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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

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

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

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

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

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

Universal chosen-ciphertext attack for a family of image encryption schemesMar 28 2019During the past decades, there is a great popularity employing nonlinear dynamics and permutation-substitution architecture for image encryption. There are three primary procedures in such encryption schemes, the key schedule module for producing encryption ... More

Wiener-Hopf factorization for time-inhomogeneous Markov chains and its applicationJan 17 2018Feb 09 2018In this paper we derive the Wiener-Hopf factorization for a finite-state time-inhomogeneous Markov chain. To the best of our knowledge, this study is the first attempt to investigate the Wiener-Hopf factorization for time-inhomogeneous Markov chains. ... 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

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

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

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

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

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

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

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

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

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

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

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

Transfer Learning for Brain-Computer Interfaces: A Euclidean Space Data Alignment ApproachAug 08 2018Apr 02 2019Objective: This paper targets a major challenge in developing practical EEG-based brain-computer interfaces (BCIs): how to cope with individual differences so that better learning performance can be obtained for a new subject, with minimum or even no ... 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

Modeling and Robust Attitude Controller Design for a Small Size HelicopterDec 20 2018This paper addresses the design and application controller for a small-size unmanned aerial vehicle (UAV). In this work, the main objective is to study the modeling and attitude controller design for a small size helicopter. Based on a non-simplified ... 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

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 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

Study of $P_c(4457)$, $P_c(4440)$, and $P_c(4312)$ in a quasipotential Bethe-Salpeter equation approachMar 28 2019Very recently, the LHCb Collaboration reported their new results about the pentaquarks at charmed energy region. Based on the new experimental results, we recalculate the molecular states composed of a $\Sigma_c^{(*)}$ baryon and a $\bar{D}^{(*)}$ meson. ... 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

Study of $P_c(4457)$, $P_c(4440)$, and $P_c(4312)$ in a quasipotential Bethe-Salpeter equation approachMar 28 2019Apr 28 2019Very recently, the LHCb Collaboration reported their new results about the pentaquarks at charm energy region. Based on the new experimental results, we recalculate the molecular states composed of a $\Sigma_c^{(*)}$ baryon and a $\bar{D}^{(*)}$ meson ... 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

An event mixing method with invariant-mass/energy hierarchy correspondence cut for Bose-Einstein correlations in $ππX$ systemOct 27 2018A new event mixing constraint, namely invariant-mass/energy hierarchy correspondence (IMEHC) cut, is introduced for the low-multiplicity event mixing technique for the purpose of measuring Bose-Einstein correlations (BEC) in exclusive reactions with $\pi ... More

Bulk eigenvalue fluctuations of sparse random matricesApr 15 2019We consider a class of sparse random matrices, which includes the adjacency matrix of Erd\H{o}s-R\'enyi graphs $\mathcal G(N,p)$ for $p \in [N^{\varepsilon-1},N^{-\varepsilon}]$. We identify the joint limiting distributions of the eigenvalues away from ... More

A new formula for $ζ(s)$Nov 22 2018Mar 12 2019In this paper, by introducing a new operation in the vector space of analytic functions, the author presents a method for derivating the well-known formulas: $\zeta(1-k)=-\frac{B_k}{k}$ and $\zeta(1-n,a)=-\frac{B_n(a)}{n}$ , where $\zeta$, $\zeta(1-n,a)$ ... More

Geometric and homological properties of affine Deligne-Lusztig varietiesJan 24 2012Sep 10 2013This paper studies affine Deligne-Lusztig varieties $X_{\tw}(b)$ in the affine flag variety of a quasi-split tamely ramified group. We describe the geometric structure of $X_{\tw}(b)$ for a minimal length element $\tw$ in the conjugacy class of an extended ... More

Spectra of elliptic potentials and supersymmetric gauge theoriesApr 03 2019We study a relation between asymptotic spectra of the quantum mechanics problem with a four component elliptic function potential, the Darboux-Treibich-Verdier (DTV) potential, and the Omega background deformed N=2 supersymmetric SU(2) QCD models with ... More

A Generic Regression Framework for Pose Recognition on Color and Depth ImagesSep 23 2017Cascaded regression method is a fast and accurate method on finding 2D pose of objects in RGB images. It is able to find the accurate pose of objects in an image by a great number of corrections on the good initial guess of the pose of objects. This paper ... More

Discretized sum-product estimates in matrix algebrasNov 29 2016Oct 17 2017We generalize Bourgain's discretized sum-product theorem to matrix algebras.

Partially Ordered Sheaves on a Locale. I (II)Jul 09 2015In this paper, we investigate the order algebraic structure in the category of sheaves on a given locale $X$. Since every localic topos has a generating set formed by its subterminal objects, we define a "point" of a partially ordered sheaf to be a morphism ... More

Isometry group of Sasaki-Einstein metricMar 12 2013We prove that the identity component of the holomorphic isometry group of a Sasaki-Einstein metric is the identity component of a maximal compact subgroup of its automorphism group.

On the space of Kahler potentialsAug 05 2012We consider the geodesic equation for the generalized Kahler potential with only mixed second derivatives bounded. We show that given such two generalized Kahler potentials, there is a unique geodesic segment such that for each point on the geodesic, ... More

$\cF$-functional and geodesic stabilityAug 05 2012Jun 06 2016We consider canonical metrics on Fano manifolds. First we introduce a norm-type functional on Fano manifolds, which has Kahler-Einstein or Kahler-Ricci soliton as its critical point and the Kahler-Ricci flow can be viewed as its (reduced) gradient flow. ... More

A new treatment for some periodic Schrödinger operators II: the wave functionAug 18 2016Apr 05 2019Following the approach of our previous paper we continue to study the asymptotic solution of periodic Schr\"{o}dinger operators. Using the eigenvalues obtained earlier the corresponding asymptotic wave functions are derived. This gives further evidence ... More

A new treatment for some periodic Schrödinger operators I: the eigenvalueDec 21 2014Apr 05 2019We study the problem of how the Floquet property manifests for periodic Schr\"{o}dinger operators which are known to have multiple of asymptotic spectral solutions. The main conclusions are made for elliptic potentials, we demonstrate that for each period ... More

On the error rate of conditional quasi-Monte Carlo for discontinuous functionsAug 31 2017Jun 06 2018This paper studies the rate of convergence for conditional quasi-Monte Carlo (QMC), which is a counterpart of conditional Monte Carlo. We focus on discontinuous integrands defined on the whole of $R^d$, which can be unbounded. Under suitable conditions, ... More

Mining Top-k Approximate Frequent PatternsMar 17 2005Frequent pattern (itemset) mining in transactional databases is one of the most well-studied problems in data mining. One obstacle that limits the practical usage of frequent pattern mining is the extremely large number of patterns generated. Such a large ... More

Approximation Algorithms for K-Modes ClusteringMar 30 2006In this paper, we study clustering with respect to the k-modes objective function, a natural formulation of clustering for categorical data. One of the main contributions of this paper is to establish the connection between k-modes and k-median, i.e., ... More

Dynamic density and spin responses of a superfluid Fermi gas in the BCS-BEC crossover: Path integral formulation and pair fluctuation theoryFeb 21 2016Aug 07 2016We present a standard field theoretical derivation of the dynamic density and spin linear response functions of a dilute superfluid Fermi gas in the BCS-BEC crossover in both three and two dimensions. The derivation of the response functions is based ... More

Finite range and upper branch effects on itinerant ferromagnetism in repulsive Fermi gases: Bethe-Goldstone ladder resummation approachMay 14 2014Oct 02 2014We investigate the ferromagnetic transition in repulsive Fermi gases at zero temperature with upper branch and effective range effects. Based on a general effective Lagrangian that reproduces precisely the two-body $s$-wave scattering phase shift, we ... More

Paramagnetism and Magnetic Singularity in Exotic Superconductivity Made Simple: Their Origin and Possible RealizationJun 13 2005Jun 23 2005This paper makes no sense. It only increases the entropy of our universe. It has been withdrawn by the author.

Mesoscopic linear statistics of Wigner matrices of mixed symmetry classMar 28 2018Mar 10 2019We prove a central limit theorem for the mesoscopic linear statistics of $N\times N$ Wigner matrices $H$ satisfying $\mathbb{E}|H_{ij}|^2=1/N$ and $\mathbb{E} H_{ij}^2= \sigma /N$, where $\sigma \in [-1,1]$. We show that on all mesoscopic scales $\eta$ ... More

Bulk eigenvalue fluctuations of sparse random matricesApr 15 2019Apr 25 2019We consider a class of sparse random matrices, which includes the adjacency matrix of Erd\H{o}s-R\'enyi graphs $\mathcal G(N,p)$ for $p \in [N^{\varepsilon-1},N^{-\varepsilon}]$. We identify the joint limiting distributions of the eigenvalues away from ... More

Ground state solution of fractional Schrödinger equations with a general nonlinearityJun 22 2017Aug 23 2017In this paper, we study the following fractional Schr\"odinger equation: \[ \left\{\begin{gathered} {(- \Delta)^s}u + mu = f(u){\text{in}}{\mathbb{R}^N}, \hfill u \in {H^s}({\mathbb{R}^N}),{\text{}}u > 0{\text{on}}{\mathbb{R}^N}, \hfill \\ \end{gathered} ... More

Well-posedness of boundary value problems for a class of second order degenerate elliptic equationsMay 02 2005Feb 28 2006In this paper, we study the well-posedness of boundary value problems for a special class of degenerate elliptic equations coming from geometry. Such problems is intimately tied to rigidity problem arising in infinitesimal isometric deformation, The characteristic ... More

A New Framework for Ranking Vulnerabilities in the CloudsNov 23 2016Dec 06 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

The Expansions of the Nahm Pole Solutions to the Kapustin-Witten EquationsAug 12 2018For a 3-manifold $X$ and compact simple Lie group $G$, we study the expansions of polyhomogeneous Nahm pole solutions to the Kapustin-Witten equations over $X\times (0,+\infty)$. Let $y$ be the coordinate of $(0,+\infty)$, we prove that the sub-leading ... More

Distance comparison principle and Grayson type theorem in the three dimensional curve shortening flowSep 24 2012In this paper, we use the distance comparison principle, first been developed by G. Huisken, to study the spatial curve shortening flow. We have got the result that if the initial curve is the helix, then the local minimum of the ratio of the extrinsic ... More

Torsions of integral homology and cohomology of real GrassmanniansSep 17 2017According to a result of Ehresmann, the torsions of integral homology of real Grassmannian are all of order $2$. In this note, We compute the $\mathbb{Z}_2$-dimensions of torsions in the integral homology and cohomology of real Grassmannian.

Multiple scattering theory for polycrystalline materials with strong grain anisotropy: theoretical fundamentals and applicationsOct 10 2017This work is a natural extension of the authors previous work, Multiple scattering theory for heterogeneous elastic continua with strong property fluctuation, theoretical fundamentals and applications, which established the foundation for developing multiple ... More

Orbits on Lagrangian GrassmanianAug 12 2006Sep 09 2015The purpose of this note is to give a classification of the orbital structure of certain reductive group actions on the Lagrangian Grassmanian. The groups under consideration are $Sp \times Sp$ and $GL$. The classification of $Sp \times Sp$ orbits is ... More

Gan-Gross-Prasad Conjecture for U(p,q)Aug 09 2015Feb 03 2017In this paper, we give a proof of the Gan-Gross-Prasad conjecture for the discrete series of U(p,q). Given a discrete series representation $D(\lambda)$ in terms of the Harish-Chandra parameter, the restriction of $D(\lambda)$ to U(p-1,q) contains $D(\mu)$ ... More

A Generalization of Correspondence Theorem and Its Application to Branching LawsDec 03 2013Dec 06 2013We begin with recalling the correspond theorem of induced modules and global sections of vector bundles. After that, we give a generalization of this theorem. Finally, we apply the result to branching laws, and give some concrete examples.

Eigenvectors and ReconstructionJul 05 2006In this paper, I study the simple eigenvectors of two hypomorphic matrices using linear algebra. I give new proofs of results of Godsil and MaKay.

The G-convex Functions Based on the Nonlinear Expectations Defined by G-BSDEsNov 25 2015In this paper, generalizing the definition of G-convex functions defined by Peng [9] during the construction of G-expectations and related properties, we define a group of G-convex functions based on the Backward Stochastic Differential Equations driven ... More

Coupled Spin and Pseudo-magnetic Field in Graphene NanoribbonsMay 02 2013May 16 2013Pseudo-magnetic field becomes an experimental reality after the observation of zero-field Landau level-like quantization in strained graphene, but it is not expected that the time-reversal symmetric pseudo-magnetic fields will have any effect on the spin ... 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

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

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

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

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

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

Educational game design: game elements for promoting engagementSep 27 2017Engagement in educational games, a recently popular academic topic, has been shown to increase learning performance, as well as a number of attitudinal factors, such as intrinsic interest and motivation. However, there is a lack of research on how games ... More

Fast and Rigorous DC Solution in Finite Element Method for Integrated Circuit AnalysisApr 24 2015Large scale circuit simulation, such as power delivery network analysis, has become increasingly challenge in the VLSI design verification flow. Power delivery network can be simulated by both SPICE-type circuit-based model and eletromagnetics-based model ... More

A new understanding of $ζ(k)$Dec 16 2018Mar 12 2019In this paper, by introducing a new operation in the vector space of Laurent series, the author derived explicit series for the values of $\zeta$-funtion at positive integers, where $\zeta$ denotes the Riemann zeta function. The values of $\zeta(k),\ ... More

Global instability of long separation bubbles in a laminar boundary layerDec 17 2018This work aims to numerically investigate the linear global instability of long separation bubbles origin from the changes in the adverse pressure gradient inside a laminar flat plate boundary layer disturbed by placing a bluff body with small clearances. ... 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}.

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.

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.

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 $\lambda>(4n+3)/5$.

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

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

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

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

Hypersurfaces with null higher order anisotropic mean curvatureDec 09 2011Jun 20 2013Given a positive function $F$ on $\mathbb S^n$ which satisfies a convexity condition, for $1\leq r\leq n$, we define for hypersurfaces in $\mathbb{R}^{n+1}$ the $r$-th anisotropic mean curvature function $H_{r; F}$, a generalization of the usual $r$-th ... More

Spin-Current Shot Noise in Mesoscopic ConductorsJul 17 2006In this paper, we present a method to investigate the spin-current shot noise in mesoscopic conductors, by using scattering matrix theory and Green's function technique. We first derive a general expression for the spin-current noise at zero-frequency ... 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.

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.