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The Effective Theory of Hole Doped Spin-1 ChainJan 22 1999An effective theory for the hole doped spin-1 antiferromagnetic chain is proposed in this paper. The two branches of low energy quasipaticle excitation is obtained by the diagrammic technique. In the large t limit(in which t is the hole hopping term), ... More

Gröbner-Shirshov Bases and Hilbert Series of Free Dendriform AlgebrasSep 01 2010In this paper, we give a Gr\"obner-Shirshov basis of the free dendriform algebra as a quotient algebra of an $L$-algebra. As applications, we obtain a normal form of the free dendriform algebra. Moreover, Hilbert series and Gelfand-Kirillov dimension ... More

Hawking Radiation of Black Rings from AnomaliesMay 21 2007May 29 2007We derive Hawking radiation of 5-dimensional black rings from gauge and gravitational anomalies using the method proposed by Robinson and Wilczek. We find as in the black hole case, the problem could reduce to a (1+1) dimensional field theory and the ... More

On 1/2-BPS Wilson-'t Hooft loopsJul 05 2006Sep 19 2006We investigate the 1/2-BPS Wilson-'t Hooft loops in ${\cal N}=4$ Super-Yang-Mills theory. We use the bulk D-brane with both electric and magnetic charges to calculate the all genus contribution of the circular loops. The expectation value of Wilson-'t ... More

$α$-vacuum and inflationary bispectrumJun 25 2008Feb 20 2009In this paper, we discuss the non-Guassianity originated from the $\alpha$-vacuum on the CMB anisotropy. For $\alpha$-vacuum, there exist correlation between points in the acausal two patches of de Sitter spactime. Such kind of correlation can lead to ... More

The Complexity of Testing Monomials in Multivariate PolynomialsJul 15 2010The work in this paper is to initiate a theory of testing monomials in multivariate polynomials. The central question is to ask whether a polynomial represented by certain economically compact structure has a multilinear monomial in its sum-product expansion. ... More

Identifying the Lens Galaxy B1152+199 as a Ghostly Damped Lyman Alpha System by the Cosmic Origin SpectrographDec 14 2016Strong quasar-galaxy lensing provides a powerful tool to probe the inter-stellar medium (ISM) of the lens galaxy using radiation from the background quasar. Using the Cosmic Origin Spectrograph (COS) on board the Hubble Space Telescope, we study the cold ... More

Two-Loop master integrals for heavy-to-light form factors of two different massive fermionsJan 02 2018Feb 06 2018We calculate the full set of the two-loop master integrals for heavy-to-light form factors of two different massive fermions for arbitrary momentum transfer in NNLO QCD or QED corrections. These integrals allow to determine the two-loop QCD or QED corrections ... More

Series-Expansion Thermal Tensor Network Approach for Quantum Lattice ModelsSep 05 2016Mar 26 2017In this work we propose a series-expansion thermal tensor network (SETTN) approach for efficient simulations of quantum lattice models. This continuous-time SETTN method is based on the numerically exact Taylor series expansion of equilibrium density ... More

Note on Bulk Reconstruction in AdS$_3$/WCFT$_2$May 12 2019The bulk reconstructions in AdS/CFT and its cousins are essential to understand the holographic nature of quantum gravity. In this work, we try to study the bulk reconstruction in the AdS$_3$/WCFT$_2$ correspondence. After deriving the bulk-boundary propagator, ... More

One loop partition function in AdS_3/CFT_2Sep 07 2015Sep 21 2015The 1-loop partition function of the handle-body solutions in the AdS$_3$ gravity have been derived some years ago using the heat-kernel and the method of images. In the semiclassical limit, such partition function should correspond to the order $O (c^0)$ ... More

Anisotropy in Inflation with Non-minimal CouplingJun 07 2014Aug 14 2014We study a new anisotropic inflation model, with an inflaton field nonminimally coupled with the gravity and a vector field. We find that the anisotropic attractor solution exists not only in the weak curvature coupling limit, but more interestingly in ... More

Higher spin entanglement entropy at finite temperature with chemical potentialApr 13 2016Jul 05 2016It is generally believed that the semiclassical AdS$_3$ higher spin gravity could be described by a two dimensional conformal field theory with ${\cal{W}}$-algebra symmetry in the large central charge limit. In this paper, we study the single interval ... More

Holographic Calculation for Large Interval Rényi Entropy at High TemperatureJun 10 2015Oct 21 2015In this paper, we study the holographic R\'enyi entropy of a large interval on a circle at high temperature for the two-dimensional conformal field theory (CFT) dual to pure AdS$_3$ gravity. In the field theory, the R\'enyi entropy is encoded in the CFT ... More

Holographic Entanglement Entropy For a Large Class of States in 2D CFTMay 22 2016Sep 01 2016In this paper, we study the entanglement entropy in a large class of states of two-dimensional conformal field theory in the the large central charge limit. This class of states includes the states created by the insertion of a finite number of local ... More

Real-time correlators in Kerr/CFT correspondenceJan 19 2010Jun 08 2010We study real-time correlators in the Kerr/CFT correspondence. The near-horizon geometry of extreme and near-extremal Kerr black holes can be taken as warped spacetimes with the warping factors depending on the transverse radius and the angular variable. ... More

Field Theory at a Lifshitz PointApr 29 2009Dec 11 2009We construct the general renormalizable actions for the scalar field and the gauge field at a Lifshitz point characterized by the dynamical critical exponent $z$. The Lorentz invariance is broken down in the UV region, but is recovered in the IR limit. ... More

Maximum Likelihood Estimation based on Random Subspace EDA: Application to Extrasolar Planet DetectionApr 18 2017Jul 21 2017This paper addresses maximum likelihood (ML) estimation based model fitting in the context of extrasolar planet detection. This problem is featured by the following properties: 1) the candidate models under consideration are highly nonlinear; 2) the likelihood ... More

Entanglement Entropy in $T\overline{T}$-Deformed CFTJul 22 2018Aug 28 2018In this paper, we study the entanglement entropy of a single interval on a cylinder in two-dimensional $T\overline{T}$-deformed conformal field theory. For such case, the (R\'enyi) entanglement entropy takes a universal form in a CFT. We compute the correction ... More

Low-Delay Distributed Source Coding for Time-Varying Sources with Unknown StatisticsOct 26 2016We consider a system in which two nodes take correlated measurements of a random source with time-varying and unknown statistics. The observations of the source at the first node are to be losslessly replicated with a given probability of outage at the ... More

Locally Repairable Codes with Multiple $(r_{i}, δ_{i})$-LocalitiesFeb 19 2017May 02 2017In distributed storage systems, locally repairable codes (LRCs) are introduced to realize low disk I/O and repair cost. In order to tolerate multiple node failures, the LRCs with \emph{$(r, \delta)$-locality} are further proposed. Since hot data is not ... More

Compressing Neural Networks using the Variational Information BottleneckFeb 28 2018Apr 19 2018Neural networks can be compressed to reduce memory and computational requirements, or to increase accuracy by facilitating the use of a larger base architecture. In this paper we focus on pruning individual neurons, which can simultaneously trim model ... More

Gauge theory on $Z_2 \times Z_2 \ti Z_2 $ Discrete Group and a Spontaneous $CP$ Violation Toy ModelAug 29 1994In the spirit of Non-commutative differential calculus on discrete group, we construct a toy model of spontaneous $CP$ violation (SCPV). Our model is different from the well-known Weinberg-Branco model although it involves three Higgs doublets and preserve ... More

Tunable pulse delay and advancement in a coupled nanomechanical resonator-superconducting microwave cavity systemDec 16 2010We theoretically study the transmission of a weak probe field under the influence of a strong pump field in a coupled nanomechanical resonator-superconducting microwave cavity system. Using the standard input-output theory, we find that both pulse delay ... More

A Simple Gravitational Lens Model For Cosmic VoidsOct 28 2013Mar 13 2015We present a simple gravitational lens model to illustrate the ease of using the embedded lensing theory when studying cosmic voids. It confirms the previously used repulsive lensing models for deep voids. We start by estimating magnitude fluctuations ... More

Embedded Lensing Time Delays, the Fermat Potential, and the Integrated Sachs-Wolfe EffectOct 23 2013Mar 13 2015We derive the Fermat potential for a spherically symmetric lens embedded in an FLRW cosmology and use it to investigate the late-time integrated Sachs-Wolfe (ISW) effect, i.e., secondary temperature fluctuations in the cosmic microwave background (CMB) ... More

Time Delay in Swiss Cheese Gravitational LensingJun 17 2010We compute time delays for gravitational lensing in a flat LambdaCDM Swiss cheese universe. We assume a primary and secondary pair of light rays are deflected by a single point mass condensation described by a Kottler metric (Schwarzschild with Lambda) ... More

On Optimal Ternary Locally Repairable CodesFeb 19 2017In an $[n,k,d]$ linear code, a code symbol is said to have locality $r$ if it can be repaired by accessing at most $r$ other code symbols. For an $(n,k,r)$ \emph{locally repairable code} (LRC), the minimum distance satisfies the well-known Singleton-like ... More

A New Hybrid Half-Duplex/Full-Duplex Relaying System with Antenna DiversityFeb 21 2018The hybrid half-duplex/full-duplex (HD/FD) relaying scheme is an effective paradigm to overcome the negative effects of the self-interference incurred by the full-duplex (FD) mode. However, traditional hybrid HD/FD scheme does not consider the diversity ... More

Inclination-Dependent AGN Flux Profiles From Strong Lensing of the Kerr Space-TimeNov 12 2012Recent quasar microlensing observations have constrained the X-ray emission sizes of quasars to be about 10 gravitational radii, one order of magnitude smaller than the optical emission sizes. Using a new ray-tracing code for the Kerr space-time, we find ... More

Polar Coding for Parallel Gaussian ChannelMay 20 2017In this paper, we propose a Polar coding scheme for parallel Gaussian channels. The encoder knows the sum rate of the parallel channels but does not know the rate of any channel. By using the nesting property of Polar code, we design a coding/decoding ... More

A Decision-Aided Parallel SC-List Decoder for Polar CodesJun 09 2015In this paper, we propose a decision-aided scheme for parallel SC-List decoding of polar codes. At the parallel SC-List decoder, each survival path is extended based on multiple information bits, therefore the number of split paths becomes very large ... More

The Fate of Massive F-StringsApr 05 2005Apr 14 2005We calculate the semi-inclusive decay rate of an average string state with compactification both in the bosonic string theory and in the superstring theory. We also apply this calculation to a brane-inflation model in a warped geometry and find that the ... More

An integrated Sachs-Wolfe effect vs redshift test for the cosmological parametersOct 16 2014Mar 14 2015We describe a method using the integrated Sachs-Wolfe (ISW) effect caused by individual inhomogeneities to determine the cosmological parameters, $H_0$, $\Omega_{\rm m}$, and $\Omega_\Lambda$, etc. This ISW-redshift test requires detailed knowledge of ... More

Image Properties of Embedded LensesJun 13 2012Jul 15 2012We give analytic expressions for image properties of objects seen around point mass lenses embedded in a flat $\Lambda$CDM universe. An embedded lens in an otherwise homogeneous universe offers a more realistic representation of the lens's gravity field ... More

Scale Invariant Power Spectrum in Hořava-Lifshitz Cosmology without MatterMay 14 2009Aug 07 2009In this paper we investigate the physical implications of the dynamical scalar mode in pure Horava-Lifshitz gravity on cosmology. We find that it can produce a scale-invariant power spectrum in UV era if the detailed balance condition on the action is ... More

Hybrid evolving clique-networks and their communicabilityMar 03 2014Aiming to understand real-world hierarchical networks whose degree distributions are neither power law nor exponential, we construct a hybrid clique network that includes both homogeneous and inhomogeneous parts, and introduce an inhomogeneity parameter ... More

The Riemannian manifolds with boundary and large symmetryJan 07 2008May 09 2009Sixty years ago, S. B. Myers and N. E. Steenrod ({\it Ann. of Math.} {\bf 40} (1939), 400-416) showed that the isometry group of a Riemannian manifold without boundary has a structure of Lie group. Recently A. V. Bagaev and N. I. Zhukova ({\it Siberian ... More

Gravity and Discrete SymmetryMay 04 1994Using the differential calculus on discrete group, we study the general relativity in the space-time which is the product of a four dimensional manifold by a two-point space. We generalize the usual concept of frame and connection in our space-time, and ... More

Wavelength tunable spectral compression in a dispersion-increasing fiberJun 01 2011Jun 13 2011Adiabatic soliton spectral compression in a dispersion-increasing fiber is demonstrated both numerically and experimentally. We show a positively-chirped pulse provides better spectral compression in a dispersion-increasing fiber with large anomalous ... More

Exponential Thermal Tensor Network Approach for Quantum Lattice ModelsDec 30 2017Oct 05 2018We speed up thermal simulations of quantum many-body systems in both one- (1D) and two-dimensional (2D) models in an exponential way by iteratively projecting the thermal density matrix $\hat\rho=e^{-\beta \hat{H}}$ onto itself. We refer to this scheme ... More

Global Regularity to the Navier-Stokes Equations for A Class of Large Initial DataMar 19 2015Apr 08 2015We prove that for initial data of the form \begin{equation}\nonumber u_0^\epsilon(x) = (v_0^h(x_\epsilon), \epsilon^{-1}v_0^n(x_\epsilon))^T,\quad x_\epsilon = (x_h, \epsilon x_n)^T, n \geq 4, \end{equation} the Cauchy problem of the incompressible Navier-Stokes ... More

Inflationary NonGaussianity from Thermal FluctuationsDec 14 2007Dec 18 2007We calculate the contribution of the fluctuations with the thermal origin to the inflationary nonGaussianity. We find that even a small component of radiation can lead to a large nonGaussianity. We show that this thermal nonGaussianity always has positive ... More

The Embedded Transparent Lens and Fermat's Least-Time PrincipleMar 26 2013Sep 27 2013We present a simplified version of the lowest-order embedded point mass gravitational lens theory and then make the extension of this theory to any embedded transparent lens. Embedding a lens effectively reduces the gravitational potential's range, i.e., ... More

The Gravitational Lens Equation for Embedded Lenses; Magnification and EllipticityJun 11 2011We give the lens equation for light deflections caused by point mass condensations in an otherwise spatially homogeneous and flat universe. We assume the signal from a distant source is deflected by a single condensation before it reaches the observer. ... More

The Entropy of Artificial Intelligence and a Case Study of AlphaZero from Shannon's PerspectiveDec 14 2018Dec 17 2018The recently released AlphaZero algorithm achieves superhuman performance in the games of chess, shogi and Go, which raises two open questions. Firstly, as there is a finite number of possibilities in the game, is there a quantifiable intelligence measurement ... More

Floquet topological insulator phase in a Weyl semimetal thin film with disorderOct 31 2018Dec 28 2018We investigate the effects of periodic fields and disorder on topological properties of a Weyl-semimetal thin film. The two periodic fields, i.e., a periodic magnetic field and elliptically polarized light, are discussed respectively. By use of the Floquet ... More

Disorder-induced topological phase transitions on Lieb latticesAug 07 2017Nov 08 2017Motivated by the very recent experimental realization of electronic Lieb lattices and research interest on topological states of matter, we study the topological phase transitions driven by Anderson disorder on spin-orbit coupled Lieb lattices in the ... More

Influence of electric fields on absorption spectra of AAB-stacked trilayer grapheneJan 02 2016The band structures and optical properties of AAB-stacked trilayer graphenes (AAB-TLG) are calculated by the tight-binding model and gradient approximation. Three pairs of the energy bands exhibit very different energy dispersions at low energy and saddle ... More

Monotonicity of eigenvalues of geometric operaters along the Ricci-Bourguignon flowDec 27 2015In this paper, we study monotonicity of eigenvalues of Laplacian-type operator $-\Delta+cR$, where $c$ is a constant, along the Ricci-Bourguignon flow. For $c\neq0$, We derive monotonicity of the lowest eigenvalue of Laplacian-type operator $-\Delta+cR$ ... More

$N=2$ and $N=4$ SUSY Yang-Mills action on $M^4\times (Z_2\oplus Z_2)$ non-commutative geometryNov 22 1994We show that the $N=2$ and $N=4$ SUSY Yang-Mills action can be reformulated in the sense of non-commutative geometry on $M^4\times (Z_2\oplus Z_2)$ in a rather simple way. In this way the scalars or pseudoscalars are viewed as gauge fields along two directions ... More

iTrace: An Implicit Trust Inference Method for Trust-aware Collaborative FilteringAug 11 2017Aug 15 2017The growth of Internet commerce has stimulated the use of collaborative filtering (CF) algorithms as recommender systems. A collaborative filtering (CF) algorithm recommends items of interest to the target user by leveraging the votes given by other similar ... More

Thermal Tensor Renormalization Group Simulations of Square-Lattice Quantum Spin ModelsApr 12 2019In this work, we benchmark the well-controlled and numerically accurate exponential thermal tensor renormalization group (XTRG) in the simulation of interacting spin models in two dimensions. Finite temperature introduces a thermal correlation length, ... More

Exotic phase separation in one-dimensional hard-core boson system with two- and three-body interactionsJul 24 2014Jul 25 2014We investigate the ground state phase diagram of hard-core boson system with repulsive two-body and attractive three-body interactions in one-dimensional optic lattice. When these two interactions are comparable and increasing the hopping rate, physically ... More

Magnetization jump in one dimensional $J-Q_{2}$ model with anisotropic exchangeDec 30 2016Dec 27 2017We investigate the adiabatic magnetization process of the one-dimensional $J-Q_{2}$ model with XXZ anisotropy $g$ in an external magnetic field $h$ by using density matrix renormalization group (DMRG) method. According to the characteristic of the magnetization ... More

Robust Particle Filter by Dynamic Averaging of Multiple Noise ModelsSep 05 2016State filtering is a key problem in many signal processing applications. From a series of noisy measurement, one would like to estimate the state of some dynamic system. Existing techniques usually adopt a Gaussian noise assumption which may result in ... More

Cluster-tilted algebras and their intermediate coveringsAug 18 2008Apr 30 2010We construct the intermediate coverings of cluster-tilted algebras by defining the generalized cluster categories. These generalized cluster categories are Calabi-Yau triangulated categories with fraction CY-dimension and have also cluster tilting objects ... More

Positive curvature property for sub-Laplace on nilpotent Lie group of rank twoDec 15 2011In this note, we concentrate on the sub-Laplace on the nilpotent Lie group of rank two, which is the infinitesimal generator of the diffusion generated by $n$ Brownian motions and their $\frac{n(n-1)}2$ L\'evy area processes, which is the simple extension ... More

Sparse Representation on Graphs by Tight Wavelet Frames and ApplicationsNov 10 2014Oct 06 2015In this paper, we introduce a new (constructive) characterization of tight wavelet frames on non-flat domains in both continuum setting, i.e. on manifolds, and discrete setting, i.e. on graphs; discuss how fast tight wavelet frame transforms can be computed ... More

On Theorem 6 in "Relative Entropy and the Multivariable Multidimensional Moment Problem" [Mar 2006 1052-1066]May 30 2018Jun 06 2018Matrix-valued covariance extension and multivariate spectral estimation are formulated as generalized moment problems in the "THREE" approach and its extensions. Under this context, we discuss Theorem 6 in \cite{Georgiou-06} concerning the bijectivity ... More

Some effects of the noise intensity upon non-linear stochastic heat equations on $[0,1]$Jun 19 2015Various effects of the noise intensity upon the solution $u(t,x)$ of the stochastic heat equation with Dirichlet boundary conditions on $[0,1]$ are investigated. We show that for small noise intensity, the $p$-th moment of $\sup_{x \in [0,1]} |u(t,x)|$ ... More

Generalized cluster complexes via quiver representationsJul 06 2006May 23 2007We give a quiver representation theoretic interpretation of generalized cluster complexes defined by Fomin and Reading. By using $d-$cluster categories which are defined by Keller as triangulated orbit categories of (bounded) derived categories of representations ... More

Equivalences between cluster categoriesNov 15 2005Jun 19 2006Tilting theory in cluster categories of hereditary algebras has been developed in [BMRRT] and [BMR]. These results are generalized to cluster categories of hereditary abelian categories. Furthermore, for any tilting object $T$ in a hereditary abelian ... More

BGP-reflection functors and cluster combinatoricsNov 15 2005Jul 14 2006We define Bernstein-Gelfand-Ponomarev reflection functors in the cluster categories of hereditary algebras. They are triangle equivalences which provide a natural quiver realization of the "truncated simple reflections" on the set of almost positive roots ... More

Applications of BGP-reflection functors: isomorphisms of cluster algebrasNov 15 2005Jun 19 2006Given a symmetrizable generalized Cartan matrix $A$, for any index $k$, one can define an automorphism associated with $A,$ of the field $\mathbf{Q}(u_1, >..., u_n)$ of rational functions of $n$ independent indeterminates $u_1,..., u_n.$ It is an isomorphism ... More

On the Well-posedness of a Generalized Moment Problem and Its Numerical SolutionFeb 26 2018We show that the unique solution to a parametric version of the generalized moment problem depends continuously on the prior function, and thus the problem is well-posed in the sense of Hadamard. Based on this result, the problem is reparametrized via ... More

Remarks on Li-Yau inequality on graphsNov 14 2013In this paper, we study Li-Yau gradient estimates for the solutions $u$ to the heat equation $\partial_tu=\Delta u$ on graphs under the curvature condition $CD(n,-K)$ introduced by Bauer et al. in \cite{BHLLMY}. As applications, we derive Harnack inequalities ... More

Gradient estimate and log-Harnack inequality for reflected SPDEs driven by multiplicative noisesMay 03 2018In this paper, the gradient estimate and the log-Harnack inequality for the stochastic partial differential equation with reflection and driven by multiplicative noises are mainly investigated. To our purposes, the penalization method and the comparison ... More

Exponential energy-preserving methods for charged-particle dynamics in a strong and constant magnetic fieldDec 28 2018In this paper, exponential energy-preserving methods are formulated and analysed for solving charged-particle dynamics in a strong and constant magnetic field. The resulting method can exactly preserve the energy of the dynamics. Moreover, it is shown ... More

Universal Knowledge Discovery from Big Data: Towards a Paradigm Shift from 'Knowledge Discovery' to 'Wisdom Discovery'Mar 28 2014Oct 28 2014Many people hold a vision that big data will provide big insights and have a big impact in the future, and big-data-assisted scientific discovery is seen as an emerging and promising scientific paradigm. However, how to turn big data into deep insights ... More

Preprojective cluster variables of acyclic cluster algebrasNov 29 2005Aug 30 2006For any valued quiver, by using BGP-reflection functors, an injection from the set of preprojective objects in the cluster category to the set of cluster variables of the corresponding cluster algebra is given, the images are called preprojective cluster ... More

Nonhomogeneous Wavelet Systems in High DimensionsFeb 11 2010It is of interest to study a wavelet system with a minimum number of generators. It has been showed by X. Dai, D. R. Larson, and D. M. Speegle in [11] that for any $d\times d$ real-valued expansive matrix M, a homogeneous orthonormal M-wavelet basis can ... More

SZ effect or Not? - Detecting most galaxy clusters' main foreground effectNov 28 2012May 06 2013Galaxy clusters are the most massive objects in the Universe and comprise a high-temperature intracluster medium of about 10^7 K, believed to offer a main foreground effect for cosmic microwave background (CMB) data in the form of the thermal Sunyaev-Zel'dovich ... More

A Study of Deep Feature Fusion based Methods for Classifying Multi-lead ECGAug 06 2018An automatic classification method has been studied to effectively detect and recognize Electrocardiogram (ECG). Based on the synchronizing and orthogonal relationships of multiple leads, we propose a Multi-branch Convolution and Residual Network (MBCRNet) ... More

The system of partial differential equations for the $C_{_0}$ functionSep 02 2018Jan 31 2019We present an approach to analyze the scalar integrals of any Feynman diagrams in detail here. This method not only completely recovers some well-known results in the literature, but also produces some brand new results on the $C_{_0}$ function. The approach ... More

Schwinger boson mean field theory of the Heisenberg Ferrimagnetic Spin ChainApr 21 1999Apr 22 1999The Schwinger boson mean field theory is applied to the quantum ferrimagnetic Heisenberg chain. There is a ferrimagnetic long range order in the ground state. We observe two branches of the low lying excitation and calculate the spin reduction, the gap ... More

L-packets of quasisplit $GSp(2n)$ and $GO(2n)$Mar 17 2015Feb 28 2017In his monograph (2013) Arthur characterizes the L-packets of quasisplit symplectic groups and orthogonal groups. By extending his work, we characterize the L-packets for the corresponding similitude groups with desired properties. In particular, we show ... More

Asymptotic estimates on the time derivative of $Φ$-entropy on Riemannian manifoldsApr 16 2011Aug 11 2011In this note, we obtain the asymptotic estimate for the time derivative of the $\Phi$-entropy in terms of the lower bound on the Bakry-Emery $\Gamma_2$ curvature. In the cases of Hyperbolic space and Heisenberg group, we show that the time derivative ... More

Clemens' conjecture: part INov 14 2005Jul 23 2011This is a series of two papers in which we solve the Clemens conjecture: there are only finitely many smooth rational curves of each degree in a generic quintic threefold. In this first paper, we deal with a family of smooth Calabi-Yau threefolds f_\epsilon ... More

On Linear Quadratic Optimal Control of Discrete-Time Complex-Valued Linear SystemsSep 15 2017We study in this paper the linear quadratic optimal control (linear quadratic regulation, LQR for short) for discrete-time complex-valued linear systems, which have shown to have several potential applications in control theory. Firstly, an iterative ... More

Pairs of Frequency-based Nonhomogeneous Dual Wavelet Frames in the Distribution SpaceJul 20 2009Dec 22 2009In this paper, we study nonhomogeneous wavelet systems which have close relations to the fast wavelet transform and homogeneous wavelet systems. We introduce and characterize a pair of frequency-based nonhomogeneous dual wavelet frames in the distribution ... More

Gibbs Phenomenon of Framelet Expansions and Quasi-projection ApproximationAug 28 2018May 24 2019The Gibbs phenomenon is widely known for Fourier expansions of periodic functions and refers to the phenomenon that the $n$th Fourier partial sums overshoot a target function at jump discontinuities in such a way that such overshoots do not die out as ... More

The Degree of Symmetry of Certain Compact Smooth Manifolds IIMay 30 2005Nov 29 2005In this paper, we give the sharp estimates for the degree of symmetry and the semi-simple degree of symmetry of certain four dimensional fiber bundles by virtue of the rigidity theorem of harmonic maps due to Schoen and Yau. As a corollary of this estimate, ... More

On a Parametric Spectral Estimation ProblemDec 19 2017Apr 18 2018We consider an open question posed in \cite{Zhu-Baggio-17} on the uniqueness of the solution to a parametric spectral estimation problem.

Original graphs of link graphsMar 25 2015Aug 31 2015Let $\ell \geqslant 0$ be an integer, and $G$ be a graph without loops. An $\ell$-link of $G$ is a walk of length $\ell$ in which consecutive edges are different. We identify an $\ell$-link with its reverse sequence. The $\ell$-link graph $\mathbb{L}_\ell(G)$ ... More

Derandomizing Polynomial Identity over Finite Fields Implies Super-Polynomial Circuit Lower Bounds for NEXPNov 11 2013We show that derandomizing polynomial identity testing over an arbitrary finite field implies that NEXP does not have polynomial size boolean circuits. In other words, for any finite field F(q) of size q, $PIT_q\in NSUBEXP\Rightarrow NEXP\not\subseteq ... More

Multivariate Polynomial Integration and Derivative Are Polynomial Time Inapproximable unless P=NPDec 10 2010We investigate the complexity of integration and derivative for multivariate polynomials in the standard computation model. The integration is in the unit cube $[0,1]^d$ for a multivariate polynomial, which has format $f(x_1,\cdots, x_d)=p_1(x_1,\cdots, ... More

Clemens' conjecture: part IINov 14 2005Jul 23 2011This is the part II of our series of two papers, "Clemens' conjecture: part I", "Clemens' conjecture: part II". Continuing from part I, in this paper we turn our attention to general quintic threefolds. In a universal quintic threefold X, we construct ... More

How and in What Sense Can the Entropy Be Measured?Aug 13 2002In this paper, a method of measuring the entropy is presented. Problems related to the entropy and the heat are also discussed.

The Neumann problem for a class of fully nonlinear elliptic partial differential equationsMar 11 2019In this paper, we establish a global $C^2$ estimates to the Neumann problem for a class of fullly nonlinear elliptic equations. By the method of continuity, we establish the existence theorem of $k$-admissible solutions of the Neumann problems.

Differential Harnack inequalities and Perelman type entropy formulae for subelliptic operatorsJul 09 2013In this paper, under the generalized curvature-dimension inequality recently introduced by F. Baudoin and N. Garofalo, we obtain differential Harnack inequalities for the positive solutions to the Sch\"odinger equation associated to subelliptic operator ... More

Homogeneous Wavelets and Framelets with the Refinable StructureJul 05 2017Homogeneous wavelets and framelets have been extensively investigated in the classical theory of wavelets and they are often constructed from refinable functions via the multiresolution analysis. On the other hand, nonhomogeneous wavelets and framelets ... More

Asymptotic behavior of $L^2$-normalized eigenfunctions of the Laplace-Beltrami operator on a closed Riemannian manifoldSep 04 2005Oct 18 2005Let $e(x,y,\l)$ be the spectral function and ${\chi}_\l$ the unit band spectral projection operator, with respect to the Laplace-Beltrami operator $\D_M$ on a closed Riemannian manifold $M$. We firstly review the one-term asymptotic formula of $e(x,x,\l)$ ... More

Additive preserving rank one maps on Hilbert $C^\ast$-modulesMay 04 2007In this paper, we characterize a class of additive maps on Hilbert $C^\ast$-modules which maps a "rank one" adjointable operators to another rank one operators.

Challenging the Long Tail RecommendationMay 30 2012The success of "infinite-inventory" retailers such as Amazon.com and Netflix has been largely attributed to a "long tail" phenomenon. Although the majority of their inventory is not in high demand, these niche products, unavailable at limited-inventory ... More

NLO QCD Corrections for $J/ψ+ c + \bar{c}$ Production in Photon-Photon CollisionAug 22 2016Sep 24 2016The $\gamma+\gamma\rightarrow J/\psi+c+\bar{c}$ inclusive process is an extremely important subprocess in $J/\psi$ production via photon-photon scattering, like at LEP\uppercase\expandafter{\romannumeral2} or various types future electron-positron colliders. ... More

GeoCapsNet: Aerial to Ground view Image Geo-localization using Capsule NetworkApr 12 2019The task of cross-view image geo-localization aims to determine the geo-location (GPS coordinates) of a query ground-view image by matching it with the GPS-tagged aerial (satellite) images in a reference dataset. Due to the dramatic changes of viewpoint, ... More

Evaluating Feynman integrals by the hypergeometryJun 26 2017Jan 11 2018The hypergeometric function method naturally provides the analytic expressions of scalar integrals from concerned Feynman diagrams in some connected regions of independent kinematic variables, also presents the systems of homogeneous linear partial differential ... More

Deep Label Distribution Learning with Label AmbiguityNov 06 2016May 10 2017Convolutional Neural Networks (ConvNets) have achieved excellent recognition performance in various visual recognition tasks. A large labeled training set is one of the most important factors for its success. However, it is difficult to collect sufficient ... More

One loop correction to $Z\rightarrow νν$ in the Minimal R-symmetric Supersymmetric Standard ModelJan 12 2019We analyze the one loop correction to $Z\rightarrow \nu\nu$ decay in framework of Minimal R-symmetric Supersymmetric Standard Model(MRSSM) in detail with normal and inverse neutrino mass orderings, as a function of $\tan\beta$, Dirac mass parameters $M_D^W$ ... More