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PRIF: A Privacy-Preserving Interest-Based Forwarding Scheme for Social Internet of VehiclesApr 06 2018Recent advances in Socially Aware Networks (SANs) have allowed its use in many domains, out of which social Internet of vehicles (SIOV) is of prime importance. SANs can provide a promising routing and forwarding paradigm for SIOV by using interest-based ... More

LPTD: Achieving Lightweight and Privacy-Preserving Truth Discovery in CIoTApr 05 2018In recent years, cognitive Internet of Things (CIoT) has received considerable attention because it can extract valuable information from various Internet of Things (IoT) devices. In CIoT, truth discovery plays an important role in identifying truthful ... More

Privacy-Preserving DDoS Attack Detection Using Cross-Domain Traffic in Software Defined NetworksSep 19 2018Existing distributed denial-of-service attack detection in software defined networks (SDNs) typically perform detection in a single domain. In reality, abnormal traffic usually affects multiple network domains. Thus, a cross-domain attack detection has ... More

Secure Phrase Search for Intelligent Processing of Encrypted Data in Cloud-Based IoTSep 21 2018Phrase search allows retrieval of documents containing an exact phrase, which plays an important role in many machine learning applications for cloud-based IoT, such as intelligent medical data analytics. In order to protect sensitive information from ... More

A Privacy-Preserving Traffic Monitoring Scheme via Vehicular CrowdsourcingFeb 12 2019The explosive growth of vehicle amount has given rise to a series of traffic problems, such as traffic congestion, road safety, and fuel waste. Collecting vehicles' speed information is an effective way to monitor the traffic condition and avoid vehicles ... More

Privacy Leakage in Smart Homes and Its Mitigation: IFTTT as a Case StudyFeb 08 2019The combination of smart home platforms and automation apps introduces much convenience to smart home users. However, this also brings the potential for privacy leakage. If a smart home platform is permitted to collect all the events of a user day and ... More

When Homomorphic Cryptosystem Meets Differential Privacy: Training Machine Learning Classifier with Privacy ProtectionDec 06 2018Machine learning (ML) classifiers are invaluable building blocks that have been used in many fields. High quality training dataset collected from multiple data providers is essential to train accurate classifiers. However, it raises concern about data ... More

Content-Based Multi-Source Encrypted Image Retrieval in Clouds with Privacy PreservationSep 22 2018Content-based image retrieval (CBIR) is one of the fundamental image retrieval primitives. Its applications can be found in various areas, such as art collections and medical diagnoses. With an increasing prevalence of cloud computing paradigm, image ... More

Cloud-Based Approximate Constrained Shortest Distance Queries Over Encrypted Graphs With Privacy ProtectionSep 21 2018Constrained shortest distance (CSD) querying is one of the fundamental graph query primitives, which finds the shortest distance from an origin to a destination in a graph with a constraint that the total cost does not exceed a given threshold. CSD querying ... More

Toward Practical Differential Privacy in Smart Grid with Capacity-Limited Rechargeable BatteriesJul 10 2015Jul 22 2015The technology of differential privacy, adding a noise drawn from the Laplace distribution, successfully overcomes a difficulty of keeping both the privacy of individual data and the utility of the statistical result simultaneously. Therefore, it is prevalent ... More

ESAS: An Efficient Semantic and Authorized Search Scheme over Encrypted Outsourced DataOct 25 2018Nowadays, a large amount of user privacy-sensitive data is outsourced to the cloud server in ciphertext, which is provided by the data owners and can be accessed by authorized data users. When accessing data, the user should be assigned with the access ... More

Towards Delay-Tolerant Flexible Data Access Control for Smart Grid with Renewable Energy ResourcesOct 25 2018In the Smart Grid with Renewable Energy Resources (RERs), the Residential Units (RUs) with Distributed Energy Resources (DERs) are considered to be both power consumers and suppliers. Specifically, RUs with excessive renewable generations can trade with ... More

EPDA: Enhancing Privacy-Preserving Data Authentication for Mobile Crowd SensingNov 09 2018As a popular application, mobile crowd sensing systems aim at providing more convenient service via the swarm intelligence. With the popularity of sensor-embedded smart phones and intelligent wearable devices, mobile crowd sensing is becoming an efficient ... More

IriTrack: Liveness Detection Using Irises Tracking for Preventing Face Spoofing AttacksOct 08 2018Face liveness detection has become a widely used technique with a growing importance in various authentication scenarios to withstand spoofing attacks. Existing methods that perform liveness detection generally focus on designing intelligent classifiers ... More

Achieving Trust-Based and Privacy-Preserving Customer Selection in Ubiquitous ComputingFeb 12 2019The recent proliferation of smart devices has given rise to ubiquitous computing, an emerging computing paradigm which allows anytime & anywhere computing possible. In such a ubiquitous computing environment, customers release different computing or sensing ... More

PPLS: A Privacy-Preserving Location-Sharing Scheme in Vehicular Social NetworksApr 06 2018Recent advances in Socially Aware Networks (SANs) have allowed its use in many domains, out of which social Internet of vehicles (SIOV) is of prime importance. SANs can provide a promising routing and forwarding paradigm for SIOV by using interest-based ... More

SDN Controllers: Benchmarking & Performance EvaluationFeb 12 2019Software Defined Networks offer flexible and intelligent network operations by splitting a traditional network into a centralized control plane and a programmable data plane. The intelligent control plane is responsible for providing flow paths to switches ... More

Lattice approximation to the dynamical $Φ_3^4$ modelAug 23 2015We study the lattice approximations to the dynamical $\Phi^4_3$ model by paracontrolled distributions proposed in [GIP13]. We prove that the solutions to the lattice systems converge to the solution to the dynamical $\Phi_3^4$ model in probability, locally ... More

Approximating three-dimensional Navier-Stokes equations driven by space-time white noiseSep 17 2014In this paper we study approximations to 3D Navier-Stokes (NS) equation driven by space-time white noise by paracontrolled distribution proposed in [GIP13]. A solution theory for this equation has been developed recently in [ZZ14] based on regularity ... More

A Wong-Zakai theorem for $Φ^4_3$ modelApr 16 2015We prove a version of the Wong-Zakai theorem for the dynamical $\Phi_3^4$ model driven by space-time white noise on $\mathbb{T}^3$. For the $\Phi^4_3$ model it is proved in [Hai14] that a renormalisation has to be performed in order to define the nonlinear ... More

Random attractor associated with the quasi-geostrophic equationMar 24 2013We study the long time behavior of the solutions to the 2D stochastic quasi-geostrophic equation on $\mathbb{T}^2$ driven by additive noise and real linear multiplicative noise in the subcritical case (i.e. $\alpha>1/2$) by proving the existence of a ... More

Dimension reduction-based significance testing in nonparametric regressionOct 13 2015A dimension reduction-based adaptive-to-model test is proposed for significance of a subset of covariates in the context of a nonparametric regression model. Unlike existing local smoothing significance tests, the new test behaves like a local smoothing ... More

Computing log-likelihood and its derivatives for restricted maximum likelihood methodsAug 25 2016Recent large scale genome wide association analysis involves large scale linear mixed models. Quantifying (co)-variance parameters in the mixed models with a restricted maximum likelihood method results in a score function which is the first derivative ... More

Eigenvalue resolution of self-adjoint matricesApr 28 2015Oct 10 2016Resolution of a compact group action in the sense described by Albin and Melrose is applied to the conjugation action by the unitary group on self-adjoint matrices. It is shown that the eigenvalues are smooth on the resolved space and that the trivial ... More

A simple proof of the strong integrality for full colored HOMFLYPT invariantsMar 13 2016By using the HOMFLY skein theory. We prove a strong integrality theorem for the reduced colored HOMFLYPT invariants defined by a basis in the full HOMFLY skein of the annulus.

The power operation structure on Morava E-theory of height 2 at the prime 3Oct 13 2012We give explicit calculations of the algebraic theory of power operations for a specific Morava E-theory spectrum and its K(1)-localization. These power operations arise from the universal degree-3 isogeny of elliptic curves associated to the E-theory. ... More

"Charged" Particle's Tunneling from Rotating Black HolesJan 24 2011The behavior of a scalar field theory near the event horizon in a rotating black hole background can be effectively described by a two dimensional field theory in a gauge field background. Based on this fact, we proposal that the quantum tunneling from ... More

Davies type estimate and the heat kernel bound under the Ricci flowNov 23 2013Feb 08 2014We prove a Davies type double integral estimate for the heat kernel $H(y,t;x,l)$ under the Ricci flow. As a result, we give an affirmative answer to a question proposed by Chow etc.. Moreover, we apply the Davies type estimate to provide a new proof of ... More

Accreting Circumplanetary Disks: Observational SignaturesAug 27 2014Oct 06 2014I calculate the spectral energy distributions (SEDs) of accreting circumplanetary disks using atmospheric radiative transfer models. Circumplanetary disks only accreting at $10^{-10} M_{\odot} yr^{-1}$ around a 1 M$_{J}$ planet can be brighter than the ... More

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

Analysis of a multigrid preconditioner for Crouzeix-Raviart discretization of elliptic PDE with jump coefficientOct 24 2011In this paper, we present a multigrid $V$-cycle preconditioner for the linear system arising from piecewise linear nonconforming Crouzeix-Raviart discretization of second order elliptic problems with jump coefficients. The preconditioner uses standard ... More

Loss Rate Estimators and the Properties for the Tree TopologyAug 05 2015A large number of explicit estimators are proposed in this paper for loss rate estimation in a network of the tree topology. All of the estimators are proved to be unbiased and consistent instead of asymptotic unbiased as that obtained in [1] for a specific ... More

Explicit Estimators for Loss TomographyMay 29 2012Aug 13 2013Full likelihood has been widely used in loss tomography because most believe it can produce accurate estimates although the full likelihood estimators proposed so far are complex in structure and expensive in execution. We in this paper advocate a different ... More

A new approach to parton recombination in a QCD evolution equationSep 15 1998Parton recombination is reconsidered in perturbation theory without using the AGK cutting rules in the leading order of the recombination. We use time-ordered perturbation theory to sum the cut diagrams, which are neglected in the GLR evolution equation. ... More

Analysis on Metric Space QJul 21 2006Jul 26 2006In this paper, we show that the metric space Q is a positively-curved space (PC-space) in the sense of Alexandrov. We also discuss some issues like metric tangent cone and exponential map of Q. Then we give a stratification of this metric space according ... More

Translation invariance of Fock spacesJan 21 2011We show that there is only one Hilbert space of entire functions that is invariant under the action of naturally defined weighted translations.

Determining All Maximum Uniquely Restricted Matching in Bipartite GraphsSep 28 2010The approach mapping from a matching of bipartite graphs to digraphs has been successfully used for forcing set problem, in this paper, it is extended to uniquely restricted matching problem. We show to determine a uniquely restricted matching in a bipartite ... More

Note on "Hydrodynamic Phase Locking of Swimming Microorganisms"Aug 29 2009We make remarks on Elfring and Lauga's [{\it Phys. Rev. Lett.} {\bf 103}, 088101 (2009)] paper. The energy dissipation or viscous dissipation plays an important role in the phase-locked state.

Beam Charge Measurement for the g2p/GEp experimentsJun 08 2016Jun 26 2016The g2p/GEp experiments used a solid NH3 polarized target, where the polarization of the target is sensitive to temperature and radiation. The beam current was limited to 5-100 nA during the experiment to avoid too much depolarization of target (The typical ... More

Solvability via viscosity solutions for a model of phase transitions driven by configurational forcesDec 29 2009Feb 04 2011In the present article, we are interested in an initial boundary value problem for a coupled system of partial differential equations arising in martensitic phase transition theory of elastically deformable solid materials, e.g., steel. This model was ... More

Regularity of solutions to a model for solid-solid phase transitions driven by configurational forcesFeb 04 2011In a previous work, we prove the existence of weak solutions to an initial-boundary value problem, with $H^1(\Omega)$ initial data, for a system of partial differential equations, which consists of the equations of linear elasticity and a nonlinear, degenerate ... More

An improved axiomatic definition of information granulationAug 27 2009To capture the uncertainty of information or knowledge in information systems, various information granulations, also known as knowledge granulations, have been proposed. Recently, several axiomatic definitions of information granulation have been introduced. ... More

Development in the Scattering Matrix Theory: From Spin-Orbit-Coupling Affected Shot Noise to Quantum PumpingNov 16 2010The review chapter starts by a pedagogical introduction to the general concept of the scattering theory: from the fundamental wave-function picture to the second-quantization language, with the aim to clear possible ambiguity in conventional textbooks. ... More

Mutually unbiased bases as minimal Clifford covariant 2-designsMay 05 2015Jul 06 2015Mutually unbiased bases (MUB) are interesting for various reasons. The most attractive example of (a complete set of) MUB is the one constructed by Ivanovi\'c as well as Wootters and Fields, which is referred to as the canonical MUB. Nevertheless, little ... More

SIC~POVMs and Clifford groups in prime dimensionsMar 18 2010Jun 30 2010We show that in prime dimensions not equal to three, each group covariant symmetric informationally complete positive operator valued measure (SIC~POVM) is covariant with respect to a unique Heisenberg--Weyl (HW) group. Moreover, the symmetry group of ... More

Tomographic and Lie algebraic significance of generalized symmetric informationally complete measurementsAug 04 2014Generalized symmetric informationally complete (SIC) measurements are SIC measurements that are not necessarily rank one. They are interesting originally because of their connection with rank-one SICs. Here we reveal several merits of generalized SICs ... More

Projective dimension and regularity of path ideals of cyclesOct 11 2016In this paper, we give a formula to compute all the top degree graded Betti numbers of the path ideals of a cycle. As a consequence we can give a formula to compute its projective dimension and regularity.

Process-Level Large Deviations for Nonlinear Hawkes Point ProcessesAug 11 2011Oct 14 2014In this paper, we prove a process-level, also known as level-3 large deviation principle for a very general class of simple point processes, i.e. nonlinear Hawkes process, with a rate function given by the process-level entropy, which has an explicit ... More

Max-Margin Nonparametric Latent Feature Models for Link PredictionJun 18 2012We present a max-margin nonparametric latent feature model, which unites the ideas of max-margin learning and Bayesian nonparametrics to discover discriminative latent features for link prediction and automatically infer the unknown latent social dimension. ... More

Interior nodal sets of Steklov eigenfunctions on surfacesJul 02 2015Oct 20 2015We investigate the interior nodal sets $\mathcal{N}_\lambda$ of Steklov eigenfunctions on connected and compact surfaces with boundary. The optimal vanishing order of Steklov eigenfunctions is shown be $C\lambda$. The singular sets $\mathcal{S}_\lambda$ ... More

Doubling property and vanishing order of Steklov eigenfunctionsJul 06 2014The paper is concerned with the doubling estimates and vanishing order of the Steklov eigenfunction on the boundary of a smooth boundary domain $\mathbb R^n$. The eigenfunction is given by a Dirichlet-to-Neumann map. We improve the doubling property shown ... More

The Hecke algebra action on Morava E-theory of height 2May 23 2015Given a one-dimensional formal group of height 2, let E be the Morava E-theory spectrum associated to its universal deformation over the Lubin-Tate ring. By computing with moduli spaces of elliptic curves, we give an explicitation for an algebra of Hecke ... More

Coherence scale of coupled Anderson impuritiesMay 27 2010Nov 30 2010For two coupled Anderson impurities, two energy scales are present to characterize the evolution from local moment state of the impurities to either of the inter-impurity singlet or the Kondo singlet ground states. The high energy scale is found to deviate ... More

Spin-lattice models: inhomogeneity and diffusionMar 31 2003Apr 27 2003In spin-lattice models with order parameter conserved, we generalize the idea of spin diffusion incorporating a variety factors as possible driving forces, including the external field and the temperature. The Kawasaki dynamics in the Gaussian model and ... More

Introducing Small-World Network Effect to Critical DynamicsDec 21 2002We analytically investigate the kinetic Gaussian model and the one-dimensional kinetic Ising model on two typical small-world networks (SWN), the adding-type and the rewiring-type. The general approaches and some basic equations are systematically formulated. ... More

Three-dimensional Navier-Stokes equations driven by space-time white noiseMay 31 2014Jun 10 2015In this paper we study 3D Navier-Stokes (NS) equation driven by space-time white noise by using regularity structure theory introduced in [Hai14] and paracontrolled distribution proposed in [GIP13]. We obtain local existence and uniqueness of solutions ... More

Circular flow number of highly edge connected signed graphsNov 14 2012This paper proves that for any positive integer $k$, every essentially $(2k+1)$-unbalanced $(12k-1)$-edge connected signed graph has circular flow number at most $2+\frac 1k$.

The higher sharpApr 02 2016Aug 02 2016We establish the descriptive set theoretic representation of the mouse $M_n^{#}$, which is called $0^{(n+1)#}$.

A Probability Method to Prove Combinatorial IdentitiesOct 30 2009A probability method is provided to prove three classes of combinatorial identities. The method is extremely simple, only one step after the proper probability setup.

On Layered Erasure Interference Channels without CSI at TransmittersJan 24 2016This paper studies a layered erasure model for two-user interference channels, which can be viewed as a simplified version of Gaussian fading interference channel. It is assumed that channel state information~(CSI) is only available at receivers but not ... More

Entity-oriented spatial coding and discrete topological spatial relationsJan 15 2016Based on a newly proposed spatial data model - spatial chromatic model (SCM), we developed a spatial coding scheme, called full-coded ordinary arranged chromatic diagram (full-OACD). Full-OACD is a type of spatial tessellation, where space is partitioned ... More

Riemann Zeta Function Expressed as the Difference of Two Symmetrized Factorials Whose Zeros All Have Real Part of 1/2Aug 06 2012Aug 20 2012In this paper, some new results are reported for the study of Riemann zeta function $\zeta(s)$ in the critical strip $0<Re(s)<1$, such as $\zeta(s)$ expressed in a generalized Euler product only involving prime numbers. Particularly, some new absolutely ... More

Statistical Properties of Loss Rate Estimators in Tree TopologyAug 06 2015Mar 25 2016Three types of explicit estimators are proposed here to estimate the loss rates of the links in a network of the tree topology. All of them are derived by the maximum likelihood principle and proved to be either asymptotic unbiased or unbiased. In addition, ... More

A Theorem on Frequency Function for Multiple-Valued Dirichlet Minimizing FunctionsJul 23 2006Jul 26 2006This paper discusses the frequency function of multiple-valued Dirichlet minimizing functions in the special case when the domain and range are both two dimensional. It shows that the frequency function must be of value k/2 for some nonnegative integer ... More

Kan replacement of simplicial manifoldsDec 22 2008Sep 03 2009We establish a functor $Kan$ from local Kan simplicial manifolds to weak Kan simplicial manifolds. It gives a solution to the problem of extending local Lie groupoids to Lie 2-groupoids.

A general detector testing system using cosmic raysAug 27 2013A cosmic ray hodoscope with two-dimensional spacial sensitivity and good time resolution has been developed. The system is designed to use the cosmic muons as probes to test the performances of charged particle sensitive detectors. This paper will present ... More

Optimal control of risk process in a regime-switching environmentSep 16 2010Dec 10 2010This paper is concerned with cost optimization of an insurance company. The surplus of the insurance company is modeled by a controlled regime switching diffusion, where the regime switching mechanism provides the fluctuations of the random environment. ... More

BSDE and generalized Dirichlet forms: the finite dimensional caseJan 16 2012We consider the following quasi-linear parabolic system of backward partial differential equations: $(\partial_t+L)u+f(\cdot,\cdot,u, \nabla u\sigma)=0$ on $[0,T]\times \mathbb{R}^d\qquad u_T=\phi$, where $L$ is a possibly degenerate second order differential ... More

High-jet relations of the heat kernel embedding map and applicationsAug 02 2013Aug 14 2013For any compact Riemannian manifold $(M,g)$ and its heat kernel embedding map $psi_t$ from M into $l^2$ constructed in [BBG], we study the higher derivatives of $psi_t$ with respect to an orthonormal basis at $x$ on $M$. As the heat flow time $t$ goes ... More

Moduli Spaces of $J$-holomorphic Curves with General Jet ConstraintsNov 09 2009In this paper, we prove that the tagent map of the holomorphic $k$- jet evaluation $j^k_{hol}$ from the mapping space to holomorphic $k$-jet bundle, when restricted on the universal moduli space of simple J-holomorphic curves with one marked point, is ... More

Lightface mice with finitely many Woodin cardinals from optimal determinacy hypothesesOct 07 2016The determinacy of lightface $\Delta^1_{2n+2}$ and boldface $\boldsymbol{\Pi}^1_{2n+1}$ sets implies the existence of an $(\omega, \omega_1)$-iterable $M_{2n+1}^{\#}$.

Super-symmetric informationally complete measurementsDec 02 2014Aug 23 2015Symmetric informationally complete measurements (SICs in short) are highly symmetric structures in the Hilbert space. They possess many nice properties which render them an ideal candidate for fiducial measurements. The symmetry of SICs is intimately ... More

Quantum state estimation with informationally overcomplete measurementsApr 14 2014Aug 05 2014We study informationally overcomplete measurements for quantum state estimation so as to clarify their tomographic significance as compared with minimal informationally complete measurements. We show that informationally overcomplete measurements can ... More

Colored HOMFLY polynomial via skein theoryJun 26 2012In this paper, we study the properties of the colored HOMFLY polynomials via HOMFLY skein theory. We prove some limit behaviors and symmetries of the colored HOMFLY polynomial predicted in some physicists' recent works.

Central Limit Theorem for Nonlinear Hawkes ProcessesApr 04 2012Oct 14 2014Hawkes process is a self-exciting point process with clustering effect whose intensity depends on its entire past history. It has wide applications in neuroscience, finance and many other fields. In this paper, we obtain a functional central limit theorem ... More

An integral representation for Besov and Lipschitz spacesJan 15 2011It is well known that functions in the analytic Besov space $B_1$ on the unit disk $\D$ admits an integral representation $$f(z)=\ind\frac{z-w}{1-z\bar w}\,d\mu(w),$$ where $\mu$ is a complex Borel measure with $|\mu|(\D)<\infty$. We generalize this result ... More

Affine Demazure modules and $T$-fixed point subschemes in the affine GrassmannianOct 27 2007Nov 20 2008Let $G$ be a simple algebraic group of type $A$ or $D$ defined over $\C$ and $T$ be a maximal torus of $G$. For a dominant coweight $\lambda$ of $G$, the $T$-fixed point subscheme $(\bar{Gr}_G^\lambda)^T$ of the Schubert variety $\bar{Gr}_G^\lambda$ in ... More

The viability property of jump diffusion processes on Riemannian manifoldsMay 18 2010In this note, we consider the necessary and sufficient condition for viability property of diffusion processes with jumps on closed submanifolds of $R^{m}$ with some concrete examples.

On the critical branching random walk II: Branching capacity and branching recurrenceDec 01 2016We continue our study of critical branching random walk and branching capacity. In this paper we introduce branching recurrence and branching transience and prove an analogous version of Wiener's Test.

Stable Cluster Core Detection in Correlated Hashtag GraphMar 02 2015Hashtags in twitter are used to track events, topics and activities. Correlated hashtag graph represents contextual relationships among these hashtags. Maximum clusters in the correlated hashtag graph can be contextually meaningful hashtag groups. In ... More

An upper bound for the probability of visiting a distant point by critical branching random walk in $\mathbb{Z}^4$Mar 01 2015Nov 27 2016In this paper, we study the probability of visiting a distant point $a\in \mathbb{Z}^4$ by critical branching random walk starting from the origin. We prove that this probability is bounded by $1/(|a|^2\log |a|)$ up to a constant.

Limit Theorems for a Cox-Ingersoll-Ross Process with Hawkes JumpsSep 22 2013Oct 14 2014In this paper, we propose a stochastic process, which is a Cox-Ingersoll-Ross process with Hawkes jumps. It can be seen as a generalization of the classical Cox-Ingersoll-Ross process and the classical Hawkes process with exponential exciting function. ... More

Group structures of elementary supersingular abelian varieties over finite fieldsAug 31 1998Let A be a supersingular abelian variety over a finite field k. We give an approximate description of the structure of the group A(k) of rational points of A over k in terms of the characteristic polynomial f of the Frobenius endomorphism of A relative ... More

Geometry and interior nodal sets of Steklov eigenfunctionsOct 25 2015We investigate the geometric properties of Steklov eigenfunctions in smooth manifolds. We derive the refined doubling estimates and Bernstein's inequalities. For the real analytic manifolds, we are able to obtain the sharp upper bound for the measure ... More

A Sharp Height Estimate for the Spacelike Constant Mean Curvature Graph in the Lorentz-Minkowski SpaceAug 11 2015May 30 2016In this paper, based on the local comparison principle in [12], we study the local behavior of the difference of two spacelike graphs in a neighborhood of a second contact point. Then we apply it to the constant mean curvature equation in 3-dimensional ... More

Dirichlet Problem of Quaternionic Monge-Ampère EquationsMar 13 2014Feb 11 2015In this paper, the author studies quaternionic Monge-Amp\`ere equations and obtains the existence and uniqueness of the solutions to the Dirichlet problem for such equations without any restriction on domains. Our paper not only answers to the open problem ... More

Optimal dividend control for a generalized risk model with investment incomes and debit interestFeb 21 2011Sep 18 2012This paper investigates dividend optimization of an insurance corporation under a more realistic model which takes into consideration refinancing or capital injections. The model follows the compound Poisson framework with credit interest for positive ... More

Electroweak results from the ATLAS and CMS experimentsSep 28 2015I summarize an extensive ATLAS and CMS electroweak physics program that involves a variety of single boson, diboson, triboson, and vector boson scattering measurements. The relevance of these studies to our understanding of the electroweak sector and ... More

On the critical branching random walk I: Branching capacity and visiting probabilityNov 30 2016We extend the theory of discrete capacity to critical branching random walk. We introduce branching capacity for any finite subset of $\Z^d, d\geq5$. Analogous to the regular discrete capacity, branching capacity is closely related to the asymptotics ... More

The stabilization of the Frobenius--Hecke traces on the intersection cohomology of orthogonal Shimura varietiesJan 29 2018The orthogonal Shimura varieties are associated to special orthogonal groups over $\mathbb Q$ of signature $(n,2)$ at infinity. We consider the intersection cohomology of their Baily--Borel compactifications, and prove a version of Morel's formula for ... More

The Z-cubes: a hypercube variant with small diameterSep 23 2015This paper introduces a new variant of hypercubes, which we call Z-cubes. The n-dimensional Z-cube $H_n$ is obtained from two copies of the (n-1)-dimensional Z-cube $H_{n-1}$ by adding a special perfect matching between the vertices of these two copies ... More

The probability of Riemann's hypothesis being true is equal to 1Sep 24 2016Apr 26 2018Let $P$ be the set of all prime numbers, ${q_1},{q_2}, \cdots ,{q_m} \in P$, $P_k$ be the k-th $(k = 1,2, \cdots m)$ element of $P$ in ascending order of size, ${\alpha _1},{\alpha _2}, \cdots ,{\alpha _m}$ be positive integers, and ${\beta _1},{\beta ... More

A Generalization of the Kodaira Vanishing and Embedding TheoremFeb 02 1995We give several generalizations of the Kodaira vanishing and embedding theorems for K\"ahler manifolds to the case where the relevent line bundle has a small region of negative curvature. To prove the vanishing theorems we adapt techniques of Elworthy-Rosenberg ... More

Spectra and elliptic flow of (multi-)strange hadrons at RHIC and LHC within viscous hydrodynamics+hadron cascade hybrid modelJul 14 2016Aug 15 2016Using the (2+1)-dimensional ultrarelativistic viscous hydrodynamics+hadron cascade, VISHNU, hybrid model, we study the $p_{\rm T}$-spectra and elliptic flow of $\Lambda$, $\Xi$, and $\Omega$ in Au+Au collisions at $\sqrt{s_{NN}}$=200 GeV and in Pb+Pb ... More

Log rationally connected surfacesDec 08 2014Jul 02 2015In this paper, combining the works of Miyanishi-Tsunoda and Keel-McKernan, we prove the log Castelnuovo's rationality criterion for smooth quasiprojective surfaces over complex numbers.

The second variation of the Ricci expander entropyJan 19 2009We compute the second variation of the Ricci expander entropy and briefly discuss the linear stability of compact negative Einstein manifolds.

Harmonic maps from degenerating Riemann surfacesMar 25 2008We study harmonic maps from degenerating Riemann surfaces with uniformly bounded energy and show the so-called generalized energy identity. We find conditions that are both necessary and sufficient for the compactness in $W^{1,2}$ and $C^{0}$ modulo bubbles ... More

On the semi-regular module and vertex operator algebrasNov 20 2007Dec 03 2007We prove a conjecture stated in a previous paper by the author about the existence of canonical filtrations for a family of vertex operator algebras in rational levels.

Some inequalities related to isoperimetric inequalities with partial free boundaryJan 09 2001Feb 16 2001The main purpose of this paper is to prove a sharp Sobolev inequality in an exterior of a convex bounded domain. There are two ingredients in the proof: One is the observation of some new isoperimetric inequalities with partial free boundary, and the ... More

When is the majority-vote classifier beneficial?Jul 24 2013In his seminal work, Schapire (1990) proved that weak classifiers could be improved to achieve arbitrarily high accuracy, but he never implied that a simple majority-vote mechanism could always do the trick. By comparing the asymptotic misclassification ... More