statistical properties of the attendance time series in the minority gameJan 16 2001Jan 17 2001We study the statistical properties of the attendance time series corresponding to the number of agents making a particular decision in the minority game (MG). We focus on the analysis of the probability distribution and the autocorrelation function of ... More

Using Mathcasts to Facilitate Student Comprehension of Physical Applications of Math ConceptsSep 25 2018Many Physics Education Researchers have discussed the positive correlation between students' incoming mathematics skills and performance in their physics classes. Thus, in order to strengthen their performance gains in their physics courses, professors ... More

On the number of representations of n as a linear combination of four triangular numbersJul 13 2015Nov 02 2015Let $\Bbb Z$ and $\Bbb N$ be the set of integers and the set of positive integers, respectively. For $a,b,c,d,n\in\Bbb N$ let $t(a,b,c,d;n)$ be the number of representations of $n$ by $ax(x-1)/2+by(y-1)/2+cz(z-1)/2 +dw(w-1)/2$ $(x,y,z,w\in\Bbb Z$). In ... More

On the number of representations of n as a linear combination of four triangular numbers IINov 02 2015Dec 08 2015Let $\Bbb Z$ and $\Bbb N$ be the set of integers and the set of positive integers, respectively. For $a,b,c,d,n\in\Bbb N$ let $N(a,b,c,d;n)$ be the number of representations of $n$ by $ax^2+by^2+cz^2+dw^2$, and let $t(a,b,c,d;n)$ be the number of representations ... More

Traffic flow and efficient routing on scale-free networks: A surveySep 04 2006Recently, motivated by the pioneer works in revealing the small-world effect and scale-free property of various real-life networks, many scientists devote themselves to studying complex networks. In this paper, we give a brief review on the studies of ... More

Nonlinear I-V Characteristics of a Mesoscopic ConductorFeb 23 1999We present a general theoretical formulation, based on nonequilibrium Green's functions, for nonlinear DC transport in multi-probe mesoscopic conductors. The theory is gauge invariant and is useful for the predictions of current-voltage characteristics ... More

Shot noise of spin currentMay 05 2003We report an exact solution for the noise spectrum of spin-current without charge-current in a spin field effect transistor (SFET). For the SFET with two leads, it is found that both auto- and cross-correlation functions are needed to characterize the ... More

Quantum spin field effect transistorAug 26 2002We propose, theoretically, a new type of quantum field effect transistor that operates purely on the flow of spin current in the absence of charge current. This spin field effect transistor (SFET) is constructed without any magnetic material, but with ... More

Nonlinear Spin Polarized Transport Through a Quantum DotOct 21 1999We present a theoretical analysis of the nonlinear bias and temperature dependence of current-voltage characteristics of a spin-valve device which is formed by connecting a quantum dot to two ferromagnetic electrodes whose magnetic moments orient at an ... More

Non-adiabatic charge pump: an exact solutionNov 24 2002We derived a general and exact expression of current for quantum parametric charge pumps in the non-adiabatic regime at finite pumping frequency and finite driving amplitude. The non-perturbative theory predicts a remarkable plateau structure in the pumped ... More

Parametric pumping at finite frequencyJul 04 2001We report on a first principles theory for analyzing the parametric electron pump at a finite frequency. The pump is controlled by two pumping parameters with phase difference $\phi$. In the zero frequency limit, our theory predicts the well known result ... More

POD/DEIM Reduced-Order Modeling of Time-Fractional Partial Differential Equations with Applications in Parameter IdentificationJun 22 2016Mar 07 2017In this paper, a reduced-order model (ROM) based on the proper orthogonal decomposition and the discrete empirical interpolation method is proposed for efficiently simulating time-fractional partial differential equations (TFPDEs). Both linear and nonlinear ... More

Entanglement production and decoherence-free subspace of two single-mode cavities embedded in a common environmentMay 12 2005A system consisting of two identical single-mode cavities coupled to a common environment is investigated within the framework of algebraic dynamics. Based on the left and right representations of the Heisenberg-Weyl algebra, the algebraic structure of ... More

Fresnel operator, squeezed state and Wigner function for Caldirola-Kanai HamiltonianDec 03 2010Based on the technique of integration within an ordered product (IWOP) of operators we introduce the Fresnel operator for converting Caldirola-Kanai Hamiltonian into time-independent harmonic oscillator Hamiltonian. The Fresnel operator with the parameters ... More

Entanglement dynamics of qubits in a common environmentApr 05 2006Jun 24 2007We use the quantum jump approach to study the entanglement dynamics of a quantum register, which is composed of two or three dipole-dipole coupled two-level atoms, interacting with a common environment. Our investigation of entanglement dynamics reflects ... More

Quantum particle confined to a thin-layer volume: Non-uniform convergence toward the curved surfaceFeb 07 2015Oct 28 2015We clearly refine the fundamental framework of the thin-layer quantization procedure, and further develop the procedure by taking the proper terms of degree one in $q_3$ ($q_3$ denotes the curvilinear coordinate variable perpendicular to curved surface) ... More

Improving the security of multiparty quantum secret splitting and quantum state sharingMay 06 2006A protocol for multiparty quantum secret splitting (MQSS) with an ordered $N$ Einstein-Podolsky-Rosen (EPR) pairs and Bell state measurements is recently proposed by Deng {\rm et al.} [Phys. Lett. A 354(2006)190]. We analyzed the security of the protocol ... More

Immunization of traffic-driven epidemic spreadingFeb 05 2018In this paper, we study the control of the traffic-driven epidemic spreading by immunization strategy. We consider the random, degree-based and betweeness-based immunization strategies, respectively. It is found that the betweeness-based immunization ... More

A Solvable High-Dimensional Model of GANMay 22 2018Despite the remarkable successes of generative adversarial networks (GANs) in many applications, theoretical understandings of their performance is still limited. In this paper, we present a simple shallow GAN model fed by high-dimensional input data. ... More

The Effects on $S$, $T$, and $U$ from Higher-Dimensional Fermion RepresentationsOct 09 2006Inspired by a new class of walking technicolor models recently proposed using higher-dimensional technifermions, we consider the oblique corrections from heavy non-degenerate fermions with two classes of higher-dimensional representations of the electroweak ... More

Convergence of Bregman alternating direction method with multipliers for nonconvex composite problemsOct 31 2014Dec 05 2014The alternating direction method with multipliers (ADMM) has been one of most powerful and successful methods for solving various convex or nonconvex composite problems that arise in the fields of image & signal processing and machine learning. In convex ... More

Quantile-adaptive model-free variable screening for high-dimensional heterogeneous dataApr 08 2013Dec 11 2013We introduce a quantile-adaptive framework for nonlinear variable screening with high-dimensional heterogeneous data. This framework has two distinctive features: (1) it allows the set of active variables to vary across quantiles, thus making it more ... More

An extension of Stern's congruenceDec 18 2010Aug 03 2012Let $\{E_n\}$ be the Euler numbers. In the paper we determine $E_{2^mk+b}-E_b$ modulo $2^{m+7}$, where $k$ and $m$ are positive integers and $b\in{0,2,4,...}$.

Peculiar $P-V$ criticality of topological Hořava-Lifshitz black holesJul 28 2017Aug 08 2017We demonstrate the existence of $P-V$ criticality of the topological Ho\v{r}ava-Lifshitz(HL) black holes with a spherical horizon $(k=1)$ in the extended phase space. With the electric charge, we find that the critical behaviors of the HL black hole are ... More

Implications of Fermi-LAT observations on the origin of IceCube neutrinosJul 09 2014Nov 07 2014The IceCube (IC) collaboration recently reported the detection of TeV-PeV extraterrestrial neutrinos whose origin is yet unknown. By the photon-neutrino connection in $pp$ and $p\gamma$ interactions, we use the \fermi-LAT observations to constrain the ... More

Convergence Analysis of a Finite Difference Scheme for the Gradient Flow associated with the ROF ModelFeb 21 2013We present a convergence analysis of a finite difference scheme for the time dependent partial different equation called gradient flow associated with the Rudin-Osher-Fatemi model. We devise an iterative algorithm to compute the solution of the finite ... More

Incidence estimates for well spaced tubesApr 10 2019We prove analogues of the Szemer\'edi-Trotter theorem and other incidence theorems using $\delta$-tubes in place of straight lines, assuming that the $\delta$-tubes are well-spaced in a strong sense.

Excited Binomial States and Excited Negative Binomial States of the Radiation Field and Some of their Statistical PropertiesMar 16 1999Apr 09 1999We introduce excited binomial states and excited negative binomial states of the radiation field by repeated application of the photon creation operator on binomial states and negative binomial states. They reduce to Fock states and excited coherent states ... More

Determination of the intrinsic velocity field in the M87 jetApr 12 2009A new method to estimate the Doppler beaming factor of relativistic large-scale jet regions is presented. It is based on multiwaveband fitting to radio-to-X-ray continua with synchrotron spectrum models. Combining our method with available observational ... More

Maximal planar networks with large clustering coefficient and power-law degree distributionDec 16 2004In this article, we propose a simple rule that generates scale-free networks with very large clustering coefficient and very small average distance. These networks are called {\bf Random Apollonian Networks}(RAN) as they can be considered as a variation ... More

Evolutionary Dynamics in Complex Networks of Competing Boolean AgentsNov 26 2004We investigate the dynamics of network minority games on Kauffman's NK networks (Kauffman nets), growing directed networks (GDNets), as well as growing directed networks with a small fraction of link reversals (GDRNets). We show that the dynamics and ... More

Low Frequency Quantum Transport in a Three-probe Mesoscopic ConductorJan 25 1997The low frequency quantum transport properties of a three-probe mesoscopic conductor are studied using B\"uttiker's AC transport formalism. The static transmission coefficients and emittance matrix of the system were computed by explicitly evaluating ... More

Weakly nonlinear quantum transport: an exactly solvable modelOct 25 1996We have studied the weakly non-linear quantum transport properties of a two-dimensional quantum wire which can be solved exactly. The non-linear transport coefficients have been calculated and interesting physical properties revealed. In particular we ... More

Spin-current induced electric fieldJan 21 2003We theoretically predict that a pure steady state spin-current without charge-current can induce an electric field. A formula for the induced electric field is derived and we investigate its characteristics. Conversely, a moving spin is affected by an ... More

ab initio modeling of open systems: charge transfer, electron conduction, and molecular switching of a C_{60} deviceJul 11 2000We present an {\it ab initio} analysis of electron conduction through a $C_{60}$ molecular device. Charge transfer from the device electrodes to the molecular region is found to play a crucial role in aligning the lowest unoccupied molecular orbital (LUMO) ... More

A spin-cell for spin currentDec 12 2002Mar 28 2003We propose and investigate a spin-cell device which provides the necessary spin-motive force to drive a spin current for future spintronic circuits. Our spin-cell have four basic characteristics: (i) it has two poles so that a spin current flows in from ... More

Correlated two-electron transport: a principle for a novel charge pumpDec 06 2002By considering a correlated two-electron transport process (TET) and using a diagrammatic analysis within the Keldysh nonequilibrium Green's function formalism, we discuss a novel charge pump by which carriers are pumped from a contact with low chemical ... More

Scattering Matrix Theory For Nonlinear TransportDec 05 1997We report a scattering matrix theory for dynamic and nonlinear transport in coherent mesoscopic conductors. In general this theory allows predictions of low frequency linear dynamic conductance, as well as weakly nonlinear DC conductance. It satisfies ... More

The second order nonlinear conductance of a two-dimensional mesoscopic conductorApr 11 1997We have investigated the weakly non-linear quantum transport properties of a two-dimensional quantum conductor. We have developed a numerical scheme which is very general for this purpose. The nonlinear conductance is computed by explicitly evaluating ... More

Numerical Analysis on Ergodic Limit of Approximations for Stochastic NLS Equation via Multi-symplectic SchemeJun 05 2016Nov 27 2016We consider a finite dimensional approximation of the stochastic nonlinear Schr\"odinger equation driven by multiplicative noise, which is derived by applying a symplectic method to the original equation in spatial direction. Both the unique ergodicity ... More

Application of Correlation Indices on Intrusion Detection Systems: Protecting the Power Grid Against Coordinated AttacksJun 09 2018The future power grid will be characterized by the pervasive use of heterogeneous and non-proprietary information and communication technology, which exposes the power grid to a broad scope of cyber-attacks. In particular, Monitoring-Control Attacks (MCA) ... More

Symplectic Runge-Kutta Methods for Hamiltonian Systems Driven by Gaussian Rough PathsApr 13 2017We consider Hamiltonian systems driven by multi-dimensional Gaussian processes in rough path sense, which include fractional Brownian motions with Hurst parameter $H\in(1/4,1/2]$. We indicate that the phase flow preserves the symplectic structure almost ... More

Approximation of Invariant Measure for Damped Stochastic Nonlinear Schrödinger Equation via an Ergodic Numerical SchemeSep 30 2015Jun 05 2016In order to inherit numerically the ergodicity of the damped stochastic nonlinear Schr\"odinger equation with additive noise, we propose a fully discrete scheme, whose spatial direction is based on spectral Galerkin method and temporal direction is based ... More

Parareal exponential $θ$-scheme for longtime simulation of stochastic Schrödinger equations with weak dampingMar 25 2018A parareal algorithm based on an exponential $\theta$-scheme is proposed for the stochastic Schr\"odinger equation with weak damping and additive noise. It proceeds as a two-level temporal parallelizable integrator with the exponential $\theta$-scheme ... More

Data-driven physics informed deep learning of solute transport with anomalous diffusionDec 04 2018Feb 11 2019The fractional advection-dispersion equation (FADE) has attracted increased attention from researchers as it provides an accurate description for challenging phenomenas with long-range time memory and spatial interactions, such as the anomalous diffusion ... More

Wellposedness of the two-sided variable coefficient Caputo flux fractional diffusion equation and error estimate of its spectral approximationNov 01 2018In this article a two-sided variable coefficient fractional diffusion equation (FDE) is investigated, where the variable coefficient occurs outside of the fractional integral operator. Under a suitable transformation the variable coefficient equation ... More

Circular Stochastic Fluctuations in SIS Epidemics with Heterogeneous Contacts Among Sub-populationsDec 20 2011The conceptual difference between equilibrium and non-equilibrium steady state (NESS) is well established in physics and chemistry. This distinction, however, is not widely appreciated in dynamical descriptions of biological populations in terms of differential ... More

Topological photonic crystal with equifrequency Weyl pointsNov 30 2015Jul 01 2016Weyl points in three-dimensional photonic crystals behave as monopoles of Berry flux in momentum space. Here, based on general symmetry analysis, we show that a minimal number of four symmetry-related (consequently equifrequency) Weyl points can be realized ... More

On exotic modular tensor categoriesOct 30 2007Jun 10 2008It has been conjectured that every $(2+1)$-TQFT is a Chern-Simons-Witten (CSW) theory labelled by a pair $(G,\lambda)$, where $G$ is a compact Lie group, and $\lambda \in H^4(BG;Z)$ a cohomology class. We study two TQFTs constructed from Jones' subfactor ... More

Collaborative similarity analysis of multilayer developer-project bipartite networkMar 09 2017To understand the multiple relations between developers and projects on GitHub as a whole, we model them as a multilayer bipartite network and analyze the degree distributions, the nearest neighbors' degree distributions and their correlations with degree, ... More

Algebraic Characterizations of Consensus Problems for Networked Dynamic SystemsFeb 16 2005In this paper, we study the consensus problem for networked dynamic systems with arbitrary initial states, and present some structural characterization and direct construction of consensus functions. For the consensus problem under similar transformation, ... More

Statistical Properties and Algebraic Characteristics of Quantum Superpositions of Negative Binomial StatesOct 23 1999We introduce new kinds of states of quantized radiation fields, which are the superpositions of negative binomial states. They exhibit remarkable non-classical properties and reduce to Schr\"odinger cat states in a certain limit. The algebras involved ... More

Curvatures at the singular points of algebraic curves and surfacesMay 18 2014In this paper, we study the computation of curvatures at the singular points of algebraic curves and surfaces. The idea is to convert the problem to compute the curvatures of the corresponding regular parametric curves and surfaces, which have intersections ... More

GANE: A Generative Adversarial Network EmbeddingMay 18 2018May 21 2018Network embedding has become a hot research topic recently which can provide low-dimensional feature representations for many machine learning applications. Current work focuses on either (1) whether the embedding is designed as an unsupervised learning ... More

Theory of Phase Transition in the Evolutionary Minority GameMay 29 2003We discover the mechanism for the transition from self-segregation (into opposing groups) to clustering (towards cautious behaviors) in the evolutionary minority game (EMG). The mechanism is illustrated with a statistical mechanics analysis of a simplified ... More

Spatial flocking: Control by speed, distance, noise and delayMay 24 2017Nov 30 2017Fish, birds, insects and robots frequently swim or fly in groups. During their 3 dimensional collective motion, these agents do not stop, they avoid collisions by strong short-range repulsion, and achieve group cohesion by weak long-range attraction. ... More

Better Synchronizability Predicted by Crossed Double CycleAug 16 2005Dec 30 2005In this brief report, we propose a network model named crossed double cycles, which are completely symmetrical and can be considered as the extensions of nearest-neighboring lattices. The synchronizability, measured by eigenratio $R$, can be sharply enhanced ... More

Distributed Consensus Observers Based H-infinity Control of Dissipative PDE Systems Using Sensor NetworksJun 20 2014Oct 16 2014This paper considers the problem of finite dimensional output feedback H-infinity control for a class of nonlinear spatially distributed processes (SDPs) described by highly dissipative partial differential equations (PDEs), whose state is observed by ... More

A local approach for global partial density of statesMar 15 1997To apply the scattering approach for the problem of AC transport through coherent quantum conductors, various partial density of states must be evaluated. If the global partial density of states (GPDOS) is calculated externally using the energy derivatives ... More

High order conformal symplectic and ergodic schemes for stochastic Langevin equation via generating functionsFeb 23 2017Feb 24 2017In this paper, we consider the stochastic Langevin equation with additive noises, which possesses both conformal symplectic geometric structure and ergodicity. We propose a methodology of constructing high weak order conformal symplectic schemes by converting ... More

A Nonconvex Splitting Method for Symmetric Nonnegative Matrix Factorization: Convergence Analysis and OptimalityMar 24 2017Symmetric nonnegative matrix factorization (SymNMF) has important applications in data analytics problems such as document clustering, community detection and image segmentation. In this paper, we propose a novel nonconvex variable splitting method for ... More

Non-Gaussian normal diffusion induced by delocalizationNov 03 2015The non-Gaussian normal diffusion, i.e., the probability distribution function (PDF) is non-Gaussian but the mean squared displacement (MSD) depends on time linearly, has been observed in particle motions. Here we show by numerical simulations that this ... More

Second-order linear structure-preserving modified finite volume schemes for the regularized long-wave equationJun 23 2018In this paper, based on the weak form of the Hamiltonian formulation of the regularized long-wave equation and a novel approach of transforming the original Hamiltonian energy into a quadratic functional, a fully implicit and three linear-implicit energy ... More

Impact of Edge States on Device Performance of Phosphorene Heterojunction Tunneling Field Effect TransistorsJul 18 2016Black phosphorus (BP) tunneling transistors (TFETs) using heterojunction (He) are investigated by atomistic quantum transport simulations. It is observed that edge states have a great impact on transport characteristics of BP He-TFETs, which result in ... More

Note on holographic entanglement entropy and complexity in St$\ddot{u}$ckelberg superconductorFeb 21 2019The holographic superconductors, as one of the most important application of gauge/gravity duality, promote the study of strongly coupled superconductors via classical general relativity living in one higher dimension. One of the interesting properties ... More

Quantum transport theory for nanostructures with Rashba spin-orbital interactionNov 18 2004We report on a general theory for analyzing quantum transport through devices in the Metal-QD-Metal configuration where QD is a quantum dot or the device scattering region which contains Rashba spin-orbital and electron-electron interactions. The metal ... More

Weakly Nonlinear AC Response: Theory and ApplicationDec 05 1997We report a microscopic and general theoretical formalism for electrical response which is appropriate for both DC and AC weakly nonlinear quantum transport. The formalism emphasizes the electron-electron interaction and maintains current conservation ... More

Spectral approximation of a variable coefficient fractional diffusion equation in one space dimensionOct 29 2018In this article we consider the approximation of a variable coefficient (two-sided) fractional diffusion equation (FDE), having unknown $u$. By introducing an intermediate unknown, $q$, the variable coefficient FDE is rewritten as a lower order, constant ... More

Gauge and Lorentz Covariant Quark Propagator in an Arbitrary Gluon FieldFeb 04 2003Feb 16 2003The quark propagator in presence of an arbitrary gluon field is calculated gauge and Lorentz covariantly order by order in terms of powers of gluon field and its derivatives. The result is independent of path connecting ends of propagator and leading ... More

Directed polymers at finite temperatures in 1+1 and 2+1 dimensionsDec 19 1999We present systematic numerical simulations for directed polymers at finite temperatures in 1+1 and 2+1 dimensions. The transverse fluctuations and free energy fluctuations tend to the strong coupling limit at any temperature in both 1+1 and 2+1 dimensions ... More

Markov partition and Thermodynamic Formalism for Hyperbolic Systems with SingularitiesSep 02 2017Apr 05 2019For 2-d hyperbolic systems with singularities, statistical properties are rather difficult to establish because of the fragmentation of the phase space by singular curves. In this paper, we construct a Markov partition of the phase space with countable ... More