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Results for "Guangzhi Sun"

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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
Two-Stage Convolutional Neural Network Architecture for Lung Nodule DetectionMay 09 2019Early detection of lung cancer is an effective way to improve the survival rate of patients. It is a critical step to have accurate detection of lung nodules in computed tomography (CT) images for the diagnosis of lung cancer. However, due to the heterogeneity ... 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
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.
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
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
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.
Exact Decoding on Latent Variable Conditional Models is NP-HardJun 18 2014Latent variable conditional models, including the latent conditional random fields as a special case, are popular models for many natural language processing and vision processing tasks. The computational complexity of the exact decoding/inference in ... More
On the Coordinate System of Space-Weather HMI Active Region Patches (SHARPs): A Technical NoteSep 10 2013We describe the coordinate systems of two streams of HMI active region vector data. A distinction is made between (a) the 2D grid on which the field vector is measured (or sampled), and (b) the 3D coordinate established at each grid point, in which the ... More
Structure Regularization for Structured Prediction: Theories and ExperimentsNov 23 2014Jan 30 2015While there are many studies on weight regularization, the study on structure regularization is rare. Many existing systems on structured prediction focus on increasing the level of structural dependencies within the model. However, this trend could have ... More
Moduli spaces of SL(r)-bundles on singular irreducible curvesMar 17 2003For a stable irreducible curve $X$ and a torsion free sheaf $L$ on $X$ of rank one and degree $d$, D.S. Nagaraj and C.S. Seshadri ([NS]) defined a closed subset $\Cal U_X(r,L)$ in the moduli space of semistable torsion free sheaves of rank $r$ and degree ... More
Monte Carlo studies of three-dimensional O(1) and O(4) \boldmath{$φ^4$} theory related to BEC phase transition temperaturesSep 20 2002The phase transition temperature for the Bose-Einstein condensation (BEC) of weakly-interacting Bose gases in three dimensions is known to be related to certain non-universal properties of the phase transition of three-dimensional O(2) symmetric $\phi^4$ ... More
Degeneration of SL(n)-bundles on a reducible curveDec 07 2001We constructed a projective moduli space of semistable torsion free sheaves with `fixed determinant' on a reducible curve. When a family of smooth curves degenerates to the reducible curve, our moduli space is a degeneration of the moduli spaces of semistable ... More
Signature-Based Gröbner Basis Algorithms --- Extended MMM Algorithm for computing Gröbner basesAug 11 2013Signature-based algorithms is a popular kind of algorithms for computing Gr\"obner bases, and many related papers have been published recently. In this paper, no new signature-based algorithms and no new proofs are presented. Instead, a view of signature-based ... More
Investigating Static and Dynamic Light ScatteringOct 08 2011A new size, static radii $R_{s}$, can be measured accurately using Static Light Scattering (SLS) technique when the Rayleigh-Gans-Debye approximation is valid for dilute homogenous spherical particles in dispersion. The method proposed in this work not ... More
Investigating Diffusion Coefficient Using Dynamic Light Scattering TechniqueDec 12 2006In this work, the Z-average, effective, apparent diffusion coefficients and their poly-dispersity indexes were investigated for dilute poly-disperse homogeneous spherical particles in dispersion where the Rayleigh-Gans-Debye approximation is valid. The ... More
Three Different Sizes Obtained Using Light Scattering TechniquesNov 23 2004Dec 08 2004The average scattered intensity is determined by the optical characteristics of particles in dispersion. The normalized time auto-correlation function of the scattered light intensity $g^{(2)}(\tau) $ includes both the optical and hydrodynamic information ... More
Discussing the Relationship between the Static and Dynamic Light ScatteringOct 11 2004Dec 08 2004Both the static $(SLS) $ and dynamic $(DLS) $ light scattering techniques are used to obtain the size information from the scattered intensity, but the static radius $R_{s}$ and the apparent hydrodynamic radius $R_{h,app}$ are different. In this paper, ... More
New Interpretation for Laser Light Scattering TechniqueNov 18 2005The new method proposed in this work not only measures the particle size distribution and the average molar mass accurately using the static light scattering (SLS) technique when the Rayleigh-Gans-Debye approximation is valid for dilute poly-disperse ... More
The Spatial Scaling Laws of Compressible TurbulenceFeb 10 2015Aug 25 2016The spatial scaling laws of velocity kinetic energy spectrum for compressible turbulence flow and its density-weighted counterpart have been formulated in terms of wavenumber, dissipation rate and Mach number by using dimensional analysis. We have applied ... More
Partial result of Yau's Conjecture of the first eigenvalue in unit sphere $\mathbb{S}^{n+1}(1)$Jul 28 2016Aug 01 2016In this paper, we partially solve Yau' Conjecture of the first eigenvalue of an embedded compact minimal hypersurface of unit sphere $\mathbb{S}^{n+1}(1)$, i.e., Corollary 1.2. In particular, Corollary 1.3 proves that the condition $\int_{\Omega_{1}}|\nabla ... More
Accurate and Efficient Solution of the Electronic Schrödinger Equation with the Coulomb Singularity by the Distributed Approximating Functional MethodApr 04 2016We proposed a distributed approximating functional method for efficiently describing the electronic dynamics in atoms and molecules in the presence of the Coulomb singularities, using the kernel of a grid representation derived by using the solutions ... More
Gutzwiller's Semiclassical Trace Formula and Maslov-Type Index Theory for Symplectic PathsAug 30 2016Gutzwiller's famous semiclassical trace formula plays an important role in theoretical and experimental quantum mechanics with tremendous success. We review the physical derivation of this deep periodic orbit theory in terms of the phase space formulation ... More
Analysis of Fully Preconditioned ADMM with Relaxation in Hilbert SpacesNov 15 2016Nov 16 2016Alternating direction method of multipliers (ADMM) is a powerful first order methods for various applications in signal processing and imaging. However, there is no clear result on the weak convergence of ADMM with relaxation studied by Eckstein and Bertsakas ... More
Multiply robust two-sample instrumental variable estimationOct 08 2018Oct 16 2018Although instrumental variable (IV) methods are widely used to estimate causal effects in the presence of unmeasured confounding, the IVs, exposure and outcome are often not measured in the same sample due to complex data harvesting procedures. Following ... More
On Plastic Dislocation Density TensorFeb 06 2019This article attempts to clarify an issue regarding the proper definition of plastic dislocation density tensor. This study shows that the Ortiz's and Berdichevsky's plastic dislocation density tensors are equivalent with each other, but not with Kondo's ... More
Singularity-free approximate analytical solution of capillary rise dynamicsJul 30 2018Capillary rise is one of the most well-known capillarity; however, no single and complete analytic solution has ever been obtained yet. This paper used the singularity-free equation, and successfully obtained its Taylor's series solution. The solution ... More
Face distributions of embeddings of complete graphsAug 07 2017Aug 30 2018A longstanding open question of Archdeacon and Craft asks whether every complete graph has a minimum genus embedding with at most one nontriangular face. We exhibit such an embedding for each complete graph except $K_8$, the complete graph on 8 vertices, ... More
The parabolic flows for complex quotient equationsDec 03 2017We apply the parabolic flow method to solving complex quotient equations on closed K\"ahler manifolds. We study the parabolic equation and prove the convergence. As a result, we solve the complex quotient equations.
Phaseless Sampling and Linear Reconstruction of Functions in Spline SpacesSep 14 2017Sep 15 2017We study phaseless sampling in spline spaces generated by B-splines with arbitrary knots. For real spline spaces, we give a necessary and sufficient condition for a sequence of sampling points to admit a local phase retrieval of any nonseparable function. ... More
Toroidal Dimer Model and Temperley's BijectionMar 02 2016Temperley's bijection relates the toroidal dimer model to cycle rooted spanning forests ($CRSF$) on the torus. The height function of the dimer model and the homology class of $CRSF$ are naturally related. When the size of the torus tends to infinity, ... More
Parabolic Flow for Generalized complex Monge-Ampère type equationsJan 18 2015We study the parabolic flow for generalized complex Monge-Amp\`ere type equations on closed Hermitian manifolds. We derive {\em a priori} $C^\infty$ estimates for normalized solutions, and then prove the $C^\infty$ convergence.
Generalized complex Monge-Ampère type equations on closed Hermitian manifoldsDec 28 2014Jun 28 2016We study generalized complex Monge-Amp\`ere type equations on closed Hermitian manifolds. We derive {\em a priori} estimates and then prove the existence of admissible solutions. Moreover, the gradient estimate is improved.
W-Operator and Hurwitz NumberNov 15 2016W-operators are differential operators on the polynomial ring. Mironov, Morosov and Natanzon construct the generalized Hurwitz numbers. They use the W-operator to prove a formula for the generating function of the generalized Hurwitz numbers. A special ... More
Permutation Group and Degree of W-OperatorOct 20 2016May 11 2017The cut-and-join operator is introduced by Goulden and Jackson. Mironov, Morosov and Natanzon gives a more general construction and call it W-operator W([n]). The cut-and-join operator is W([2]). In this paper, we show that W([n]) can be written as the ... More
Science Education in the 21st CenturyJun 21 2018The traditional university science curriculum was designed to train specialists in specific disciplines. However, in universities all over the world, science students are going into increasingly diverse careers and the current model does not fit their ... More
Enumeration of standard Young tableaux of shifted strips with constant widthJun 24 2015Let $g_{n_1,n_2}$ be the number of standard Young tableau of truncated shifted shape with $n_1$ rows and $n_2$ boxes in each row. By using of the integral method this paper derives the recurrence relations of $g_{3,n}$, $g_{n,4}$ and $g_{n,5}$ respectively. ... More
Geometric Stability of Pseudo-plane Ideal FlowsJan 25 2017Geometric analysis of steady pseudo-plane ideal flow reveals a fundamental relation between vertical coherence and streamline topology. It shows vertical alignment only exists in straightline jet and circular vortex. A geometric stability theory is then ... More
A simple bijection between binary trees and colored ternary treesMay 09 2008In this short note, we first present a simple bijection between binary trees and colored ternary trees and then derive a new identity related to generalized Catalan numbers.
A new additive decomposition of velocity gradientJul 25 2019To avoid the infinitesimal rotation nature of the Cauchy-Stokes decomposition of velocity gradient, the letter proposes an new additive decomposition in which one part is a SO(3) rotation tensor $Q=\exp W$.
Hybrid bounds for twists of $GL(3)$ $L$-functionsMay 02 2017Let $\pi$ be a Hecke-Maass cusp form for $SL(3,\mathbb{Z})$ and $\chi=\chi_1\chi_2$ a Dirichlet character with $\chi_i$ primitive modulo $M_i$. Suppose that $M_1$, $M_2$ are primes such that $\max\{(M|t|)^{1/3+2\delta/3},M^{2/5}|t|^{-9/20}, M^{1/2+2\delta}|t|^{-3/4+2\delta}\}(M|t|)^{\varepsilon}<M_1< ... More
The physical origin of hydrophobic effectsJan 26 2016Aug 15 2016The strength of hydrogen bonding in water is stronger than that of van der waals interaction, therefore water may play an important role in the process of hydrophobic effects. When a hydrophobic solute is dissolved into water, an interface appears between ... More
Recovery of sparsest signals via $\ell^q$-minimizationMay 03 2010In this paper, it is proved that every $s$-sparse vector ${\bf x}\in {\mathbb R}^n$ can be exactly recovered from the measurement vector ${\bf z}={\bf A} {\bf x}\in {\mathbb R}^m$ via some $\ell^q$-minimization with $0< q\le 1$, as soon as each $s$-sparse ... More
Homogeneous nucleation mechanism of NaCl in aqueous solutionsNov 28 2018In this study, molecular dynamic simulations are employed to investigate the nucleation of NaCl crystal in solutions. According to the simulations, the dissolved behaviors of NaCl in water are dependent on ion concentrations. With increasing NaCl concentrations, ... More
A Generalization of Gauss-Kuzmin-Lévy TheoremMay 08 2017Nov 09 2017We prove a generalized Gauss-Kuzmin-L\'evy theorem for the $p$-numerated generalized Gauss transformation $$T_p(x)=\{\frac{p}{x}\}.$$ In addition, we give an estimate for the constant that appears in the theorem.
A Generalization of the Gauss-Kuzmin-Wirsing constantJun 14 2017We generalize the result of Wirsing on Gauss transformation to the generalized tranformation $T_p(x)=\{\cfrac{p}{x}\}$ for any positive integer $p$. We give an estimate for the generalized Gauss-Kuzmin-Wirsing constant.
Potential Polynomials and Motzkin PathsMay 28 2008A {\em Motzkin path} of length $n$ is a lattice path from $(0,0)$ to $(n,0)$ in the plane integer lattice $\mathbb{Z}\times\mathbb{Z}$ consisting of horizontal-steps $(1, 0)$, up-steps $(1,1)$, and down-steps $(1,-1)$, which never passes below the x-axis. ... More
Local and Global Phaseless Sampling in Real Spline SpacesMay 02 2017May 07 2017We study the recovery of functions in real spline spaces from unsigned sampled values. We consider two types of recovery. The one is to recover functions locally from finitely many unsigned samples. And the other is to recover functions on the whole line ... More
On representations of real Jacobi groupsApr 30 2010Oct 12 2010We consider a category of continuous Hilbert space representations and a category of smooth Frechet representations, of a real Jacobi group $G$. By Mackey's theory, they are respectively equivalent to certain categories of representations of a real reductive ... More
Potential Quality Improvement of Stochastic Optical Localization Nanoscopy Images Obtained by Frame-by-Frame Localization AlgorithmsMar 14 2018Jan 17 2019A data movie of stochastic optical localization nanoscopy contains spatial and temporal correlations, both providing information of emitter locations. The majority of localization algorithms in the literature estimate emitter locations by frame-by-frame ... More
A new integral formula for Heckman-Opdam hypergeometric functionsJun 14 2014Dec 07 2015We provide Harish-Chandra type formulas for the multivariate Bessel functions and Heckman-Opdam hypergeometric functions as representation-valued integrals over dressing orbits. Our expression is the quasi-classical limit of the realization of Macdonald ... More
Laguerre and Jacobi analogues of the Warren processOct 05 2016Jul 24 2017We define Laguerre and Jacobi analogues of the Warren process. That is, we construct local dynamics on a triangular array of particles so that the projections to each level recover the Laguerre and Jacobi eigenvalue processes of K\"onig-O'Connell and ... More
Rank $n$ swapping algebra for $\operatorname{PGL}_n$ Fock-Goncharov $\mathcal{X}$ moduli spaceMar 03 2015Feb 08 2019The {\em rank $n$ swapping algebra} is a Poisson algebra defined on the set of ordered pairs of points of the circle using linking numbers, whose geometric model is given by a certain subspace of $(\mathbb{K}^n \times \mathbb{K}^{n*})^r/\operatorname{GL}(n,\mathbb{K})$. ... More
A supercharacter theory for Sylow $p$-subgroups of the Steinberg triality groupsNov 28 2016Aug 09 2018We 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 ${^3}D_4^{syl}(q^3)$.
Generic Base Change, Artin's Comparison Theorem, and the Decomposition Theorem for Complex Artin stacksNov 04 2015We prove the generic base change theorem for stacks, and give an exposition on the lisse-analytic topos of complex analytic stacks, proving some comparison theorems between various derived categories of complex analytic stacks. This enables us to deduce ... More
Ergodic measures of intermediate entropies for dynamical systems with approximate product propertyJun 24 2019Aug 03 2019We study dynamical systems with approximate product property and asymptotic entropy expansiveness. We show that such systems have ergodic measures of arbitrary intermediate entropies and arbitrary intermediate pressures. In fact, we show that ergodic ... More
Mean-Field Stochastic Linear Quadratic Optimal Control Problems: Open-Loop SolvabilitiesSep 07 2015Sep 15 2015This paper is concerned with a mean-field linear quadratic (LQ, for short) optimal control problem with deterministic coefficients. It is shown that convexity of the cost functional is necessary for the finiteness of the mean-field LQ problem, whereas ... More
Unique ergodicity for zero-entropy dynamical systems with approximate product propertyAug 03 2019Aug 18 2019We show that for every topological dynamical system with approximate product property, zero topological entropy is equivalent to unique ergodicity. Hence the space of invariant measures for such a system is a Poulsen simplex if and only if the topological ... More
Bridgeland stability conditions on some threefolds of general typeJul 19 2019We prove the Bogomolov-Gieseker type inequality conjectured by Bayer, Macri and Toda for some products of three curves. This gives the first examples of Bridgeland stability conditions on some threefolds of general type. The key ingredients are the spreading ... More
Deformation of Locally Free Sheaves and Hitchin Pairs over Nodal CurveApr 04 2019In this article, we study the deformation theory of locally free sheaves and Hitchin pairs over a nodal curve. As a special case, the infinitesimal deformation of these objects gives the tangent space of the corresponding moduli spaces, which can be used ... More
A characterization on separable subgroups of 3-manifold groupsMay 22 2018In this paper, we give a complete characterization on which finitely generated subgroups of finitely generated $3$-manifold groups are separable. Our characterization generalizes Liu's spirality character on $\pi_1$-injective immersed surface subgroups ... More
A Formula about W-operator and Its Application to Hurwitz NumberNov 15 2016Jun 19 2019W-operators are differential operators on the polynomial ring. Mironov, Morosov and Natanzon construct the generalized Hurwitz numbers. They use the W-operator to prove a formula for the generating function of the generalized Hurwitz numbers. A special ... More
Probing the diffractive production of Z boson pair at forward rapidities at the LHCMar 08 2017Mar 09 2017In this paper, we present the results from phenomenological analysis of Z boson pair hard diffractive production at the LHC. The calculation is based on the Regge factorization approach. Diffractive parton density functions extracted by the H1 Collaboration ... More
Tilt-stability, vanishing theorems and Bogomolov-Gieseker type inequalitiesSep 12 2016Dec 09 2017We investigate the tilt-stability of stable sheaves on projective varieties with respect to certain tilt-stability conditions depends on two parameters constructed by Bridgeland. For a stable sheaf, we give effective bounds of these parameters such that ... 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
The Spatial Scaling Laws of Compressible TurbulenceFeb 10 2015Oct 17 2016The spatial scaling laws of velocity kinetic energy spectrum for compressible turbulence flow and its density-weighted counterpart have been formulated in terms of wavenumber, dissipation rate and Mach number by using dimensional analysis. We have applied ... 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
A probabilistic approach to enumeration of Gessel walksMar 02 2009We consider Gessel walks in the plane starting at the origin $(0, 0)$ remaining in the first quadrant $i, j \geq 0$ and made of West, North-East, East and South-West steps. Let $F(m; n_1, n_2)$ denote the number of these walks with exact $m$ steps ending ... 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.
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
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
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
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
Graphene oxide adsorptive power from better to more via an enhanced route in perspectiveApr 25 2017Adsorption is one important way applied to water decontamination, where carbon is commonly used as highly effective absorbent. Carbon of different morphologies and structures normally demonstrate distinct capabilities to adsorption-typed decontaminations. ... 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.
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.
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
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
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
Gaussian Approximations for Maxima of Random Vectors under $(2+ι)$-th MomentsMay 27 2019We derive a Gaussian approximation result for the maximum of a sum of random vectors under $(2+\iota)$-th moments. Our main theorem is abstract and nonasymptotic, and can be applied to a variety of statistical learning problems. The proof uses the Lindeberg ... 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
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
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
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
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