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Partial Differential Chow Forms and a Type of Partial Differential Chow varietiesSep 07 2017We first present an intersection theory of partial differential varieties with quasi-generic differential hypersurfaces. Then based on the generic intersection theory, we define the partial differential Chow form for an irreducible partial differential ... More

Correlations and fluctuations measured by the CMS experiment in pp and PbPbJul 13 2011Measurements of charged dihadron angular correlations are presented in proton-proton (pp) and Lead-Lead (PbPb) collisions, over a broad range of pseudorapidity and azimuthal angle, using the CMS detector at the LHC. In very high multiplicity pp events ... More

Computation of Differential Chow Forms for Prime Differential IdealsJan 12 2015In this paper, we propose algorithms to compute differential Chow forms for prime differential ideals which are given by their characteristic sets. The main algorithm is based on an optimal bound for the order of a prime differential ideal in terms of ... More

Two point extremal Gromov-Witten invariants of Hilbert schemes of points on surfacesMar 24 2007Given an algebraic surface $X$, the Hilbert scheme $X^{[n]}$ of $n$-points on $X$ admits a contraction morphism to the $n$-fold symmetric product $X^{(n)}$ with the extremal ray generated by a class $\beta_n$ of a rational curve. We determine the two ... More

A homotopy theory of additive categories with suspensionsOct 08 2015Jul 03 2016We define partial one-sided triangulated categories by weakening the axioms of one-sided triangulated categories. We show that additive categories, exact categories, one-sided triangulated categories, complete cotorsion pairs in exact categories, torsion ... More

Neutrino Masses, Dark Matter and B-L Symmetry at the LHCApr 02 2010Oct 18 2010We establish a hybrid seesaw mechanism to explain small neutrino masses and predict cold dark matter candidate in the context of the B-L gauge symmetry extension of the Standard Model. In this model a new scalar doublet and two new fermion singlets are ... More

Tuning Parameter Calibration in High-dimensional Logistic Regression With Theoretical GuaranteesOct 01 2016Feature selection is a standard approach to understanding and modeling high-dimensional classification data, but the corresponding statistical methods hinge on tuning parameters that are difficult to calibrate. In particular, existing calibration schemes ... More

Multi-Output Recommender: Items, Groups and Friends, and Their Mutual Contributing EffectsApr 10 2012Oct 16 2012Due to the development of social media technology, it becomes easier for users to gather together to form groups. Take the Last.fm for example, users can join groups they may be interested where they can share their loved songs and discuss topics about ... More

Towards generalized prehomogeneous zeta integralsOct 19 2016Oct 16 2017Let $X$ be a prehomogeneous vector space under a connected reductive group $G$ over $\mathbb{R}$. Assume that the open $G$-orbit $X^+$ admits a finite covering by a symmetric space. We study certain zeta integrals involving (i) Schwartz functions on $X$, ... More

Spectral transfer for metaplectic groups. I. Local character relationsSep 22 2014Oct 30 2016Let $\widetilde{\mathrm{Sp}}(2n)$ be the metaplectic covering of $\mathrm{Sp}(2n)$ over a local field of characteristic zero. The core of the theory of endoscopy for $\widetilde{\mathrm{Sp}}(2n)$ is the geometric transfer of orbital integrals to its elliptic ... More

New rigorous perturbation bounds for the LU and QR factorizationsMay 01 2014May 23 2014Combining the modified matrix-vector equation approach with the technique of Lyapunov majorant function and the Banach fixed point principle, we obtain new rigorous perturbation bounds for the LU and QR factorizations with normwise or componentwise perturbations ... More

Sharp diameter estimates for compact manifold with boundaryJun 17 2013Let $(N,g)$ be an $n$-dimensional complete Riemannian manifold with nonempty boundary $\pt N$. Assume that the Ricci curvature of $N$ has a negative lower bound $Ric\geq -(n-1)c^2$ for some $c>0$, and the mean curvature of the boundary $\pt N$ satisfies ... More

Automorphism groups of smooth cubic threefoldsJun 30 2019In this paper, we classify groups which faithfully act on smooth cubic threefolds. It turns out that there are exactly $6$ maximal ones and we describe them with explicit examples of target cubic threefolds.

The realization of Verdier quotients as triangulated subfactorsDec 26 2016Sep 15 2017We give a method to realize Verdier quotients as triangulated subfactors of an arbitrary triangulated category. We show that Iyama-Yoshino triangulated subfactors are Verdier quotients under suitable conditions.

Stable conjugacy and epipelagic L-packets for Brylinski-Deligne covers of Sp(2n)Mar 13 2017Apr 26 2017Let $F$ be a local field of characteristic not $2$. We propose a definition of stable conjugacy for all the covering groups of $\mathrm{Sp}(2n,F)$ constructed by Brylinski and Deligne, whose degree we denote by $m$. To support this notion, we follow Kaletha's ... More

Complete cotorsion pairs in exact categoriesDec 18 2014We discuss a generalized version of Quillen's small object argument in arbitrary categories. We use it to give a criterion for the construction of complete cotorsion pairs in arbitrary exact categories, which is a generalization of the recent result due ... More

Spherical Collapse for Viscous Generalized Chaplygin Gas ModelApr 03 2014Jul 18 2014The nonlinear collapse for viscous generalized Chaplygin gas Model (VGCG) was analyzed in the framework of spherical top-hat collapse. As the VGCG and baryons are essential to form the large scale structure, we focused on their nonlinear collapse in this ... More

Growth of Metastable High-Order Commensurate Overlayers of Pb on Cu(001)Sep 14 1992We studied the growth and ordering of a Pb layer deposited on Cu(001) at 150 K. Contrary to the case of adsorption of Pb at room temperature, islands readily form. These islands order in a high-order commensurate structure of symmetry ( sqrt(61) x sqrt(61) ... More

Holography and Entanglement in Flat SpacetimeOct 18 2010Apr 01 2011We propose a holographic correspondence of the flat spacetime based on the behavior of the entanglement entropy and the correlation functions. The holographic dual theory turns out to be highly non-local. We argue that after most part of the space is ... More

Existence and Asymptotic Stability of Periodic Solutions for Impulsive Delay Evolution EquationsJan 02 2018In this paper, we are devoted to consider the periodic problem for the impulsive evolution equations with delay in Banach space. By using operator semigroups theory and fixed point theorem, we establish some new existence theorems of periodic mild solutions ... More

Stochastic differential games for fully coupled FBSDEs with jumpsFeb 05 2013This paper is concerned with stochastic differential games (SDGs) defined through fully coupled forward-backward stochastic differential equations (FBSDEs) which are governed by Brownian motion and Poisson random measure. For SDGs, the upper and the lower ... More

A hidden spatial-temporal Markov random field model for network-based analysis of time course gene expression dataMar 27 2008Microarray time course (MTC) gene expression data are commonly collected to study the dynamic nature of biological processes. One important problem is to identify genes that show different expression profiles over time and pathways that are perturbed ... More

Global hypoelliptic estimates for a linear model of non-cutoff Boltzmann equationJun 05 2011In this paper we study a linear model of spatially inhomogeneous Boltzmann equation without angular cutoff. Using the multiplier method introduced by F. H\'{e}rau and K. Pravda-Starov (2011), we establish the optimal global hypoelliptic estimate with ... More

Fuzzy alternating $\mathrm{B\ddot{u}chi}$ automata over distributive latticesMar 15 2016We give a new version of fuzzy alternating $\mathrm{B\ddot{u}chi}$ automata over distributive lattices: weights are putting in every leaf node of run trees rather than along with edges from every node to its children. Such settings are great benefit to ... More

An Average Analysis of Backtracking on Random Constraint Satisfaction ProblemsMay 09 2000In this paper we propose a random CSP model, called Model GB, which is a natural generalization of standard Model B. It is proved that Model GB in which each constraint is easy to satisfy exhibits non-trivial behaviour (not trivially satisfiable or unsatisfiable) ... More

The SAT Phase TransitionMay 22 2000May 23 2000Phase transition is an important feature of SAT problem. For random k-SAT model, it is proved that as r (ratio of clauses to variables) increases, the structure of solutions will undergo a sudden change like satisfiability phase transition when r reaches ... More

Aspect Based Sentiment Analysis with Gated Convolutional NetworksMay 18 2018Aspect based sentiment analysis (ABSA) can provide more detailed information than general sentiment analysis, because it aims to predict the sentiment polarities of the given aspects or entities in text. We summarize previous approaches into two subtasks: ... More

A note on model structures on arbitrary Frobenius categoriesOct 14 2015Dec 29 2016We show that there is a model structure in the sense of Quillen on an arbitrary Frobenius category $\F$ such that the homotopy category of this model structure is equivalent to the stable category $\underline{\F}$ as triangulated categories.

A survey of recent results in (generalized) graph entropiesMay 18 2015May 19 2015The entropy of a graph was first introduced by Rashevsky \cite{Rashevsky} and Trucco \cite{Trucco} to interpret as the structural information content of the graph and serve as a complexity measure. In this paper, we first state a number of definitions ... More

Hierarchical Gated Recurrent Neural Tensor Network for Answer TriggeringSep 17 2017In this paper, we focus on the problem of answer triggering ad-dressed by Yang et al. (2015), which is a critical component for a real-world question answering system. We employ a hierarchical gated recurrent neural tensor (HGRNT) model to capture both ... More

Global Hypoellipticity and Compactness of Resolvent for Fokker-Planck OperatorOct 06 2009Sep 11 2010In this paper we study the Fokker-Planck operator with potential V(x), and analyze some kind of conditions imposed on the potential to ensure the validity of global hypoelliptic estimates. As a consequence, we obtain the compactness of resolvent of the ... More

Lower volume growth estimates for Self-shrinkers of mean curvature flowDec 05 2011Jan 23 2012We obtain a Calabi-Yau type lower volume growth estimates for complete noncompact self-shrinkers of the mean curvature flow, more precisely, every complete noncompact properly immersed self-shrinker has at least linear volume growth.

$f$-minimal surface and manifold with positive $m$-Bakry-Émery Ricci curvatureSep 05 2012In this paper, we first prove a compactness theorem for the space of closed embedded $f$-minimal surfaces of fixed topology in a closed three-manifold with positive Bakry-\'{E}mery Ricci curvature. Then we give a Lichnerowicz type lower bound of the first ... More

A homotopy theory of additive categories with suspensionsMar 08 2017We develop a homotopy theory for additive categories endowed with endofunctors, analogous to the concept of a model structure. We use it to construct the homotopy theory of a Hovey triple (which consists of two compatible complete cotorsion pairs) in ... More

Spectral transfer for metaplectic groups. I. Local character relationsSep 22 2014Dec 03 2014Let $\widetilde{\mathrm{Sp}}(2n)$ be the metaplectic covering of $\mathrm{Sp}(2n)$ over a local field of characteristic zero. The core of the theory of endoscopy for $\widetilde{\mathrm{Sp}}(2n)$ is the geometric transfer of orbital integrals to its elliptic ... More

Electron multipacting in long-bunch beamSep 25 2015Sep 28 2015The electron multipacting is an important factor for the development of the electron cloud. There is a trailing-edge multipacting in the tail of the long-bunch beam. It can be described by the energy gain and motion of electrons. The analyses are in agreement ... More

Hard X-ray emissions from Cassiopeia A observed by INTEGRALMay 02 2016Cassiopeia A (Cas A) as the nearby young remnant of a core-collapse supernova is the best candidate for astrophysical studies in supernova explosion and its environment. We studied hard X-ray emissions from Cas A using the ten-year data of INTEGRAL observations, ... More

Contragredient representations over local fields of positive characteristicFeb 25 2018Jan 10 2019It is conjectured by Adams-Vogan and Prasad that under the local Langlands correspondence, the L-parameter of the contragredient representation equals that of the original representation composed with the Chevalley involution of the L-group. We verify ... More

Local Unitary Representation of Braids and N-Qubit EntanglementsJun 05 2017In this paper, by utilizing the idea of stabilizer codes, we give some relationships between one local unitary representation of braid group in N-qubit tensor space and the corresponding entanglement properties of the N-qubit pure state $|\Psi\rangle$, ... More

Transfert d'intégrales orbitales pour le groupe métaplectiqueJun 22 2009Jan 11 2010This paper develops a formalism of endoscopy for the metaplectic group. We define the notions of stable conjugacy, elliptic endoscopic groups, correspondence of semisimple geometric conjugacy classes and the transfer factors in this setting, then we establish ... More

Contragredient representations over local fields of positive characteristicFeb 25 2018Jun 27 2019It is conjectured by Adams-Vogan and Prasad that under the local Langlands correspondence, the L-parameter of the contragredient representation equals that of the original representation composed with the Chevalley involution of the L-group. We verify ... More

La formule des traces pour les revêtements de groupes réductifs connexes. III. Le développement spectral finJul 12 2011We pursue Arthur's invariant trace formula for certain coverings of connected reductive groups by deducing explicit formulas for its spectral side. This is based on some results in local harmonic analysis from an earlier preprint. The arguments are due ... More

La formule des traces pour les revêtements de groupes réductifs connexes. II. Analyse harmonique localeJul 10 2011Apr 22 2012We establish some results in local harmonic analysis which are necessary for Arthur's invariant trace formula for coverings of connected reductive groups. More precisely, for local coverings we will study (1) the Plancherel formula and its preparations, ... More

La formule des traces pour les revêtements de groupes réductifs connexes. I. Le développement géométrique finApr 22 2010Jul 06 2011We study the genuine part of the Arthur-Selberg trace formula for some nonlinear covers of connected reductive groups. As a first step towards the invariant trace formula, we express the geometric side in terms of weighted orbital integrals. In particular, ... More

Optimal control problems of fully coupled FBSDEs and viscosity solutions of Hamilton-Jacobi-Bellman equationsFeb 05 2013In this paper we study stochastic optimal control problems of fully coupled forward-backward stochastic differential equations (FBSDEs). The recursive cost functionals are defined by controlled fully coupled FBSDEs. We study two cases of diffusion coefficients ... More

Zeta integrals, Schwartz spaces and local functional equationsAug 23 2015Dec 15 2018According to Sakellaridis, many zeta integrals in the theory of automorphic forms can be produced or explained by appropriate choices of a Schwartz space of test functions on a spherical homogeneous space, which are in turn dictated by the geometry of ... More

Exact Phase Transitions in Random Constraint Satisfaction ProblemsApr 16 2000In this paper we propose a new type of random CSP model, called Model RB, which is a revision to the standard Model B. It is proved that phase transitions from a region where almost all problems are satisfiable to a region where almost all problems are ... More

Closed-form, robust and accurate multi-frequency phase unwrapping: frequency design and algorithmApr 29 2016Feb 18 2017A closed-form algorithm, named "concerto", is proposed for phase-based distance estimation in multi-frequency phase unwrapping (MFPU) system. The concerto method consists of three coherent estimation stages,i.e., initial modified BW estimation, residual ... More

On the generalized Feynman-Kac transformation for nearly symmetric Markov processesJan 01 2010Jan 05 2010Suppose $X$ is a right process which is associated with a non-symmetric Dirichlet form $(\mathcal{E},D(\mathcal{E}))$ on $L^{2}(E;m)$. For $u\in D(\mathcal{E})$, we have Fukushima's decomposition: $\tilde{u}(X_{t})-\tilde{u}(X_{0})=M^{u}_{t}+N^{u}_{t}$. ... More

A class of generalized positive linear maps on matrix algebrasApr 05 2017We construct a class of positive linear maps on matrix algebras. We find conditions when these maps are atomic, decomposable and completely positive. We obtain a large class of atomic positive linear maps. As applications in quantum information theory, ... More

On inverse mean curvature flow in Schwarzschild space and Kottler spaceDec 18 2012Jul 18 2015In this paper, we first study the behavior of inverse mean curvature flow in Schwarzschild manifold. We show that if the initial hypersurface $\Sigma$ is strictly mean convex and star-shaped, then the flow hypersurface $\Sigma_t$ converges to a large ... More

Zeta integrals, Schwartz spaces and local functional equationsAug 23 2015According to Sakellaridis, many zeta integrals in the theory of automorphic forms can be produced or explained by appropriate choices of a Schwartz space of test functions on a spherical homogeneous space, which are in turn dictated by the geometry of ... More

On a pairing of Goldberg-Shahidi for even orthogonal groupsMar 21 2012Jan 10 2013Let {\sigma}\otimes{\pi} be a supercuspidal representation of SO(2n) \times GL(2n) over a p-adic field with {\pi} selfdual, where SO(2n) stands for a quasisplit even special orthogonal group. In order to study its normalized parabolic induction to SO(6n), ... More

Basic functions and unramified local L-factors for split groupsNov 11 2013Feb 24 2014According to a program of Braverman, Kazhdan and Ng\^o Bao Ch\^au, for a large class of split unramified reductive groups $G$ and representations $\rho$ of the dual group $\hat{G}$, the unramified local $L$-factor $L(s,\pi,\rho)$ can be expressed as the ... More

Many Hard Examples in Exact Phase Transitions with Application to Generating Hard Satisfiable InstancesFeb 01 2003Nov 11 2003This paper first analyzes the resolution complexity of two random CSP models (i.e. Model RB/RD) for which we can establish the existence of phase transitions and identify the threshold points exactly. By encoding CSPs into CNF formulas, it is proved that ... More

On the Average Similarity Degree between Solutions of Random k-SAT and Random CSPsAug 11 2000Apr 07 2002To study the structure of solutions for random k-SAT and random CSPs, this paper introduces the concept of average similarity degree to characterize how solutions are similar to each other. It is proved that under certain conditions, as r (i.e. the ratio ... More

Computing the permanental polynomials of bipartite graphs by Pfaffian orientationOct 06 2010The permanental polynomial of a graph $G$ is $\pi(G,x)\triangleq\mathrm{per}(xI-A(G))$. From the result that a bipartite graph $G$ admits an orientation $G^e$ such that every cycle is oddly oriented if and only if it contains no even subdivision of $K_{2,3}$, ... More

A homotopy theory of Nakaoka twin cotorsion pairsMar 25 2017May 07 2017We show that the Verdier quotients can be realized as subfactors by the homotopy theory of additive categories with suspensions developed in \cite{ZWLi2, ZWLi3}. As applications, we develop the homotopy theory of Nakaoka twin cotorsion pairs of triangulated ... More

Asymptotic results for exponential functionals of Levy processesJan 11 2016Feb 06 2016In this work we give a complete description to the asymptotic behaviors of exponential functionals of L\'evy processes and divide them into five different types according to their convergence rates. Not only their exact convergence speeds are proved, ... More

The triangulation of the subfactor categories of additive categories with suspensionsOct 08 2015Feb 22 2017We provide a framework to triangulate subfactor categories of additive categories with additive endofunctors. It is proved that such a framework is sufficiently flexible to cover many instances in algebra and geometry where abelian, exact and triangulated ... More

The generalized connectivity of complete bipartite graphsDec 28 2010Let $G$ be a nontrivial connected graph of order $n$, and $k$ an integer with $2\leq k\leq n$. For a set $S$ of $k$ vertices of $G$, let $\kappa (S)$ denote the maximum number $\ell$ of edge-disjoint trees $T_1,T_2,...,T_\ell$ in $G$ such that $V(T_i)\cap ... More

$L^p$ estimates for fully coupled FBSDEs with jumpsFeb 05 2013In this paper we study useful estimates, in particular $L^p$-estimates, for fully coupled forward-backward stochastic differential equations (FBSDEs) with jumps. These estimates are proved at one hand for fully coupled FBSDEs with jumps under the monotonicity ... More

On the regularity of D-modules generated by relative charactersMay 20 2019Following the ideas of Ginzburg, for a subgroup $K$ of a connected reductive $\mathbb{R}$-group $G$ we introduce the notion of $K$-admissible $D$-modules on a homogeneous $G$-variety $Z$. We show that $K$-admissible $D$-modules are regular holonomic when ... More

La formule des traces pour les revêtements de groupes réductifs connexes. IV. Distributions invariantesSep 19 2012Apr 27 2014We establish the invariant trace formula (\`a la Arthur) for the ad\'elic covers of connected reductive groups over a number field, under the hypothesis that the trace Paley-Wiener theorem is verified for all Levi subgroups at the real archimedean places. ... More

Optimization in Multi-Frequency Interferometry Ranging: Theory and ExperimentFeb 07 2012Oct 07 2012Multi-frequency interferometry (MFI) is well known as an accurate phase-based measurement scheme. The paper reveals the inherent relationship of the unambiguous measurement range (UMR), the outlier probability, the MSE performance with the frequency pattern ... More

An External Knowledge Enhanced Multi-label Charge Prediction Approach with Label Number LearningJul 04 2019Multi-label charge prediction is a task to predict the corresponding accusations for legal cases, and recently becomes a hot topic. However, current studies use rough methods to deal with the label number. These methods manually set parameters to select ... More

Complete cotorsion pairs in exact categoriesDec 18 2014Mar 07 2018We show a cotorsion pair cogenerated by a class is complete under suitable conditions in an arbitrary exact category using the generalized small object argument given by Chorny. This recovers Saor\'in and \v{S}\v{t}ov\'{i}\v{c}ek's criterion of the completeness ... More

Classification and rigidity of self-shrinkers in the Mean curvature flowJan 23 2012Sep 28 2012In this paper, we first use the method of Colding and Minicozzi [5] to show that K. Smoczyk's classification theorem [16] for complete self-shrinkers in higher codimension also holds under a weaker condition. Then as an application, we give some rigidity ... More

Le lemme fondamental pondéré pour le groupe métaplectiqueJun 24 2010We state a variant of Arthur's weighted fundamental lemma for the metaplectic group of Weil, which will be an essential ingredient of the stable trace formula. Over a local field of large enough residual characteristic, we give a proof using the method ... More

On the regularity of D-modules generated by relative charactersMay 20 2019Jun 27 2019Following the ideas of Ginzburg, for a subgroup $K$ of a connected reductive $\mathbb{R}$-group $G$ we introduce the notion of $K$-admissible $D$-modules on a homogeneous $G$-variety $Z$. We show that $K$-admissible $D$-modules are regular holonomic when ... More

Closed-Form Error Analysis on RSS-based Indoor Localization MethodFeb 07 2017Dec 13 2017Received Signal Strength (RSS) is considered as a promising measurement for indoor positioning. Lots of RSS-based localization methods have been proposed by its convenience and low cost. This paper focuses on two challenging issues in RSS-based localization ... More

Thermal Tensor Network Simulations of the Heisenberg Model on the Bethe LatticeMay 29 2019We have extended the canonical tree tensor network (TTN) method, which was initially introduced to simulate the zero-temperature properties of quantum lattice models on the Bethe lattice, to finite temperature simulations. By representing the thermal ... More

Relationship between Characteristic Lengths and Effective Saffman Length in Colloidal Monolayers near a Water-Oil InterfaceDec 27 2018The hydrodynamic interactions (HIs) in colloidal monolayers are strongly influenced by the boundary conditions and can be directly described in terms of the cross-correlated diffusion of the colloid particles. In this work, we experimentally measured ... More

Synchronized output regulation of nonlinear multi-agent systemsJun 30 2013This paper considers the synchronized output regulation (SOR) problem of nonlinear multi-agent systems with switching graph. The SOR means that all agents regulate their outputs to synchronize on the output of a predefined common exosystem. Each agent ... More

Effect of atmospheric turbulence on propagation properties of optical vortices formed by using coherent laser beam arraysJun 10 2008In this paper, we consider the effect of the atmospheric turbulence on the propagation of optical vertex formed from the radial coherent laser beam array, with the initially well-defined phase distribution. The propagation formula of the radial coherent ... More

Modular Properties of 3D Higher Spin TheoryAug 13 2013Dec 18 2013In the three-dimensional sl(N) Chern-Simons higher-spin theory, we prove that the conical surplus and the black hole solution are related by the S-transformation of the modulus of the boundary torus. Then applying the modular group on a given conical ... More

PersonRank: Detecting Important People in ImagesNov 06 2017Always, some individuals in images are more important/attractive than others in some events such as presentation, basketball game or speech. However, it is challenging to find important people among all individuals in images directly based on their spatial ... More

Privacy-Preserving Outsourcing of Large-Scale Nonlinear Programming to the CloudOct 02 2018The increasing massive data generated by various sources has given birth to big data analytics. Solving large-scale nonlinear programming problems (NLPs) is one important big data analytics task that has applications in many domains such as transport ... More

Positive periodic solutions for abstract evolution equations with delayJan 02 2018In this paper, we discuss the existence and asymptotic stability of the positive periodic mild solutions for the abstract evolution equation with delay in an ordered Banach space $E$, $$u'(t)+Au(t)=F(t,u(t),u(t-\tau)),\ \ \ \ t\in\R,$$ where $A:D(A)\subset ... More

Rainbow triangles in arc-colored digraphsOct 14 2018Let $D$ be an arc-colored digraph. The arc number $a(D)$ of $D$ is defined as the number of arcs of $D$. The color number $c(D)$ of $D$ is defined as the number of colors assigned to the arcs of $D$. A rainbow triangle in $D$ is a directed triangle in ... More

STORE: Sparse Tensor Response Regression and Neuroimaging AnalysisSep 15 2016Nov 24 2017Motivated by applications in neuroimaging analysis, we propose a new regression model, Sparse TensOr REsponse regression (STORE), with a tensor response and a vector predictor. STORE embeds two key sparse structures: element-wise sparsity and low-rankness. ... More

Optimal Linear Instrumental Variables ApproximationsMay 08 2018Dec 11 2018Ordinary least squares provides the optimal linear approximation to the true regression function. This paper investigates the Instrumental Variables (IV) version of this problem. The resulting parameter is called the Optimal Linear IV Approximation (OLIVA). ... More

Well-posedness in Gevrey space for the Prandtl equations with non-degenerate critical pointsSep 27 2016Aug 29 2017In the paper, we study the Prandtl system with initial data admitting non-degenerate critical points. For any index $\sigma\in[3/2, 2],$ we obtain the local in time well-posedness in the space of Gevrey class $G^\sigma$ in the tangential variable and ... More

Remarks on CLEO New Measurements for Upsilon(1S) Decays to Charmonium Final States and Investigations on Associate Strange Particle Enhancement in Upsilon to J/Psi +XJul 22 2006Dec 17 2006The recent measurements by CLEO Collaboration for the inclusive J/Psi and Psi(2S) production in Upsilon(1S) decay and our previous calculation are analyzed. The J/Psi momentum spectrum and the production ratio of Psi(2S) versus J/Psi favour Upsilon to ... More

On the Euler numbers of certain moduli spaces of curves and pointsAug 07 2005Aug 09 2005We determine the topological Euler number of certain moduli space of 1-dimensional closed subschemes in a smooth projective variety which admits a Zariski-locally trivial fibration with 1-dimensional fibers. The main approach is to use virtual Hodge polynomials ... More

1-point Gromov-Witten invariants of the moduli spaces of sheaves over the projective planeJun 15 2009The Gieseker-Uhlenbeck morphism maps the Gieseker moduli space of stable rank-2 sheaves on a smooth projective surface to the Uhlenbeck compactification, and is a generalization of the Hilbert-Chow morphism for Hilbert schemes of points. When the surface ... More

Stopping waveguide photons with controllable atomic cavityMar 16 2016Slowing/stopping the light travelling in free space with electromagnetically induced transparency to im- plement the optical quantum information processings and store information has been paid much attention in recent years. For the waveguide photons, ... More

Order-Independent Texture SynthesisJun 28 2014Search-based texture synthesis algorithms are sensitive to the order in which texture samples are generated; different synthesis orders yield different textures. Unfortunately, most polygon rasterizers and ray tracers do not guarantee the order with which ... More

Birational Models of the Moduli Spaces of Stable Vector Bundles over CurvesApr 08 1997We give a method to construct stable vector bundles whose rank divides the degree over curves of genus bigger than one. The method complements the one given by Newstead. Finally, we make some systematic remarks and observations in connection with rationality ... More

Dynamic Tensor ClusteringAug 24 2017Sep 14 2018Dynamic tensor data are becoming prevalent in numerous applications. Existing tensor clustering methods either fail to account for the dynamic nature of the data, or are inapplicable to a general-order tensor. Also there is often a gap between statistical ... More

Estimating the number of neurons in multi-neuronal spike trainsApr 14 2011A common way of studying the relationship between neural activity and behavior is through the analysis of neuronal spike trains that are recorded using one or more electrodes implanted in the brain. Each spike train typically contains spikes generated ... More

Holographic Entanglement Entropy and Van der Waals transitions in Einstein-Maxwell-dilaton theorySep 11 2018Mar 10 2019According to the gauge/gravity duality, the Van der Waals transition of charged AdS black holes in extended phase space is conjectured to be dual to a renormalization group flow on the space of field theories. So exploring the Van der Waals transition ... More

The Donaldson-Thomas invariants under blowups and flopsMay 25 2005Using the degeneration formula for Doanldson-Thomas invariants, we proved formulae for blowing up a point and simple flops.

Equivariant cohomology of incidence Hilbert schemes and loop algebrasFeb 12 2008Let $S$ be the affine plane $\C^2$ together with an appropriate $\mathbb T = \C^*$ action. Let $\hil{m,m+1}$ be the incidence Hilbert scheme. Parallel to \cite{LQ}, we construct an infinite dimensional Lie algebra that acts on the direct sum $$\Wft = ... More

Incidence Hilbert schemes and infinite dimensional Lie algebrasJun 20 2006Given a projetive surface $S$, using correspondences, we construct an infinite dimensional Lie algebra that acts on the direct sum $\Wfock$ of the cohomology groups of the incidence Hilbert schemes $S^{[n,n+1]}$ over all $n$. The algebra is related to ... More

A note on the invariance principle of the product of sums of random variablesOct 17 2006In literature, the central limit theorems for the product of sums of various random variables have studied. The purpose of this note is to show that this kind of results are corollary of the invariance principle.

Modified "complexity equals action" conjectureMar 12 2019In this paper, we first use the "complexity equals action" conjecture to discuss the complexity growth rate in both perturbation Einsteinian cubic gravity and non-perturbation Einstein-Weyl gravity. We find that the CA complexity rate in these cases is ... More

Privacy-Preserving Multiparty Learning For Logistic RegressionOct 04 2018In recent years, machine learning techniques are widely used in numerous applications, such as weather forecast, financial data analysis, spam filtering, and medical prediction. In the meantime, massive data generated from multiple sources further improve ... More

Nonlinear traveling waves as a framework for understanding turbulent drag reductionJan 24 2006Nonlinear traveling waves that are precursors to laminar-turbulent transition and capture the main structures of the turbulent buffer layer have recently been found to exist in all the canonical parallel flow geometries. We study the effect of polymer ... More

J/psi with large pT probing the early stage of relativistic heavy ion collisionsJan 27 2018Jul 22 2018We study the charmonium suppression in different evolutions of quark gluon plasma (QGP) based on the transport model. In the colliding energies of Large Hadron Collider, charmonium final yields are dominated by the recombination of charm and anti-charm ... More