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Diffusion Adaptation Framework for Compressive Sensing ReconstructionDec 03 2017Jun 22 2018Compressive sensing(CS) has drawn much attention in recent years due to its low sampling rate as well as high recovery accuracy. As an important procedure, reconstructing a sparse signal from few measurement data has been intensively studied. Many reconstruction ... More

Robust Matrix Completion via Maximum Correntropy Criterion and Half Quadratic OptimizationMar 14 2019Robust matrix completion aims to recover a low-rank matrix from a subset of noisy entries perturbed by complex noises, where traditional methods for matrix completion may perform poorly due to utilizing $l_2$ error norm in optimization. In this paper, ... More

Maximum Total Correntropy Diffusion Adaptation over Networks with Noisy LinksFeb 14 2018Distributed estimation over networks draws much attraction in recent years. In many situations, due to imperfect information communication among nodes, the performance of traditional diffusion adaptive algorithms such as the diffusion LMS (DLMS) may degrade. ... More

Maximum Correntropy Adaptive Filtering Approach for Robust Compressive Sensing ReconstructionJun 10 2017Robust compressive sensing(CS) reconstruction has become an attractive research topic in recent years. Robust CS aims to reconstruct the sparse signals under non-Gaussian(i.e. heavy tailed) noises where traditional CS reconstruction algorithms may perform ... More

Trajectory Fitting Estimators for SPDEs Driven by Additive NoiseJul 17 2016Nov 13 2016In this paper we study the problem of estimating the drift/viscosity coefficient for a large class of linear, parabolic stochastic partial differential equations (SPDEs) driven by an additive space-time noise. We propose a new class of estimators, called ... More

Robust Preconditioners for Incompressible MHD ModelsMar 09 2015In this paper, we develop two classes of robust preconditioners for the structure-preserving discretization of the incompressible magnetohydrodynamics (MHD) system. By studying the well-posedness of the discrete system, we design block preconditioners ... More

Color Face Recognition using High-Dimension Quaternion-based Adaptive RepresentationNov 19 2017Recently, quaternion collaborative representation-based classification (QCRC) and quaternion sparse representation-based classification (QSRC) have been proposed for color face recognition. They can obtain correlation information among different color ... More

On Duality Of Multiple Target Tracking and SegmentationOct 14 2016Traditionally, object tracking and segmentation are treated as two separate problems and solved independently. However, in this paper, we argue that tracking and segmentation are actually closely related and solving one should help the other. On one hand, ... More

Discriminant Projection Representation-based Classification for Vision RecognitionNov 19 2017Representation-based classification methods such as sparse representation-based classification (SRC) and linear regression classification (LRC) have attracted a lot of attentions. In order to obtain the better representation, a novel method called projection ... More

Prospects of type-II seesaw at future colliders in light of the DAMPE $e^+ e^-$ excessDec 11 2017Apr 24 2018The DAMPE $e^+ e^-$ excess at around 1.4 TeV could be explained in the type-II seesaw model with a scalar dark mater $D$ which is stabilized by a discrete $Z_2$ symmetry. The simplest scenario is the annihilation $DD \to H^{++} H^{--}$ followed by the ... More

Vision Recognition using Discriminant Sparse Optimization LearningNov 19 2017To better select the correct training sample and obtain the robust representation of the query sample, this paper proposes a discriminant-based sparse optimization learning model. This learning model integrates discriminant and sparsity together. Based ... More

Nonlinear Chaotic Processing ModelDec 14 2016Designing chaotic maps with complex dynamics is a challenging topic. This paper introduces the nonlinear chaotic processing (NCP) model, which contains six basic nonlinear operations. Each operation is a general framework that can use existing chaotic ... More

A note on parameter estimation for discretely sampled SPDEsOct 04 2017We consider a parameter estimation problem for one dimensional stochastic heat equations, when data is sampled discretely in time or spatial component. We establish some general results on derivation of consistent and asymptotically normal estimators ... More

A Combined Astrophysical and Dark Matter Interpretation of the IceCube HESE and Throughgoing Muon EventsApr 13 2018Jul 05 2018We perform a combined likelihood analysis for the IceCube 6-year high-energy starting events (HESE) and 8-year throughgoing muon events above 10 TeV using a two-component neutrino flux model. The two-component flux can be motivated either from purely ... More

Transfer Learning for Brain-Computer Interfaces: An Euclidean Space Data Alignment ApproachAug 08 2018Almost all EEG-based brain-computer interfaces (BCIs) need some labeled subject-specific data to calibrate a new subject, as neural responses are different across subjects to even the same stimulus. So, a major challenge in developing high-performance ... More

Optimal Monotone Drawings of TreesApr 13 2016A monotone drawing of a graph G is a straight-line drawing of G such that, for every pair of vertices u,w in G, there exists abpath P_{uw} in G that is monotone in some direction l_{uw}. (Namely, the order of the orthogonal projections of the vertices ... More

Transfer Learning Enhanced Common Spatial Pattern Filtering for Brain Computer Interfaces (BCIs): Overview and a New ApproachAug 08 2018The electroencephalogram (EEG) is the most widely used input for brain computer interfaces (BCIs), and common spatial pattern (CSP) is frequently used to spatially filter it to increase its signal-to-noise ratio. However, CSP is a supervised filter, which ... More

Trajectory Fitting Estimators for SPDEs Driven by Additive NoiseJul 17 2016In this paper we study the problem of estimating the drift/viscosity coefficient for a large class of linear, parabolic stochastic partial differential equation (SPDE) driven by an additive space-time noise. We propose a new class of estimators, called ... More

Stable Finite Element Methods Preserving $\nabla \cdot \boldsymbol{B} = 0$ Exactly for MHD ModelsOct 04 2014This paper is devoted to the design and analysis of some structure-preserving finite element schemes for the magnetohydrodynamics (MHD) system. The main feature of the method is that it naturally preserves the important Gauss law, namely $\nabla\cdot\boldsymbol{B}=0$. ... More

Mixed-Granularity Human-Swarm InteractionJan 24 2019We present an augmented reality human-swarm interface that combines two modalities of interaction: environment-oriented and robot-oriented. The environment-oriented modality allows the user to modify the environment (either virtual or physical) to indicate ... More

Error estimates for structure-preserving discretization of the incompressible MHD systemAug 10 2016In this paper, we carry out the error analysis for the structure-preserving discretization of the incompressible MHD system. This system, as a coupled system of Navier-Stokes equations and Maxwell's equations, is nonlinear. We use its energy estimate ... More

Cross-View Image Matching for Geo-localization in Urban EnvironmentsMar 22 2017In this paper, we address the problem of cross-view image geo-localization. Specifically, we aim to estimate the GPS location of a query street view image by finding the matching images in a reference database of geo-tagged bird's eye view images, or ... More

An Analytic Expression of Performance Rate, Fitness Value and Average Convergence Rate for a Class of Evolutionary AlgorithmsNov 11 2015Feb 16 2016An important theoretical question in evolutionary computation is how good solutions evolutionary algorithms can produce. This paper aims to provide an analytic analysis of solution quality of evolutionary algorithms in terms of the performance rate, which ... More

Kottwitz-Rapoport conjecture on unions of affine Deligne-Lusztig varietiesAug 25 2014Sep 24 2015In this paper, we prove a conjecture of Kottwitz and Rapoport on a union of (generalized) affine Deligne-Lusztig varieties $X(\mu, b)_J$ for any tamely ramified group $G$ and its parahoric subgroup $P_J$. We show that $X(\mu, b)_J \neq \emptyset$ if and ... More

Lebesgue approximation of $(2,β)$-superprocessesJan 31 2012Feb 01 2012Let $\xi=(\xi_t)$ be a locally finite $(2,\beta)$-superprocess in $\RR^d$ with $\beta<1$ and $d>2/\beta$. Then for any fixed $t>0$, the random measure $\xi_t$ can be a.s. approximated by suitably normalized restrictions of Lebesgue measure to the $\varepsilon$-neighborhoods ... More

Closure of Steinberg fibers and affine Deligne-Lusztig varietiesMar 01 2010We discuss some connections between the closure $\bar F$ of a Steinberg fiber in the wonderful compactification of an adjoint group and the affine Deligne-Lusztig varieties $X_w(1)$ in the affine flag variety. Among other things, we describe the emptiness/nonemptiness ... More

The $G$-stable pieces of the wonderful compactificationDec 15 2004Feb 01 2006Let $G$ be a connected, simple algebraic group over an algebraically closed field. There is a partition of the wonderful compactification $\bar{G}$ of $G$ into finite many $G$-stable pieces, which were introduced by Lusztig. In this paper, we will investigate ... More

Cocenters of $p$-adic groups, I: Newton decompositionOct 15 2016In this paper, we introduce the Newton decomposition on a connected reductive $p$-adic group $G$. Based on it we give a nice decomposition on the cocenter of its Hecke algebra. Here we consider both the ordinary cocenter associated to the usual conjugation ... More

Rotated sphere packing designsAug 12 2016We propose a new class of space-filling designs called rotated sphere packing designs for computer experiments. The approach starts from the asymptotically optimal positioning of identical balls that covers the unit cube. Properly scaled, rotated, translated ... More

On the cohomology ring of associated flag bundleOct 25 2016In this expository note, we survey the cohomology rings of flag bundles associated to vector bundles in terms of characteristic classes.

A New Framework for Ranking Vulnerabilities in the CloudsNov 23 2016Qualifying and ranking threat degrees of vulnerabilities in cloud service are known to be full of challenges. Although there have been several efforts aiming to address this problem, most of them are too simple or cannot be applied into cloud infrastructure. ... More

On Bilinear Maximal Bochner-Riesz OperatorsJul 12 2016We prove that the bilinear maximal Bochner-Riesz operator $T_*^\lambda$ is bounded from $L^{p_1}(\mathbb R^n)\times L^{p_2}(\mathbb R^n)$ to $L^p(\mathbb R^n)$ for appropriate $(p_1,p_2,p)$ when $\lambda>(4n+3)/5$.

GKM graphs for odd dimensional manifolds with torus actionsAug 15 2016Oct 25 2016Let torus $T$ act on a manifold $M$, if the equivariant cohomology $H^*_T(M)$ is a free module of $H^*_T(pt)$, then according to the Chang-Skjelbred Lemma, $H^*_T(M)$ can be determined by the $1$-skeleton $M_1$ consisting of fixed points and $1$-dimensional ... More

Classification of Compatible Parabolic Subalgebras for Complex Symmetric PairsMar 19 2014Mar 20 2014In this paper, we shall recall and arrange the relationship between hyperbolic elements and parabolic subalgebras at first. And then, we shall classify all the compatible parabolic subalgebras containing a $\tau$-stable Borel subalgebra for complex symmetric ... More

Reconstruction and Higher Dimensional GeometryNov 18 2005Jun 26 2006In this paper, we give a new proof on a Theorem of Tutte which says that the determinants of the adjacency matrices of two hypomorphic graphs are the same. We also study the lowest eigenvectors.

Possible Prescription to Avoid Chromomagnetic Instability in the g2SC and gCFL PhasesJun 07 2005Jun 12 2005This paper has been withdrawn.

Classification of Klein Four Symmetric Pairs of Holomorphic Type for $\mathrm{E}_{7(-25)}$Apr 10 2018The author classifies Klein four symmetric pairs of holomorphic type for the non-compact Lie group of Hermitian type $\mathrm{E}_{7(-25)}$, and applies the results to branching rules.

Unipotent Representations and Quantum InductionOct 23 2002Mar 02 2007In this paper, we construct certain unipotent representations for the real orthogonal group and the metaplectic group in the sense of Vogan. In particular, our results imply that there are irreducible unitary representations attached to each special nilpotent ... More

Discretely decomposable restrictions of $(\mathfrak{g},K)$-modules for Klein four symmetric pairs of exceptional Lie groups of Hermitian typeAug 30 2018Let $(G,G')$ be a Klein four symmetric pair. If $\pi_K$ is a unitarizable simple $(\mathrm{g},K)$-module, the author shows some necessary conditions when $\pi_K$ is discretely decomposable as a $(\mathfrak{g}',K')$-module. In particular, if $G$ is an ... More

Theta Correspondence and Quantum InductionOct 23 2002Oct 24 2005In his article "Transcending Classical Invariant Theory" (J.A.M.S., 1989, Vol 2), Roger Howe established a correspondence between representations of a dual pair of reductive groups. This correspondence is known as Howe's correspondence or local theta ... More

Nonperturbative contribution to the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi and Gribov-Levin-Ryskin equationApr 20 1999By studying the nonperturbative contribution to the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi and Gribov-Levin-Ryskin equation, it is found that (i) the nonperturbative contribution suppresses the evolution rate at the low $Q^2$, small-x region; (ii) ... More

Suppression of blow-up in Parabolic-Parabolic Patlak-Keller-Segel via strictly monotone shear flowsOct 27 2017In this paper we consider the parabolic-parabolic Patlak-Keller-Segel models in $\mathbb{T}\times\mathbb{R}$ with advection by a large strictly monotone shear flow. Without the shear flow, the model is $L^1$ critical in two dimensions with critical mass ... More

A sufficient condition for a finite-time $ L_2 $ singularity of the 3d Euler EquationSep 24 2002A sufficient condition is derived for a finite-time $L_2$ singularity of the 3d incompressible Euler equations, making appropriate assumptions on eigenvalues of the Hessian of pressure. Under this condition $\lim_{t \to T_*} \sup | \frac{D \o} {Dt} |_{L_2(\vO)} ... More

Remarks on the extension of the Ricci flowJun 04 2012Jul 14 2012We present two new conditions to extend the Ricci flow on a compact manifold over a finite time, which are improvements of some known extension theorems.

Equivariant cohomology rings of the real flag manifoldsOct 25 2016Jan 11 2019We give Leray-Borel-type descriptions for the mod-$2$ and the rational equivariant cohomology rings of the real and the oriented flag manifolds under the canonical torus or 2-torus actions.

On W_2 lifting of Frobenius of Algebraic SurfacesSep 03 2013We completely decide which minimal algebraic surfaces in positive characteristics allow a lifting of their Frobenius over the trucated witt rings of lengh 2.

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

On Matrix-Valued Square Integrable Positive Definite FunctionsMay 01 2009Sep 09 2015In this paper, we study matrix valued positive definite functions on a unimodular group. We generalize two important results of Godement on square integrable positive definite functions to matrix valued square integrable positive definite functions. We ... More

A finite field analogue for Appell series F_3Apr 04 2017Dec 13 2017In this paper we introduce a finite field analogue for the Appell series F_3 and give some reduction formulae and certain generating functions for this function over finite fields.

Mori Dream Spaces and blow-ups of weighted projective spacesMar 30 2018Jan 24 2019For every $n\geq 3$, we find a sufficient condition for the blow-up of a weighted projective space $\mathbb{P}(a,b,c,d_1,\cdots,d_{n-2})$ at the identity point not to be a Mori Dream Space. We exhibit several infinite sequences of weights satisfying this ... More

Inverse Conditional Probability Weighting with Clustered Data in Causal InferenceAug 05 2018Estimating the average treatment causal effect in clustered data often involves dealing with unmeasured cluster-specific confounding variables. Such variables may be correlated with the measured unit covariates and outcome. When the correlations are ignored, ... More

Sharp estimate of lower bound for the first eigenvalue in the Laplacian operator on compact Riemannian manifoldsOct 21 2012The aim of this paper is give a simple proof of some results in \cite{Jun Ling-2006-IJM} and \cite{JunLing-2007-AGAG}, which are very deep studies in the sharp lower bound of the first eigenvalue in the Laplacian operator on compact Riemannian manifolds ... More

Proof of the Pólya conjectureNov 05 2014Nov 09 2014In this paper, we study lower bounds for higher eigenvalues of the Dirichlet eigenvalue problem of the Laplacian on a bounded domain $\Omega$ in $\mathbb{R}^n$. It is well known that the $k$-th Dirichlet eigenvalue $\lambda_k$ obeys the Weyl asymptotic ... More

On the affineness of Deligne-Lusztig varietiesJul 02 2007We prove that the Deligne-Lusztig variety associated to minimal length elements in any $\d$-conjugacy class of the Weyl group is affine, which was conjectured by Orlik and Rapoport in \cite{OR}.

Real-time calibration and alignment of the LHCb RICH detectorsNov 01 2016In 2015, the LHCb experiment established a new and unique software trigger strategy with the purpose of increasing the purity of the signal events by applying the same algorithms online and offline. To achieve this, real-time calibration and alignment ... More

Geometric Progression-Free Sequences with Small Gaps IIMar 24 2015When $k$ is a constant at least $3$, a sequence $S$ of positive integers is called $k$-GP-free if it contains no nontrivial $k$-term geometric progressions. Beiglb\"ok, Bergelson, Hindman and Strauss first studied the existence of a $ $$k$-GP-free sequence ... More

Cross Number Invariants of Finite Abelian GroupsAug 18 2013Oct 31 2013The cross number of a sequence over a finite abelian group $G$ is the sum of the inverse orders of the terms of that sequence. We study two group invariants, the maximal cross number of a zero-sum free sequence over $G$, called $\mathsf{k}(G)$, introduced ... More

On the Classification of Universal Rotor-RoutersNov 06 2011The combinatorial theory of rotor-routers has connections with problems of statistical mechanics, graph theory, chaos theory, and computer science. A rotor-router network defines a deterministic walk on a digraph G in which a particle walks from a source ... More

On some partitions of an affine flag varietyOct 27 2009In this paper, we discuss some partitions of affine flag varieties. These partitions include as special cases the partition of affine flag variety into affine Deligne-Lusztig varieties and the affine analogue of the partition of flag varieties into $\cb_w(b)$ ... More

A Generalization of Lifting Non-proper Tropical IntersectionsJun 14 2016Let X and X' be closed subschemes of an algebraic torus T over a non-archimedean field. We prove the rational equivalence as tropical cycles, in the sense of Henning Meyer's graduate thesis, between the tropicalization of the intersection product of X ... More

Search for Rare and Forbidden Decays D^+ --> h^pm e^mp e^+Aug 12 2005Nov 28 2005Using 0.8 million D^+D^- pairs collected with the CLEO-c detector at the psi(3770) resonance, we have searched for flavor-changing neutral current and lepton-number-violating decays of D^+ mesons to final states with dielectrons. We find no indication ... More

A Lauricella hypergeometric series over finite fieldsOct 12 2016Oct 25 2016In this paper we introduce a finite field analogue of a Lauricella hypergeometric series. An integral formula for the Lauricella hypergeometric series and its finite field analogue are deduced. Transformation and reduction formulae and several generating ... More

Pruning Levy trees via an admissible family of branching mechanismsMar 03 2014By studying an admissible family of branching mechanisms introduced in Li (2014), we obtain a pruning procedure on L\'evy trees. Then we could construct a decreasing L\'evy-CRT-valued process $\{\T_t\}$ by pruning L\'evy trees and an analogous process ... More

Mislearning from Censored Data: The Gambler's Fallacy in Optimal-Stopping ProblemsMar 21 2018Nov 21 2018I study endogenous learning dynamics for people expecting systematic reversals from random sequences -- the "gambler's fallacy." Biased agents face an optimal-stopping problem, such as managers conducting sequential interviews. They are uncertain about ... More

Equilibrium statistical mechanics for self-gravitating systems: local ergodicity and extended Boltzmann-Gibbs/White-Narayan statisticsMar 29 2011Oct 27 2011The long-standing puzzle surrounding the statistical mechanics of self-gravitating systems has not yet been solved successfully. We formulate a systematic theoretical framework of entropy-based statistical mechanics for spherically symmetric collisionless ... More

Weakness in a Mutual Authentication Scheme for Session Initiation Protocol using Elliptic Curve CryptographyAug 20 2011The session initiation protocol (SIP) is a powerful signaling protocol that controls communication on the Internet, establishing, maintaining, and terminating the sessions. The services that are enabled by SIP are equally applicable in the world of mobile ... More

Certain Unitary Langlands-Vogan Parameters for Special Orthogonal Groups IJan 03 2011Mar 18 2013A Langlands parameter, in the Langlands dual group, can be decomposed into a product of a tempered parameter and a positive quasi-character. Fixing a tempered parameter, Arthur conjectured that positive quasi-characters corresponding to certain weighted ... More

Unitary Representations and Theta Correspondence for Type I Classical GroupsOct 23 2002In this paper, we prove that theta correspondence preserves unitarity under certain restrictions.

A Link Representation for Gravity AmplitudesJul 17 2012We derive a link representation for all tree amplitudes in N=8 supergravity, from a recent conjecture by Cachazo and Skinner. The new formula explicitly writes amplitudes as contour integrals over constrained link variables, with an integrand naturally ... More

A new way to deduce $ζ(1-k)=-B_k/k$Nov 22 2018Dec 18 2018In this paper, by introducing a new operation in the vector space of analytic functions, the author presents a method for derivating the well-known formula $\zeta(1-k)=-\frac{B_k}{k}$, where $\zeta$ denotes the Riemann zeta function and $B_k$ is the $k$-th ... More

Gradient Yamabe Solitons on Warped ProductsSep 11 2011The special nature of gradient Yamabe soliton equation which was first observed by Cao-Sun-Zhang\cite{CaoSunZhang} shows that a complete gradient Yamabe soliton with non-constant potential function is either defined on the Euclidean space with rotational ... More

Interaction energy and itinerant ferromagnetism in a strongly interacting Fermi gas in the absence of molecule formationMay 20 2014Nov 26 2014We investigate the interaction energy and the possibility of itinerant ferromagnetism in a strongly interacting Fermi gas at zero temperature in the absence of molecule formation. The interaction energy is obtained by summing the perturbative contributions ... More

On the transverse scalar curvature of a compact Sasaki manifoldMay 20 2011We show that the standard picture regarding the notion of stability of constant scalar curvature metrics in K\"ahler geometry described by S.K. Donaldson, which involves the geometry of infinite-dimensional groups and spaces, can be applied to the constant ... More

On regularity of complex Monge-Ampere equationFeb 25 2010Mar 02 2010We shall consider the regularity problem of solutions for complex Monge-Ampere equations. First we prove interior $C^2$ estimates of solutions in a bounded domain for complex Monge-Ampere equation with assumption of certain $L^p$ bound for Laplacian u, ... More

The spin evolution of spin-3 $^{52}$Cr Bose-Einstein condensateAug 19 2009The spin evolution of a Bose-Einstein condensate starting from a mixture of two or three groups of $^{52}$Cr (spin-3) atoms in an optical trap has been studied theoretically. The initial state is so chosen that the system does not distinguish up and down. ... More

Frobenius splitting of projective toric bundlesApr 08 2014We give several mild conditions on a toric bundle on a nonsingular toric variety under which the projectivization of the toric bundle is Frobenius split.

Unitary Representations and Heisenberg Parabolic SubgroupMay 28 2010Mar 27 2011In this paper, we study the restriction of an irreducible unitary representation $\pi$ of the universal covering $\widetilde{Sp}_{2n}(\mb R)$ to a Heisenberg maximal parabolic group $\tilde P$. We prove that if $\pi|_{\tilde P}$ is irreducible, then $\pi$ ... More

Discontinuous Superprocesses with Dependent Spatial MotionJul 01 2008We construct a class of discontinuous superprocesses with dependent spatial motion and general branching mechanism. The process arises as the weak limit of critical interacting-branching particle systems where the spatial motions of the particles are ... More

Certain Induced Complementary Series of the Universal Covering of the Symplectic GroupMay 28 2010In this paper, we give a construction of certain induced complementary series of the universal covering of the symplectic groups. There are abundant such representations besides those of linear groups. We achieve this by applying invariant tensor product ... More

Scalar curvature and properness on Sasaki manifoldsFeb 11 2018We study (transverse) scalar curvature type equation on compact Sasaki manifolds, in view of recent breakthrough of Chen-Cheng \cite{CC1, CC2, CC3} on existence of K\"ahler metrics with constant scalar curvature (csck) on compact K\"ahler manifolds. Following ... More

Evolve nondegenerate two formsOct 29 2015We introduce geometric flows on a compact almost complex manifold, with the aim to flow a nondegenerate two form to a symplectic two form. We discuss mainly two flows, $d^*d$-flow and $d^*d$-Ricci flow. Among others, we prove the uniqueness and short ... More

The Sasaki-Ricci flow and compact Sasakian manifolds of positive transverse holomorphic bisectional curvatureMar 30 2011We show that Perelman's W-functional can be generalized to Sasaki-Ricci flow. When the basic first Chern class is positive, we prove a uniform bound on the scalar curvature, the diameter and a uniform $C^1$ bound for the transverse Ricci potential along ... More

Local solution and extension to the Calabi flowApr 06 2009Apr 19 2009We consider the local solution to the Calabi flow for C^\alpha initial metric. We also prove that the Calabi flow on compact Kaehler surfaces can be extended once the metrics along the flow are bounded in L^\infty sense. This can be viewed as obtaining ... More

Remarks on the existence of bilaterally symmetric extremal Kähler metrics on $\mathbb{CP}^2\sharp 2\bar{\mathbb{CP}^2}$May 28 2007Jun 07 2007In this short note we show that the existence of bilaterally symmetric extremal K\"ahler metrics on $\mathbb{CP}^2\sharp 2\bar{\mathbb{CP}^2}$.

Total positivity in the De Concini-Procesi compactificationOct 02 2003Mar 11 2004We study the nonnegative part \bar{G_{>0}} of the De Concini-Procesi compactification of a reductive algebraic group G, as defined by Lusztig. Using positivity properties of the canonical basis and parametrization of flag varieties, we will give an explicit ... More

Topological Conjugacy of Non-hyperbolic Linear FlowsMar 13 2017The topological equivalence classification for linear flows on $\mathbb{R}^n$ had been completely solved by Kuiper and independently Ladis in 1973. However, Ladis' proof was published in a Russian journal which isn't easily available, Kuiper's proof is ... More

Minimal length elements in conjugacy classes of extended affine Weyl groupApr 23 2010We study the minimal length elements in an integral conjugacy class of a classical extended affine Weyl group and we show that these elements are quite "special" in the sense of Geck and Pfeiffer \cite{GP93}. We also discuss some application on extended ... More

Spatial Filtering for Brain Computer Interfaces: A Comparison between the Common Spatial Pattern and Its VariantAug 08 2018The electroencephalogram (EEG) is the most popular form of input for brain computer interfaces (BCIs). However, it can be easily contaminated by various artifacts and noise, e.g., eye blink, muscle activities, powerline noise, etc. Therefore, the EEG ... More

GKM graphs for odd dimensional manifolds with torus actionsAug 15 2016Aug 22 2016Let torus $T$ act on a manifold $M$, if the equivariant cohomology $H^*_T(M)$ is a free module of $H^*_T(pt)$, then according to the Chang-Skjelbred Lemma, $H^*_T(M)$ can be determined by the $1$-skeleton $M_1$ consisting of fixed points and $1$-dimensional ... More

Lauricella hypergeometric series over finite fieldsOct 12 2016In this paper we introduce a finite field analogue of the Lauricella hypergeometric series. An integral formula for the Lauricella hypergeometric series and its finite field analogue are deduced. Some transformation and reduction formulae and several ... More

Hecke algebras and $p$-adic groupsNov 04 2015Apr 14 2016This survey article, is written as an extended note and supplement of my lectures in the current developments in mathematics conference in 2015. We discuss some recent developments on the conjugacy classes of affine Weyl groups and $p$-adic groups, and ... More

Centers and Cocenters of $0$-Hecke algebrasFeb 07 2015Mar 31 2015In this paper, we give explicit descriptions of the centers and cocenters of $0$-Hecke algebras associated to finite Coxeter groups.

Geometric Progression-Free Sequences with Small GapsJan 16 2015Various authors, including McNew, Nathanson and O'Bryant, have recently studied the maximal asymptotic density of a geometric progression free sequence of positive integers. In this paper we prove the existence of geometric progression free sequences ... More

GKM theory, characteristic classes and the equivariant cohomology ring of the real GrassmannianSep 20 2016We use GKM theory to understand equivariant cohomology of real Grassmannian and oriented Grassmannian, then confirm Casian\&Kodama's conjecture on the Borel description which says the ring generators are equivariant Pontryagin classes, Euler classes in ... More

Existence, Lifespan and Transfer Rate of Ricci Flows on Manifolds with Small Ricci CurvatureApr 27 2016We show that in dimension 4 and above, the lifespan of Ricci flows depends on the relative smallness of the Ricci curvature compared to the Riemann curvature on the initial manifold. We can generalize this lifespan estimate to the local Ricci flow, using ... More

Uncertainty of data obtained in SRF cavity vertical testOct 15 2013Vertical test is a commonly used experimental method to qualify Superconducting Radio Frequency (SRF) cavities. Taking the experiences at Jefferson Lab (JLab) in US for example, over thousand of vertical tests have been performed on over 500 different ... More

Existence and applications of Ricci flows via pseudolocalityOct 06 2016We prove the short-time existence of Ricci flows on complete manifolds with scalar curvature bounded below uniformly, Ricci curvature bounded below by a negative quadratic function, and with almost Euclidean isoperimetric inequality holds locally. In ... More

Understanding spin parities of $P_c(4450)$ and $Y(4274)$ in hadronic molecular state pictureJul 12 2016Sep 05 2016The hidden-charmed pentaquark $P_c(4450)$ and the charmonium-like state $Y(4274)$ are investigated as a $\bar{D}^*\Sigma_c$ and a $D_s\bar{D}_{s0}(2317)$ molecular state, respectively. The spin parities of these two states can not be well understood if ... More

$\bar{D}Σ^*_c$ and $\bar{D}^*Σ_c$ interactions and LHCb pentaquarksNov 22 2016Recently, LHCb collaboration reported the observation of two hidden-charmed resonances $P_c(4380)$ and $P_c(4450)$ consistent with hidden-charmed pentaquarks. We perform a dynamical investigation about the $\bar{D}\Sigma_c^*(2520)$ and $\bar{D}^*\Sigma_c(2455)$ ... More

First Observation of Exclusive chi_cJ Decays to Two Charged and Two Neutral HadronsJun 06 2008We study exclusive chi_c0, chi_c1 and chi_c2 decays to four-hadron final states involving two charged and two neutral mesons: pi^+pi^-pi^0pi^0, K^+K^-pi^0pi^0, pppi^0pi^0, K^+K^-etapi^0, and K^+-pi^-+K^0pi^0o. The chi_c states are produced in radiative ... More