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Speaker diarisation using 2D self-attentive combination of embeddingsFeb 08 2019Speaker diarisation systems often cluster audio segments using speaker embeddings such as i-vectors and d-vectors. Since different types of embeddings are often complementary, this paper proposes a generic framework to improve performance by combining ... More

An Expandable Local and Parallel Two-Grid Finite Element SchemeSep 09 2015An expandable local and parallel two-grid finite element scheme based on superposition principle for elliptic problems is proposed and analyzed in this paper by taking example of Poisson equation. Compared with the usual local and parallel finite element ... More

Gridbot: An autonomous robot controlled by a Spiking Neural Network mimicking the brain's navigational systemJul 05 2018It is true that the "best" neural network is not necessarily the one with the most "brain-like" behavior. Understanding biological intelligence, however, is a fundamental goal for several distinct disciplines. Translating our understanding of intelligence ... More

North Atlantic Right Whale Contact Call DetectionApr 30 2013Jun 07 2013The North Atlantic right whale (Eubalaena glacialis) is an endangered species. These whales continuously suffer from deadly vessel impacts alongside the eastern coast of North America. There have been countless efforts to save the remaining 350 - 400 ... More

Spiking Neural Network on Neuromorphic Hardware for Energy-Efficient Unidimensional SLAMMar 06 2019Energy-efficient simultaneous localization and mapping (SLAM) is crucial for mobile robots exploring unknown environments. The mammalian brain solves SLAM via a network of specialized neurons, exhibiting asynchronous computations and event-based communications, ... More

Projective embedding of log Riemann surfaces and K-stabilityMay 03 2016Aug 16 2016Given a smooth polarized Riemann surface (X, L) endowed with a hyperbolic metric $\omega$ with cusp singularities along a divisor D, we show the L^2 projective embedding of (X, D) defined by L^k is asymptotically almost balanced in a weighted sense. The ... More

Projective embedding of log Riemann surfaces and K-stabilityMay 03 2016Sep 25 2017Given a smooth polarized Riemann surface (X, L) endowed with a hyperbolic metric $\omega$ with cusp singularities along a divisor D, we show the L^2 projective embedding of (X, D) defined by L^k is asymptotically almost balanced in a weighted sense. The ... More

SPLZ: An Efficient Algorithm for Single Source Shortest Path Problem Using Compression MethodAug 11 2014Jan 11 2015Efficient solution of the single source shortest path (SSSP) problem on road networks is an important requirement for numerous real-world applications. This paper introduces an algorithm for the SSSP problem using compression method. Owning to precomputing ... More

Sphere theorems for submanifolds in Kähler ManifoldOct 17 2018In this paper, we prove some differentiable sphere theorems and topological sphere theorems for submanifolds in K\"ahler manifold, especially in complex space forms.

Sphere theorems for Lagrangian and Legendrian submanifoldsOct 22 2018In this paper, we prove some differentiable sphere theorems and topological sphere theorems for Lagrangian submanifolds in K\"ahler manifold and Legendrian submanifolds in Sasaki space form.

Investigation Solvation Dynamics and Isomerization of Dye IR-140 Using pump supercontinuum-probing TechniqueNov 06 2001The solvation dynamics and isomerization process of an organic dye, IR-140, in polar solvents and nonpolar solvents have been investigated using pump supercontinuum-probing (PSCP) technique. In all solvents, the dynamics exhibits solvent-dependent. Solvent ... More

Different Particle Sizes Obtained from Static and Dynamic Laser Light ScatteringMay 31 2004Dec 08 2004Detailed investigation of static and dynamic laser light scattering has been attempted in this work both theoretically and experimentally based on dilute water dispersions of two different homogenous spherical particles, polystyrene latexes and poly($N$-isopropylacrylamide) ... More

Note on K-stability of pairsAug 23 2011Nov 23 2012We prove that a pair (X, D) with X Fano and D a smooth anti-canonical divisor is K-unstable for negative angles, and K-semistable for zero angle.

Infinite Mixtures of Multivariate Gaussian ProcessesJul 26 2013This paper presents a new model called infinite mixtures of multivariate Gaussian processes, which can be used to learn vector-valued functions and applied to multitask learning. As an extension of the single multivariate Gaussian process, the mixture ... More

Independence of $\ell$ for the supports in the Decomposition TheoremDec 04 2015In this note, we prove a result on the independence of $\ell$ for the supports of irreducible perverse sheaves occurring in the Decomposition Theorem, as well as for the family of local systems on each support. It generalizes Gabber's result on the independence ... More

W-Operators and Permutation GroupsOct 20 2016W-operators are differential operators on the polynomial ring. A special example of W-operators is the cut-and-join operator. We study the relation between W-operators and permutation groups. We find the W-operator $W([d])$ can be written as the sum of ... More

Stability of sheaves of locally closed and exact formsMay 13 2009For any smooth projective variety $X$ of dimension $n$ over an algebraically closed field $k$ of characteristic $p>0$ with $\mu(\Omega^1_X)>0$. If ${\rm T}^{\ell}(\Omega^1_X)$ ($0<\ell<n(p-1)$) are semi-stable, then the sheaf $B^1_X$ of exact 1-forms ... More

Suspicion on Engrafting HBT From Astronomy to Heavy Ion CollisionDec 13 2004Aug 19 2005HBT method in astronomy and heavy ion collision is contrasted in present article.Some differences are found and validity of using HBT in heavy ion collision is suspected.

Factorization of generalized theta functions at reducible caseApr 17 2000We proved the factorization of generalized theta functions when the curve has two irreducible components meeting at one node.

Topological Phases of Fermionic Ladders with Periodic Magnetic FieldsDec 14 2015In recent experiments bosonic [Atala et al., Nat. Phys. 10, 588 (2014), B. K. Stuhl et al., Science 349, 1514 (2015)] as well as fermionic ladders [M. Mancini et al., Science 349, 1510 (2015)] with a uniform flux were studied and different interesting ... More

Compactness of Constant Mean Curvature Surfaces in Three Manifold with Positive Ricci CurvatureApr 25 2018Dec 06 2018In this paper we prove a compactness theorem for constant mean curvature surfaces with area and genus bound in three manifold with positive Ricci curvature. As an application, we give a lower bound of first eigenvalue of constant mean curvature surfaces ... More

Physarum-inspired Network Optimization: A ReviewDec 08 2017The popular Physarum-inspired Algorithms (PAs) have the potential to solve challenging network optimization problems. However, the existing researches on PAs are still immature and far from being fully recognized. A major reason is that these researches ... More

Shifted convolution sums of $GL_3$ cusp forms with $θ$-seriesSep 25 2015Sep 10 2016Let $A_f(1,n)$ be the normalized Fourier coefficients of a Hecke-Maass cusp form $f$ for $SL_3(\mathbb{Z})$ and $$ r_3(n)=\#\left\{(n_1,n_2,n_3)\in \mathbb{Z}^3:n_1^2+n_2^2+n_3^2=n\right\}. $$ Let $1\leq h\leq X$ and $\phi(x)$ be a smooth function compactly ... More

Shifted convolution sums involving theta seriesMay 02 2017Let $f$ be a cuspidal newform (holomorphic or Maass) of arbitrary level and nebentypus and denote by $\lambda_f(n)$ its $n$-th Hecke eigenvalue. Let $$ r(n)=\#\left\{(n_1,n_2)\in \mathbb{Z}^2:n_1^2+n_2^2=n\right\}. $$ In this paper, we study the shifted ... More

Co-iterative augmented Hessian method for orbital optimizationOct 26 2016Jan 10 2017Orbital optimization procedure is widely called in electronic structure simulation. To efficiently find the orbital optimization solution, we developed a new second order orbital optimization algorithm, co-iteration augmented Hessian (CIAH) method. In ... More

An exact axisymmetric spiral solution of incompressible 3D Euler equationsJan 29 2011Jul 31 2011Spiral structure is one of the most common structures in the nature flows. A general steady spiral solution of incompressible inviscid axisymmetric flow was obtained analytically by applying separation of variables to the 3D Euler equations. The solution, ... More

Zero-Entropy Dynamical Systems with Gluing Orbit PropertyOct 21 2018We show that a dynamical system with gluing orbit property and zero topological entropy is equicontinuous, hence it is topologically conjugate to a minimal rotation.

Measures of Intermediate Entropies for Skew Product DiffeomorphismsJun 10 2009Jan 18 2010In this paper we study a skew product map $F$ with a measure $\mu$ of positive entropy. We show that if on the fibers the map are $C^{1+\alpha}$ diffeomorphisms with nonzero Lyapunov exponents, then $F$ has ergodic measures of intermediate entropies. ... More

Frobenius morphism and semi-stable bundlesApr 09 2009This article is the expanded version of a talk given at the conference: Algebraic geometry in East Asia 2008, Seoul. In this notes, I intend to give a brief survey of results on the behavior of semi-stable bundles under the Frobenius pullback and direct ... More

W-Operator and Differential Equation for 3-Hurwitz NumberDec 09 2016We consider a new type of Hurwitz number, the number of ordered transitive factorizations of an arbitrary permutation into d-cycles. In this paper, we focus on the special case d = 3. The minimal number of transitive factorizations of any permutation ... More

Private Information DeliveryJun 14 2018Mar 25 2019We introduce the problem of private information delivery (PID), comprised of $K$ messages, a user, and $N$ servers (each holds $M\leq K$ messages) that wish to deliver one out of $K$ messages to the user privately, i.e., without revealing the delivered ... More

Dark Matter Searches in Jet plus Missing Energy in $\rm γp$ collision at CERN LHCJul 21 2014Aug 01 2014In this paper, we investigate the $\rm \gamma p$ photoproduction of jet plus missing energy signal to set limits on the couplings of the fermionic dark matter to the quarks at the LHC via the main reaction $\rm pp\rightarrow p\gamma p\rightarrow p \chi\chi ... More

On the Clifford theorem for surfacesMar 04 2012We give two generalizations of the Clifford theorem to algebraic surfaces. As an application, we obtain some bounds for the number of moduli of surfaces of general type.

Counting Hypergraphs in Data StreamsApr 28 2013We present the first streaming algorithm for counting an arbitrary hypergraph $H$ of constant size in a massive hypergraph $G$. Our algorithm can handle both edge-insertions and edge-deletions, and is applicable for the distributed setting. Moreover, ... More

Pluricanonical maps of varieties of Albanese fiber dimension twoNov 28 2012Feb 23 2014In this paper we prove that for any smooth projective variety of Albanese fiber dimension two and of general type, the 6-canonical map is birational. And we also show that the 5-canonical map is birational for any such variety with some geometric restrictions. ... More

Overview of top quark physics at the ep collidersOct 17 2017In this talk we present a short overview of top physics at the electron-proton (ep) colliders. Currently, the proposed ep collider is the Large Hadron Electron Collider (LHeC), which is a combination of 60 GeV electron beam and 7 TeV proton beam of the ... More

Orlicz-Besov imbedding and globally $n$-regular domainsOct 09 2018Denote by $ {\bf\dot B}^{\alpha,\phi}(\Omega)$ the Orlicz-Besov space, where $\alpha\in\mathbb{R}$, $\phi$ is a Young function and $\Omega\subset\mathbb{R}^n$ is a domain. For $\alpha\in(-n,0)$ and optimal $\phi$, in this paper we characterize domains ... More

Topics in Quantum NetworkingMar 07 2019It is an era full of imaginations and lack of impossibilities. The knowledge boundaries have been being pushed back on and on. The quantum age is on the edge of transforming quantum theories into quantum technologies. We present a sketch of the advances ... More

Universal central extensions of twisted forms of split simple Lie algebras over ringsNov 17 2010Nov 19 2010We give sufficient conditions for the descent construction to be the universal central extension of a twisted form of a split simple Lie algebra over a ring. In particular, the universal central extensions of twisted multiloop Lie tori are obtained by ... More

On uniform estimate of complex elliptic equations on closed Hermitian manifoldsDec 16 2014Feb 10 2015In this paper, we study Hessian equations and complex quotient equations on closed Hermitian manifolds. We directly derive the uniform estimate for the admissible solution. As an application, we solve general Hessian equations on closed K\"ahler manifolds. ... More

An estimate on energy of min-max Seiberg-Witten Floer generatorsJan 08 2018Jan 20 2018Previously, Cristofaro-Gardiner, Hutchings and Ramos have proved that embedded contact homology (ECH) capacities can recover the volume of a contact 3-manifod in their paper "the asymptotics of ECH capacities" . There were two main steps to proving this ... More

On a class of fully nonlinear elliptic equations on closed Hermitian manifoldsOct 01 2013We study a class of fully nonlinear elliptic equations on closed Hermitian manifolds. We derive $C^\infty$ {\em a priori} estimates, and then prove the existence of admissible solutions. In the approach, a new Hermitian metic is constructed to launch ... More

Exact Controllability of linear KP-I equationFeb 28 2018We prove the exact controllability of linear KP-I equation if the control input is added on a vertical domain. More generally, we have obtained the least dispersion needed to insure observability for fractional linear KP I equation.

Strichartz-type Estimates for Wave Equation for Normally Hyperbolic Trapped DomainsJul 20 2015We establish a mixed-norm Strichartz type estimate for the wave equation on Riemannian manifolds $(\Omega,g)$, for the case that $\Omega$ is the exterior of a smooth, normally hyperbolic trapped obstacle in $n$ dimensional Euclidean space, and $n$ is ... More

Direct images of bundles under Frobenius morphismsNov 13 2006Mar 31 2008Let $X$ be a smooth projective variety of dimension $n$ over an algebraically closed field $k$ with ${\rm char}(k)=p>0$ and $F:X\to X_1$ be the relative Frobenius morphism. For any vector bundle $W$ on $X$, we prove that instability of $F_*W$ is bounded ... More

A New Formula for the Inverse Wavelet TransformJun 20 2010Aug 30 2010Finding a computationally efficient algorithm for the inverse continuous wavelet transform is a fundamental topic in applications. In this paper, we show the convergence of the inverse wavelet transform.

A Transcendental Invariant of Pseudo-Anosov MapsSep 12 2012May 09 2013For each pseudo-Anosov map $\phi$ on surface $S$, we will associate it with a $\mathbb{Q}$-submodule of $\mathbb{R}$, denoted by $A(S,\phi)$. $A(S,\phi)$ is defined by an interaction between the Thurston norm and dilatation of pseudo-Anosov maps. We will ... More

The Star of David RuleMay 09 2008In this note, a new concept called {\em $SDR$-matrix} is proposed, which is an infinite lower triangular matrix obeying the generalized rule of David star. Some basic properties of $SDR$-matrices are discussed and two conjectures on $SDR$-matrices are ... More

A representation-theoretic proof of the branching rule for Macdonald polynomialsDec 01 2014We give a new representation-theoretic proof of the branching rule for Macdonald polynomials using the Etingof-Kirillov Jr. expression for Macdonald polynomials as traces of intertwiners of U_q(gl_n). In the Gelfand-Tsetlin basis, we show that diagonal ... More

Virtual Domination of $3$-manifoldsJan 27 2014For any closed oriented hyperbolic $3$-manifold $M$, and any closed oriented $3$-manifold $N$, we will show that $M$ admits a finite cover $M'$, such that there exists a degree-$2$ map $f:M'\rightarrow N$, i.e. $M$ virtually $2$-dominates $N$.

Virtual Homological Torsion of Closed Hyperbolic 3-manifoldsSep 05 2013Jun 05 2014In this paper, we will use Kahn-Markovic's almost totally geodesic surfaces to construct certain $\pi_1$-injective 2-complexes in closed hyperbolic 3-manifolds. Such 2-complexes are locally almost totally geodesic except along a 1-dimensional subcomplex. ... More

A New Bound on Hrushovski's Algorithm for Computing the Galois Group of a Linear Differential EquationMar 19 2018Feb 16 2019The complexity of computing the Galois group of a linear differential equation is of general interest. In a recent work, Feng gave the first degree bound on Hrushovski's algorithm for computing the Galois group of a linear differential equation. This ... More

Two laws of large numbers for sublinear expectationsNov 18 2015In this paper, we consider the sublinear expectation on bounded random vari- ables. With the notion of uncorrelatedness for random variables under the sublinear expectation, a weak law of large numbers is obtained. With the no- tion of independence for ... More

Chebyshev Interpolation for Function in 1DSep 24 2018This research is concerned with finding the roots of a function in an interval using Chebyshev Interpolation. Numerical results of Chebyshev Interpolation are presented to show that this is a powerful way to simultaneously calculate all the roots in an ... More

Linear Quadratic Optimal Control Problems with Fixed Terminal States and Integral Quadratic ConstraintsMay 10 2017This paper is concerned with a linear quadratic (LQ, for short) optimal control problem with fixed terminal states and integral quadratic constraints. A Riccati equation with infinite terminal value is introduced, which is uniquely solvable and whose ... More

Rank $n$ swapping algebra for the $\operatorname{PSL}(n, \mathbb{R})$ Hitchin componentNov 11 2014Oct 24 2015F. Labourie [arXiv:1212.5015] characterized the Hitchin components for $\operatorname{PSL}(n, \mathbb{R})$ for any $n>1$ by using the swapping algebra, where the swapping algebra should be understood as a ring equipped with a Poisson bracket. We introduce ... More

Ordinary p-adic automorphic formsSep 18 2017Generalizing the completed cohomology groups introduced by Matthew Emerton, we define certain spaces of "ordinary $p$-adic automorphic forms along a parabolic subgroup" and show that they interpret all classical ordinary automorphic forms.

Virtual homological eigenvalue and mapping torus of pseudo-Anosov mapsAug 25 2016In this note, we show that, if a pseudo-Anosov map $\phi:S\to S$ admits a finite cover which has a homological eigenvalue with modulus greater than $1$, then the monodromy of any fibered structure of any finite cover of $M_{\phi}$ has this property.

On Noether approach in the cosmological model with scalar and gauge fields: symmetries and the selection ruleApr 18 2015In this paper, based on the works of Capozziello et al., we have studied the Noether symmetry approach in the cosmological model with scalar and gauge fields proposed recently by Soda et al. The correct Noether symmetries and related Lie algebra are given ... More

Decomposition Theorem for Perverse sheaves on Artin stacks over finite fieldsSep 22 2010Mar 11 2012We generalize the decomposition theorem for perverse sheaves to Artin stacks with affine stabilizers over finite fields.

L-series of Artin stacks over finite fieldsAug 22 2010Mar 28 2011We reprove the Lefschetz trace formula for stacks (in the context of derived categories and the six operations for stacks developed by Laszlo and Olsson), and give the meromorphic continuation of L-series (in particular, zeta functions) of Artin stacks ... More

Axisymmetrically Tropical Cyclone-like Vortices with Secondary CirculationsSep 07 2013The secondary circulation of the tropical cyclone (TC) is related to its formation and intensification, thus becomes very important in the studies. The analytical solutions have both the primary and secondary circulation in a three-dimensionally nonhydrostatic ... More

Identify the diapycnical eddy diffusivities by salt fingers and turbulence with vertical microstructure measurementsJun 23 2014Diapycnical eddy diffusivities are formulated from physical relations according to a simple fact that the different formulas are identical for the same parameter. It is found that the dispassion ratio \Gamma is a crucial parameter. When it is above a ... More

Fock-Goncharov coordinates and rank $n$ swapping algebraMar 03 2015Jun 10 2016In our previous paper arXiv:math/1411.2796, we introduced the rank $n$ swapping algebra---a Poisson algebra associated to an affine variety defined by pairs of points on a circle and their determinant relations. Let the rank $n$ swapping multifraction ... More

Character tables of Sylow $p$-subgroups ${^3}D_4^{syl}(q^3)$ of the Steinberg triality groupsJun 20 2016We determine the character tables of Sylow $p$-subgroups ${^3}D_4^{syl}(q^3)$ of the Steinberg triality groups ${^3}D_4(q^3)$.

NonLERFness of arithmetic hyperbolic manifold groupsAug 17 2016We will show that, for any noncompact arithmetic hyperbolic $m$-manifold with $m\geq 4$, and any compact arithmetic hyperbolic $m$-manifold with $m\geq 5$ which is not a $7$-dimensional arithmetic hyperbolic manifold defined by octonions, its fundamental ... More

Non-elementary convergence groups are acylindrically hyperbolicDec 01 2016We proved that non-elementary discrete convergence groups are acylindrically hyperbolic.

A supercharacter theory for Sylow $p$-subgroups ${^3}D_4^{syl}(q^3)$ of the Steinberg triality groupsNov 28 2016We determine a supercharacter theory for the matrix Sylow $p$-subgroup ${^3}D_4^{syl}(q^3)$ of the Steinberg triality group ${^3}D_4(q^3)$, and establish the supercharacter table of ${^3}D_4^{syl}(q^3)$.

Towards Shockingly Easy Structured Classification: A Search-based Probabilistic Online Learning FrameworkMar 29 2015There are two major approaches for structured classification. One is the probabilistic gradient-based methods such as conditional random fields (CRF), which has high accuracy but with drawbacks: slow training, and no support of search-based optimization ... More

Demosaicing and Superresolution for Color Filter Array via Residual Image Reconstruction and Sparse RepresentationSep 29 2012Jul 04 2013A framework of demosaicing and superresolution for color filter array (CFA) via residual image reconstruction and sparse representation is presented.Given the intermediate image produced by certain demosaicing and interpolation technique, a residual image ... More

Cohomologically induced distinguished representations and cohomological test vectorsNov 11 2011Jan 30 2015Let $G$ be a real reductive group, and let $\chi$ be a character of a reductive subgroup $H$ of $G$. We construct $\chi$-invariant linear functionals on certain cohomologically induced representations of $G$, and show that these linear functionals do ... More

Non-elementary convergence groups are acylindrically hyperbolicDec 01 2016Oct 19 2017We proved that non-elementary discrete convergence groups are acylindrically hyperbolic.

Eisenstein integrals for theta stable parabolic subalgebrasMar 25 2004Nov 28 2004Let $G$ be a connected semisimple Lie group with a finite center, with a maximal compact subgroup $K$. There are two general methods to construct representations of $G$, namely, ordinary parabolic induction and cohomological parabolic induction. We define ... More

The dependence of hydrophobic interactions on the solute sizeMay 09 2017Mar 06 2018Based on our recent study on physical origin of hydrophobic effects, this is applied to investigate the dependence of hydrophobic interactions on the solute size. As two same hydrophobic solutes are dissolved into water, the hydration free energy is determined, ... More

Libcint: An efficient general integral library for Gaussian basis functionsDec 01 2014An efficient integral library Libcint was designed to automatically implement general integrals for Gaussian-type scalar and spinor basis functions. The library can handle arbitrary integral expressions on top of $\mathbf{p}$, $\mathbf{r}$ and $\sigma$ ... More

A note on simultaneous nonvanishing of Dirichlet $L$-functions and twists of Hecke-Maass $L$-functionsSep 10 2016In this note, we prove that given a Hecke-Maass cusp form $f$ for $SL_2(\mathbb{Z})$ and a sufficiently large integer $q=q_1q_2$ with $q_j\asymp \sqrt{q}$ being prime numbers for $j=1,2$, there exists a primitive Dirichlet character $\chi$ of conductor ... More

Solving the Steiner Tree Problem in Graphs using Physarum-inspired AlgorithmsMar 21 2019Some biological experiments show that the tubular structures of Physarum polycephalum are often analogous to those of Steiner trees. Therefore, the emerging Physarum-inspired Algorithms (PAs) have the potential of computing Steiner trees. In this paper, ... More

Conformally invariant scaling limits in planar critical percolationNov 02 2009Oct 21 2011This is an introductory account of the emergence of conformal invariance in the scaling limit of planar critical percolation. We give an exposition of Smirnov's theorem (2001) on the conformal invariance of crossing probabilities in site percolation on ... More

Almost linear Nash groupsOct 30 2013Nov 21 2013A Nash group is said to be almost linear if it has a Nash representation with finite kernel. Structures and basic properties of these groups are studied.

Mott-Hubbard Scenario for the Metal-Insulator Transition in the Two Dimensional Electron GasAug 01 2006By comparing the responses to an in-plane magnetic field near the metal-insulator transition (MIT), we find that the observed MIT in Si MOSFETs can be described by the non-perturbative Mott-Hubbard scenario. Interrelations between independent measurables ... More

Organics in the Solar SystemJan 15 2019Complex organics are now commonly found in meteorites, comets, asteroids, planetary satellites, and interplanetary dust particles. The chemical composition and possible origin of these organics are presented. Specifically, we discuss the possible link ... More

Morphological Structures of Planetary NebulaeNov 30 2009Since various structural components of planetary nebulae manifest themselves differently, a combination of optical, infrared, submm, and radio techniques is needed to derive a complete picture of planetary nebulae. The effects of projection can also make ... More

A note on equivariantization of additive and triangulated categoriesAug 17 2017Oct 25 2018In this article, we investigate the category $\mathcal{A}^G$ of equivariant objects of an additive category $\mathcal{A}$ with respect to an action of a finite group $G$. We show that if $G$ is solvable then we can reconstruct $\mathcal{A}$ from $\mathcal{A}^G$ ... More

Confining the light wave by using non-Euclidean transformation opticsFeb 03 2013Sep 24 2013A new way to understand why some inhomogeneous dielectric medium can be used for confining the light wave has been given by using non-Euclidean transformation optics. We show that special inhomogeneous dielectric medium, which corresponds to a dip in ... More

Magnetic Manifestation of Discrete Scaling Symmetry in Dirac SemimetalsMay 05 2018Aug 09 2018Two-dimensional and three-dimensional massless Dirac fermions can form a sequence of quasibound states with an attractive charged impurity. These quasibound states exhibit a discrete scaling symmetry, i.e., the energy ratio between two successive states ... More

Why are there strong radio AGNs in the center of "non-cool core" clusters?Oct 05 2009Radio AGN feedback in X-ray cool cores has been proposed as a crucial ingredient in the evolution of baryonic structures. However, it has long been known that strong radio AGNs also exist in "noncool core" clusters, which brings up the question whether ... More

Every BCG with a strong radio AGN has an X-ray cool core: is the cool core - noncool core dichotomy too simple?Apr 13 2009Sep 20 2009Radio AGN feedback in X-ray cool cores has been proposed as a crucial ingredient in the evolution of baryonic structures. However, it has long been known that strong radio AGN also exist in "noncool core" clusters, which brings up the question whether ... More

Arithmetic genus of integral space curvesMay 23 2016We give an estimation for the arithmetic genus of an integral space curve, which are not contained in a surface of degree $k-1$. Our main technique is the Bogomolov-Gieseker type inequality for $\mathbb{P}^3$ proved by Macri.

Large Extra Dimension effects through Light-by-Light Scattering at the CERN LHCJun 16 2014Jul 31 2014Observing light-by-light scattering at the Large Hadron Collider (LHC) has received quite some attention and it is believed to be a clean and sensitive channel to possible new physics. In this paper, we study the diphoton production at the LHC via the ... More

Black Hole - Never Forms, or Never EvaporatesFeb 13 2011Mar 21 2011Many discussion about the black hole conundrums, such as singularity and information loss, suggested that there must be some essential irreconcilable conflict between quantum theory and classical gravity theory, which cannot be solved with any semiclassical ... More

Multiple recurrence and convergence for certain averages along shifted primesMar 15 2013Feb 03 2014We show any subset $A\subset\mathbb{N}$ with positive upper Banach density contains the pattern $\{m,m+[n\alpha],\dots,m+k[n\alpha]\}$, for some $m\in\mathbb{N}$ and $n=p-1$ for some prime $p$, where $\alpha\in\mathbb{R}\backslash\mathbb{Q}$. Making use ... More

The complement value problem for non-local operatorsMar 31 2018Aug 26 2018Let $D$ be a bounded Lipschitz domain of $\mathbb{R}^d$. We consider the complement value problem $$ \left\{\begin{array}{l}(\Delta+a^{\alpha}\Delta^{\alpha/2}+b\cdot\nabla+c)u+f=0\ \ {\rm in}\ D,\\ u=g\ \ {\rm on}\ D^c. \end{array}\right.$$ Under mild ... More

The complement value problem for a class of second order elliptic integro-differential operatorsMay 17 2018We consider the complement value problem for a class of second order elliptic integro-differential operators. Let $D$ be a bounded Lipschitz domain of $\mathbb{R}^d$. Under mild conditions, we show that there exists a unique bounded continuous weak solution ... More

Localized nonlinear functional equations and two sampling problems in signal processingApr 09 2013Let $1\le p\le \infty$. In this paper, we consider solving a nonlinear functional equation $$f(x)=y,$$ where $x, y$ belong to $\ell^p$ and $f$ has continuous bounded gradient in an inverse-closed subalgebra of ${\mathcal B}(\ell^2)$, the Banach algebra ... More

Local Entropy and Generic Multiplicity One Singularities of Mean Curvature Flow of SurfacesOct 18 2018Nov 12 2018In this paper we prove that the generic singularity of mean curvature flow of closed embedded surfaces in $\mathbb R^3$ modelled by closed self-shrinkers with multiplicity has multiplicity one. Together with the previous result by Colding-Minicozzi in ... More

Geometrically finite amalgamations of hyperbolic 3-manifold groups are not LERFMay 09 2017We prove that, for any two finite volume hyperbolic $3$-manifolds, the amalgamation of their fundamental groups along any nontrivial geometrically finite subgroup is not LERF. This generalizes the author's previous work on nonLERFness of amalgamations ... More

On the low-regularity global well-posedness of a system of nonlinear Schrodinger EquationApr 17 2017In this article, we study the low-regularity Cauchy problem of a one dimensional quadratic Schrodinger system with coupled parameter $\alpha\in (0, 1)$. When $\frac{1}{2}<\alpha<1$,we prove the global well-posedness in $H^s(\mathbb{R})$ with $s>-\frac{1}{4}$, ... More

Carleman Estimate for Surface in Euclidean Space at InfinityMar 26 2017This paper develops a Carleman type estimate for immersed surface in Euclidean space at infinity. With this estimate, we obtain an unique continuation property for harmonic functions on immersed surfaces vanishing at infinity, which leads to rigidity ... More

Exponential Decay of Lebesgue NumbersFeb 02 2010Nov 20 2010We study the exponential rate of decay of Lebesgue numbers of open covers in topological dynamical systems. We show that topological entropy is bounded by this rate multiplied by dimension. Some corollaries and examples are discussed.

Changes to the t-J Model From Inclusion of Two-Site Nearest-Neighbor Coulomb InteractionsApr 27 2017To date, the Hubbard model and its strong coupling limit, the t-J model, serve as the canonical model for strongly correlated electron systems in solids. Approximating the Coulomb interaction by only the on-site term (Hubbard U-term), however, may not ... More