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Representation Learning Models for Entity SearchOct 28 2016We focus on the problem of learning distributed representations for entity search queries, named entities, and their short descriptions. With our representation learning models, the entity search query, named entity and description can be represented ... More

Representation Learning Models for Entity SearchOct 28 2016Jan 15 2017We focus on the problem of learning distributed representations for entity search queries, named entities, and their short descriptions. With our representation learning models, the entity search query, named entity and description can be represented ... More

Biomimetic Polymer Film with Brilliant Brightness Using a One-Step Water Vapor-Induced Phase Separation MethodJun 11 2019The scales of the white Cyphochilus beetles are endowed with unusual whiteness arising from the exceptional scattering efficiency of their disordered ultrastructure optimized through millions of years of evolution. Here, a simple, one-step method based ... More

New Techniques for Preserving Global Structure and Denoising with Low Information Loss in Single-Image Super-ResolutionMay 09 2018Jun 16 2018This work identifies and addresses two important technical challenges in single-image super-resolution: (1) how to upsample an image without magnifying noise and (2) how to preserve large scale structure when upsampling. We summarize the techniques we ... More

An Annealed Sequential Monte Carlo Method for Bayesian PhylogeneticsJun 22 2018Jan 19 2019We describe an "embarrassingly parallel" method for Bayesian phylogenetic inference, annealed Sequential Monte Carlo, based on recent advances in the Sequential Monte Carlo literature such as adaptive determination of annealing parameters. The algorithm ... More

An Annealed Sequential Monte Carlo Method for Bayesian PhylogeneticsJun 22 2018Mar 13 2019We describe an "embarrassingly parallel" method for Bayesian phylogenetic inference, annealed Sequential Monte Carlo, based on recent advances in the Sequential Monte Carlo literature such as adaptive determination of annealing parameters. The algorithm ... More

On the Idiosyncrasies of the Mandarin Chinese Classifier SystemFeb 26 2019While idiosyncrasies of the Chinese classifier system have been a richly studied topic among linguists (Adams and Conklin, 1973; Erbaugh, 1986; Lakoff, 1986), not much work has been done to quantify them with statistical methods. In this paper, we introduce ... More

Upper triangular matrices and Billiard ArraysAug 18 2015Jan 15 2016Fix a nonnegative integer $d$, a field $\mathbb{F}$, and a vector space $V$ over $\mathbb{F}$ with dimension $d+1$. Let $T$ denote an invertible upper triangular matrix in ${\rm Mat}_{d+1}(\mathbb{F})$. Using $T$ we construct three flags on $V$. We find ... More

Random Tessellation ForestsJun 13 2019Space partitioning methods such as random forests and the Mondrian process are powerful machine learning methods for multi-dimensional and relational data, and are based on recursively cutting a domain. The flexibility of these methods is often limited ... More

The Inverse Problem for the Dirichlet-to-Neumann map on Lorentzian manifoldsJul 29 2016Sep 27 2016We consider the Dirichlet-to-Neumann map $\Lambda$ on a cylinder-like Lorentzian manifold related to the wave equation related to the metric $g$, a magnetic field $A$ and a potential $q$. We show that we can recover the jet of $g,A,q$ on the boundary ... More

Application of EOS-ELM with binary Jaya-based feature selection to real-time transient stability assessment using PMU dataSep 08 2018Recent studies show that pattern-recognition-based transient stability assessment (PRTSA) is a promising approach for predicting the transient stability status of power systems. However, many of the current well-known PRTSA methods suffer from excessive ... More

Smooth Adjustment for Correlated EffectsJan 16 2019This paper considers a high dimensional linear regression model with corrected variables. A variety of methods have been developed in recent years, yet it is still challenging to keep accurate estimation when there are complex correlation structures among ... More

Botnets Drilling Away Privacy InfrastructureDec 20 2015In this paper, we explore various technologies and their roles in subverting the privacy infrastructure of the Internet. We also provide mitigation techniques on the attack vectors the technologies provide, and assess the overall severity of these threats. ... More

Thermo and photoacoustic Tomography with variable speed and planar detectorsMay 03 2016We analyze the mathematical model of multiwave tomography with a variable speed with integrating measurements on planes tangent to a sphere surrounding the source. We prove sharp uniqueness and stability estimates with full and partial data and propose ... More

Multiwave tomography with reflectors: Landweber's iterationMar 23 2016Apr 19 2016We use the Landweber method for numerical simulations for the multiwave tomography problem with a reflecting boundary and compare it with the averaged time reversal method. We also analyze the rate of convergence and the dependence on the step size for ... More

Boundedness of Linear Operators via Atoms on Hardy Spaces with Non-doubling MeasuresJun 07 2009Let $\mu$ be a non-negative Radon measure on ${\mathbb R}^d$ which only satisfies the polynomial growth condition. Let ${\mathcal Y}$ be a Banach space and $H^1(\mu)$ the Hardy space of Tolsa. In this paper, the authors prove that a linear operator $T$ ... More

On some properties of nonnegative weakly irreducible tensorsNov 03 2011Mar 13 2012In this paper, we mainly focus on how to generalize some conclusions from nonnegative irreducible tensors to nonnegative weakly irreducible tensors. To do so, a basic and important lemma is proven using new tools. First, we give the definition of stochastic ... More

A note on the geometric simplicity of the spectral radius of nonnegative irreducible tensorsJan 13 2011Mar 13 2012We prove that the spectral radius of even order nonnegative irreducible tensors is real geometrically simple. In the case when the order of the tensor is odd, or in the complex field, some conditions are given to guarantee the geometric simplicity of ... More

Atomic and Maximal Function Characterizations of Musielak-Orlicz-Hardy Spaces Associated to Non-negative Self-adjoint Operators on Spaces of Homogeneous TypeAug 30 2018Let $\mathcal{X}$ be a metric space with doubling measure and $L$ a non-negative self-adjoint operator on $L^2(\mathcal{X})$ whose heat kernels satisfy the Gaussian upper bound estimates. Assume that the growth function $\varphi:\ \mathcal{X}\times[0,\infty) ... More

Musielak-Orlicz Hardy Spaces Associated with Operators and Their ApplicationsJan 26 2012Jun 29 2012Let $\mathcal{X}$ be a metric space with doubling measure and $L$ a nonnegative self-adjoint operator in $L^2(\mathcal{X})$ satisfying the Davies-Gaffney estimates. Let $\varphi:\,\mathcal{X}\times[0,\infty)\to[0,\infty)$ be a function such that $\varphi(x,\cdot)$ ... More

Real-variable Characterizations of Orlicz-Hardy Spaces on Strongly Lipschitz Domains of $\mathbb{R}^n$Jul 17 2011Let $\Omega$ be a strongly Lipschitz domain of $\mathbb{R}^n$, whose complement in $\mathbb{R}^n$ is unbounded. Let $L$ be a second order divergence form elliptic operator on $L^2 (\Omega)$ with the Dirichlet boundary condition, and the heat semigroup ... More

Research on Information Security Enhancement Approaches and the Applications on HCI SystemsFeb 02 2016With rapid development of computer techniques, the human computer interaction scenarios are becoming more and more frequent. The development history of the human-computer interaction is from a person to adapt to the computer to the computer and continually ... More

$L^2$ Forms and Ricci flow with bounded curvature on Complete Non-compact manifoldsSep 11 2005In this paper, we study the evolution of $L^2$ one forms under Ricci flow with bounded curvature on a non-compact Rimennian manifold. We show on such a manifold that the $L^2$ norm of a smooth one form with compact support is non-increasing along the ... More

Decay of correlations for maximal measure of maps derived from Anosov: I: mostly contracting centerOct 03 2016It was proven by Ures that $C^1$ diffeomorphism on three dimensional torus that is derived from Anosov admits a unique maximal measure. Here we show that the maximal measure has exponential decay of correlations for H\"older observables, assuming the ... More

Full quantum theory of control-not gate in ion-trap quantum computationNov 26 2015We investigate the exact effect on ion trap quantum computation after field quantization. First an exact expression of failure probability from field quantization after many CNOT operations in Cirac-Zoller scheme is given. It is proportional to operation ... More

Adaptive elastic net and Separate Selection from Least Squares for ultra-high dimensional regression modelsOct 14 2014This paper studies the asymptotic properties of the adaptive elastic net in ultra-high dimensional sparse linear regression models and proposes a new method called SSLS (Separate Selection from Least Squares) to improve prediction accuracy. Besides, we ... More

The Heart-shaped Supernova Remnant 3C391 viewed in Multi-bandsMar 29 2007Using Chandra X-ray, Spitzer mid-IR, and 1.5 GHz radio data, we examine the spatial structure of SNR 3C391. The X-ray surface brightness is generally anti-correlative with the IR and radio brightness. The multiband data clearly exhibit a heart-shaped ... More

Narrow Band Chandra X-ray Analysis of Supernova Remnant 3C391May 02 2005We present the narrow-band and the equivalent width (EW) images of the thermal composite supernova remnant (SNR) 3C391 for the X-ray emission lines of elements Mg, Si, & S using the Chandra ACIS Observational data. These EW images reveal the spatial distribution ... More

Further Results for Perron-Frobenius Theorem for Nonnegative Tensors IIApr 02 2011Nov 20 2012In this paper, we generalize some conclusions from the nonnegative irreducible tensor to the nonnegative weakly irreducible tensor and give more properties of eigenvalue problems.

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 supercritical nonlinear Schrödinger equations with ellipse-shaped potentialsMay 23 2019In this paper, we study the existence and concentration of normalized solutions to the supercritical nonlinear Schr\"{o}dinger equation \begin{equation*} \left\{ \begin{array}{l} -\Delta u + V(x) u = \mu_q u + a|u|^q u \quad {\rm in}\quad \mathbb{R}^2,\\ ... More

Bott-Chern blow-up formula and bimeromorphic invariance of the $\partial\bar{\partial}$-Lemma for threefoldsDec 24 2017Sep 22 2018The purpose of this paper is to study the bimeromorphic invariants of compact complex manifolds in terms of Bott-Chern cohomology. We prove a blow-up formula for Bott-Chern cohomology. As an application, we show that for compact complex threefolds the ... 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

Real-Variable Characterizations Of Hardy Spaces Associated With Bessel OperatorsFeb 07 2011Let $\lambda>0$, $p\in((2\lz+1)/(2\lz+2), 1]$, and $\triangle_\lambda\equiv-\frac{d^2}{dx^2}-\frac{2\lambda}{x} \frac d{dx}$ be the Bessel operator. In this paper, the authors establish the characterizations of atomic Hardy spaces $H^p((0, \infty), dm_\lambda)$ ... More

Bound-preserving discontinuous Galerkin method for compressible miscible displacement in porous mediaJul 18 2017In this paper, we develop bound-preserving discontinuous Galerkin (DG) methods for the coupled system of compressible miscible displacement problems. We consider the problem with two components and the (volumetric) concentration of the $i$th component ... More

Unique determination of a transversely isotropic perturbation in a linearized inverse boundary value problem for elasticityAug 04 2018Jan 04 2019We consider a linearized inverse boundary value problem for the elasticity system. From the linearized Dirichlet-to-Neumann map at zero frequency, we show that a transversely isotropic perturbation of a homogeneous isotropic elastic tensor can be uniquely ... More

Geometric Measure of non-Commuting Simultaneous Measurement based on K-Means ClusteringDec 13 2018Considering the simultaneous measurement of non-commuting observables, we define a geometric measure for the degree of non-commuting behavior of quantum measurements coming from the initial and final states of the measurements. The rationality of our ... 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

Decay of correlations for maximal measure of maps derived from AnosovOct 03 2016Oct 23 2017It was proven by Ures that $C^1$ diffeomorphism on three dimensional torus that is derived from Anosov admits a unique maximal measure. Here we show that the maximal measure has exponential decay of correlations for H\"older observables, assuming the ... More

Local Hardy Spaces of Musielak-Orlicz Type and Their ApplicationsAug 13 2011Jun 28 2012Let $\phi: \mathbb{R}^n\times[0,\fz)\rightarrow[0,\fz)$ be a function such that $\phi(x,\cdot)$ is an Orlicz function and $\phi(\cdot,t)\in A^{\mathop\mathrm{loc}}_{\infty}(\mathbb{R}^n)$ (the class of local weights introduced by V. S. Rychkov). In this ... More

Existence and nondegeneracy of ground states in critical free boundary problemsMay 06 2014Mar 17 2015Existence and regularity of minimizers in elliptic free boundary problems have been extensively studied in the literature. The corresponding study of higher critical points was recently initiated in Jerison and Perera [30, 31]. In particular, the existence ... More

Penalized pairwise pseudo likelihood for variable selection with nonignorable missing dataMar 19 2017Jul 28 2017The regularization approach for variable selection was well developed for a completely observed data set in the past two decades. In the presence of missing values, this approach needs to be tailored to different missing data mechanisms. In this paper, ... More

Observability transition in real networksJul 25 2016We consider the observability model in networks with arbitrary topologies. We introduce a system of coupled nonlinear equations, valid under the locally tree-like ansatz, to describe the size of the largest observable cluster as a function of the fraction ... More

Finite Heat conduction in 2D LatticesJul 30 2001This paper gives a 2D hamonic lattices model with missing bond defects, when the capacity ratio of defects is enough large, the temperature gradient can be formed and the finite heat conduction is found in the model. The defects in the 2D harmonic lattices ... More

Multiwave tomography in a closed domain: averaged sharp time reversalDec 29 2014Feb 05 2015We study the mathematical model of multiwave tomography including thermo and photoacoustic tomography with a variable speed for a fixed time interval $[0,T]$. We assume that the waves reflect from the boundary of the domain. We propose an averaged sharp ... More

A Parallel Best-Response Algorithm with Exact Line Search for Nonconvex Sparsity-Regularized Rank MinimizationNov 13 2017In this paper, we propose a convergent parallel best-response algorithm with the exact line search for the nondifferentiable nonconvex sparsity-regularized rank minimization problem. On the one hand, it exhibits a faster convergence than subgradient algorithms ... More

A Unified Successive Pseudo-Convex Approximation FrameworkJun 16 2015Apr 07 2016In this paper, we propose a successive pseudo-convex approximation algorithm to efficiently compute stationary points for a large class of possibly nonconvex optimization problems. The stationary points are obtained by solving a sequence of successively ... More

$(N,q)$-Laplacian problems with critical Trudinger-Moser nonlinearitiesNov 09 2014Oct 29 2015We obtain nontrivial solutions of a $(N,q)$-Laplacian problem with a critical Trudinger-Moser nonlinearity in a bounded domain. In addition to the usual difficulty of the loss of compactness associated with problems involving critical nonlinearities, ... More

$N$-Laplacian problems with critical Trudinger-Moser nonlinearitiesJun 24 2014Jan 03 2016We prove existence and multiplicity results for a $N$-Laplacian problem with a critical exponential nonlinearity that is a natural analog of the Brezis-Nirenberg problem for the borderline case of the Sobolev inequality. This extends results in the literature ... More

Detecting Abnormal Profiles in Collaborative Filtering Recommender SystemsJun 18 2015Jun 23 2015Personalization collaborative filtering recommender systems (CFRSs) are the crucial components of popular e-commerce services. In practice, CFRSs are also particularly vulnerable to "shilling" attacks or "profile injection" attacks due to their openness. ... More

Defending Grey Attacks by Exploiting Wavelet Analysis in Collaborative Filtering Recommender SystemsJun 17 2015Jun 19 2015"Shilling" attacks or "profile injection" attacks have always major challenges in collaborative filtering recommender systems (CFRSs). Many efforts have been devoted to improve collaborative filtering techniques which can eliminate the "shilling" attacks. ... More

Approximation forte pour les variétés avec une action d'un groupe linéaireApr 12 2016May 08 2016Let $G$ be a connected linear algebraic group over a number field. Let $U \hookrightarrow X$ be a $G$-equivariant open embedding of a $G$-homogeneous space with connected stabilizers into a smooth $G$-variety. We prove that $X$ satisfies strong approximation ... More

Background Study on Supernova Relic Neutrinos Search in SuperK-GdOct 29 2016The detection of supernova relic neutrinos could provide precious information on the evolution of the universe, the formation of stars, the mechanism of supernova bursts and the related neutrino physics. Many experiments, such as Kamland, Borexino, Sudbury ... More

On Legendrian foliations in contact manifolds II: Deformation theoryNov 23 2014Using the structural theorems developed in [Hua13], we study the deformation theory of coisotropic submanifolds in contact manifolds, under the assumption that the characteristic foliation is nonsingular. In the "middle" dimensions, we find an interesting ... More

Controllability of Spacecraft Using Only Magnetic TorquesJul 24 2015Spacecraft attitude control using only magnetic torques is a time-varying system. Many designs were proposed using LQR and H-infinity formulations. The existence of the solutions depends on the controllability of the linear time-varying systems which ... More

On plastikstufe, bordered Legendrian open book and overtwisted contact structuresJul 27 2016Oct 06 2016In this paper we prove the presence of an embedded plastikstufe implies overtwistedness of the contact structure in any dimension. Moreover, we show in dimension 5 that the presence of an embedded bordered Legendrian open book (bLob) also implies overtwistedness. ... More

On List-decodability of Random Rank Metric CodesJan 13 2014Jan 23 2014In the present paper, we consider list decoding for both random rank metric codes and random linear rank metric codes. Firstly, we show that, for arbitrary $0<R<1$ and $\epsilon>0$ ($\epsilon$ and $R$ are independent), if $0<\frac{n}{m}\leq \epsilon$, ... More

A Construction for Constant-Composition CodesFeb 13 2008By employing the residue polynomials, a construction of constant-composition codes is given. This construction generalizes the one proposed by Xing[16]. It turns out that when d=3 this construction gives a lower bound of constant-composition codes improving ... More

The thermal entropy density of spacetimeOct 26 2011May 18 2012We introduce the notion of thermal entropy density, and first obtain the thermal entropy density of any arbitrary spacetime without firstly assuming a temperature or a horizon. The results indicate that gravity possesses thermal effects or therm entropy ... More

Multidimensional viscosity solutions theory of semi-linear partial differential equationsAug 07 2016In this study, we concern the multidimensional viscosity solutions theory of a kind of semi-linear partial differential equations (PDEs). A new definition of viscosity solution for this multidimensional semi-linear PDEs which is related to a type of multidimensional ... More

Propensity score weighting for causal inference with multi-stage clustered dataJul 26 2016Propensity score weighting is a tool for causal inference to adjust for measured confounders. Survey data are often collected under complex sampling designs such as multistage cluster sampling, which presents challenges for propensity score modeling and ... More

On Kernel of the regulator mapJun 10 2016Based on the infinitesimal methods due to Bloch. Green and Griffiths, we construct an infinitesimal form of the regulator map and verify that its kernel is $\Omega^{1}_{\mathbb{C}/\mathbb{Q}}$, which suggests Question 1.1 seems reasonable at the infinitesimal ... More

Separate Random Number Generation from Correlated SourcesSep 05 2014Apr 29 2016This work studies the problem of separate random number generation from correlated general sources with side information at the tester under the criterion of statistical distance. Tight one-shot lower and upper performance bounds are obtained using the ... More

Global stability of solutions to nonlinear wave equationsMay 18 2012We consider the problem of global stability of solutions to a class of semilinear wave equations with null condition in Minkowski space. We give sufficient conditions on the given solution which guarantees stability. Our stability result can be reduced ... More

On the quasilinear wave equations in time dependent inhomogeneous mediaDec 27 2013We consider the problem of small data global existence for quasilinear wave equations with null condition on a class of Lorentzian manifolds $(\mathbb{R}^{3+1}, g)$ with \textbf{time dependent} inhomogeneous metric. We show that sufficiently small data ... More

Higher algebraic K-theory and tangent spaces to Chow groupsOct 24 2013This is a reproduction of my thesis. By using higher K-theory(Chern character, cyclic homology, effacement theorem and etc), we provide an answer to a question by Green- Griffiths which says the tangent sequence to Bloch-Gersten-Quillen sequence is Cousin ... More

A New Fixed Point Theorem for Non-expansive Mappings and Its ApplicationAug 05 2012We use $KKM$ theorem to prove the existence of a new fixed point theorem for non-expansive mapping:Let M be a bounded closed convex subset of Hilbert space H, and $A:M\rightarrow M$ be a non-expansive mapping, then exists a fixed point of A in M, we also ... More

Isospectral Deformations of Eguchi-Hanson Spaces as Nonunital Spectral TriplesApr 14 2008We study the isospectral deformations of the Eguchi-Hanson spaces along a torus isometric action in the noncompact noncommutative geometry. We concentrate on locality, smoothness and summability conditions of the nonunital spectral triples, and relate ... More

Scalar curvature in conformal geometry of Connes-Landi noncommutative manifoldsNov 27 2016We first propose a conformal geometry for Connes-Landi noncommutative manifolds and study the associated scalar curvature. The new scalar curvature contains its Riemannian counterpart as the commutative limit. Similar to the results on noncommutative ... More

Hamiltonian L-stability of Lagrangian Translating SolitonsJul 23 2014In this paper, we compute the first and second variation formulas for the F-functional of translating solitons and study the Hamiltonian L-stability of Lagrangian translating solitons. We prove that any Lagrangian translating soliton is Hamiltonian L-stable. ... More

Hamiltonian F-stability of complete Lagrangian self-shrinkersDec 30 2013Mar 14 2014In this paper, we study the Lagrangian F-stability and Hamiltonian F-stability of Lagrangian self-shrinkers. We prove a characterization theorem for the Hamiltonian F-stability of $n$-dimensional complete Lagrangian self-shrinkers without boundary, with ... More

Game-theoretic Modeling of Players' Ambiguities on External FactorsOct 23 2015Mar 19 2016We propose a game-theoretic framework that incorporates both incomplete information and general ambiguity attitudes on factors external to all players. Our starting point is players' preferences on payoff-distribution vectors, essentially mappings from ... More

Can parity-time-symmetric potentials support continuous families of non-parity-time-symmetric solitons?Sep 06 2013For the one-dimensional nonlinear Schroedinger equations with parity-time (PT) symmetric potentials, it is shown that when a real symmetric potential is perturbed by weak PT-symmetric perturbations, continuous families of asymmetric solitary waves in ... More

Mating the Basilica with a Siegel DiskOct 13 2014Consider a quadratic polynomial with a fixed Siegel disc of bounded type. Using an adaptation of complex a priori bounds for critical circle maps, we prove that this Siegel polynomial is conformally mateable with the basilica polynomial.

Extremal functions for Trudinger-Moser inequalities of Adimurthi-Druet type in dimension twoJan 01 2015Combining Carleson-Chang's result with blow-up analysis, we prove existence of extremal functions for certain Trudinger-Moser inequalities in dimension two. This kind of inequality was originally proposed by Adimurthi and O. Druet, extended by the author ... More

Associated production of the Higgs boson and a single top quark in the littlest Higgs model at Large Hadron CollierApr 10 2009In the context of the littlest Higgs model, we study the associated production of the Higgs boson and a top quark ($th$ production) at the CERN Large Hadron Collider (LHC). The cross sections for s-channel, t-channel processes and the relative correction ... More

Stability Analysis of the Laser System for the TTF Photoinjector at FermilabJul 12 2004A solid-state laser system that produces a 1MHz pulse train of 800 pulses with 18 mJ per pulse at the wavelength of 263.5 nm has been developed to meet the requirements of the TESLA Test Facility (TTF) at Fermilab and in operation since 1998.[1,2] Besides ... More

Analytical Solution for BPM Reading the Multi-bunch Average in BoosterJan 06 2005The BPM system in Booster only can provide the beam position from the average of about 15 bunches due to the electronic limitation. Numerically calculating the difference made by this average can nearly give all the information, which is needed for extrapolating ... More

On the Rationality of the Appearance of ConsciousnessNov 17 2013This paper tries to reveal the rationality of the appearance of consciousness in the evolution of the universe. Difficulties in understanding consciousness can be boiled down to two problems: the possibility of causality breaking and the origination of ... More

Strong solutions to the Cauchy problem of the two-dimensional compressible Navier-Stokes-Smoluchowski equations with vacuumAug 29 2016This paper studies the local existence of strong solutions to the Cauchy problem of the 2D fluid-particle interaction model with vacuum as far field density. Notice that the technique used by Ding et al.\cite{SBH} for the corresponding 3D local well-posedness ... More

Asymptotic behavior of positive solutions to a nonlinear biharmonic equation near isolated singularitiesDec 16 2018In this paper, we consider the asymptotic behavior of positive solutions of the biharmonic equation $$ \Delta^2 u = u^p~~~~~~~in ~ B_1 \backslash \{0\}$$ with an isolated singularity, where the punctured ball $B_1 \backslash \{0\} \subset \mathbb{R}^n$ ... More

Multiscale method, Central extensions and a generalized Craik-Leibovich equationJun 30 2016In this paper we develop perturbation theory on the reduced space of a principal $G-$bundle. This theory uses a multiscale method and is related to vibrodynamics. For a fast oscillating motion with the symmetry Lie group $G$, we prove that the averaged ... More

Inspiraling eccentric binary neutron stars: orbital motion and tidal resonanceApr 24 2019We study the orbital evolution of eccentric binary neutron stars. The orbit is described as a Quasi-Keplarian orbit with perturbations due to tidal couplings. We find that the tidal interaction between stars contributes to orbital precession, in addition ... 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

On continuation properties after blow-up time for $L^2$-critical gKdV equationsSep 25 2017Nov 14 2018In this paper, we consider a blow-up solution $u(t)$ to the $L^2$-critical gKdV equation $\partial_tu+(u_{xx}+u^5)_x=0$, with finite blow-up time $T<+\infty$. We expect to construct a natural extension of $u(t)$ after the blow-up time. To do this, we ... More

On asymptotic dynamics for $L^2$ critical generalized KdV equations with a saturated perturbationSep 16 2016Sep 04 2017In this paper, we consider the $L^2$ critical gKdV equation with a saturated perturbation: $\partial_t u+(u_{xx}+u^5-\gamma u|u|^{q-1})_x=0$, where $q>5$ and $0<\gamma\ll1$. For any initial data $u_0\in H^1$, the corresponding solution is always global ... More

A Convex Optimization Approach to Dynamic Programming in Continuous State and Action SpacesOct 09 2018Apr 10 2019A convex optimization-based method is proposed to numerically solve dynamic programs in continuous state and action spaces. This approach using a discretization of the state space has the following salient features. First, by introducing an auxiliary ... More

Injectivity radius for non-simply connected symmetric spaces via Cartan polyhedronMar 18 2007We determine the cut locus of arbitrary non-simply connected, compact and irreducible Riemannian symmetric space explicitly, and compute injectivity radius and diameter for every type of them.

Injectivity radius and Cartan polyhedron for simply connected symmetric spacesSep 22 2006We explore relationship between the cut locus of an arbitrary simply connected and compact Riemannian symmetric space and the Cartan polyhedron of corresponding restricted root system, and compute injectivity radius and diameter for every type of irreducible ... More

A compact group action which raises dimension to infinityDec 11 2002Feb 27 2003I give a construction of compact group action on a finite dimensional space Y, whose orbit space is infinite dimensional.

Diagnostics for Regression Models with Discrete Outcomes Using Surrogate Empirical Residual Distribution FunctionsJan 14 2019Feb 20 2019Making informed decisions about model adequacy has been an outstanding issue for regression models with discrete outcomes. Standard residuals for such outcomes show a large discrepancy from the hypothesized pattern even under the true model and are often ... More

A simple collinear limit of scattering amplitudes at strong couplingJun 16 2010Mar 19 2011Collinear limit usually provides strong constraints for scattering amplitudes. At strong coupling, collinear limit of the amplitudes in N=4 SYM is related to the large mass limit of the corresponding Y system. In this paper, we consider a special case ... More

Ferromagnetic Transition in One-Dimensional Itinerant Electron SystemsJan 09 2004Aug 04 2004We use bosonization to derive the effective field theory that properly describes ferromagnetic transition in one-dimensional itinerant electron systems. The resultant theory is shown to have dynamical exponent z=2 at tree leve and upper critical dimension ... More

Spin mapping, phase diagram, and collective modes in double layer quantum Hall systems at $ν=2$Mar 30 1999An exact spin mapping is identified to simplify the recently proposed hard-core boson description (Demler and Das Sarma, Phys. Rev. Lett., to be published) of the bilayer quantum Hall system at filling factor 2. The effective spin model describes an easy-plane ... More

Inertial force, Hawking Temperature and Quantum StatisticsNov 09 2018To explore the mechanism for the entropic gradient proposed in Entropic Gravity theory, we propose a thermal reversible process for 1-particle Rindler states thermalized in redshifted Hawking Temperature $T(r)$. We find when Casini's version of Bekenstein ... More

Reproducing kernel of the space $R^t(K,μ)$Apr 30 2019For $1 \le t < \infty ,$ a compact subset $K$ of the complex plane $\mathbb C,$ and a finite positive measure $\mu$ supported on $K,$ $R^t(K, \mu)$ denotes the closure in $L^t (\mu )$ of rational functions with poles off $K$. Let $\Omega$ be a connected ... More

Modular unit and cuspidal divisor class groups of X_1(N)Dec 05 2007In this article, we consider the group $F_1^\infty(N)$ of modular units on $X_1(N)$ that have divisors supported on the cusps lying over $\infty$ of $X_0(N)$, called the $\infty$-cusps. For each positive integer $N$, we will give an explicit basis for ... More

Symplectic Convexity for OrbifoldsJul 17 2003We generalize symplectic convexity theorems for Hamiltonian actions with proper momentum maps to symplectic actions on orbifolds with mod-$\Gamma$ proper momentum maps.

Linear systems in $\mathbb{P}^2$ with base points of bounded multiplicityJun 29 2004Feb 14 2009We present a proof of the Harbourne-Hirschowitz conjecture for linear systems with base points of multiplicity seven or less. This proof uses a well-known degeneration of the projective plane, as well as a combinatorial technique that arises from specializing ... More