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A Reflectance Based Method For Shadow Detection and RemovalJul 11 2018Shadows are common aspect of images and when left undetected can hinder scene understanding and visual processing. We propose a simple yet effective approach based on reflectance to detect shadows from single image. An image is first segmented and based ... More

AV1 Video Coding Using Texture Analysis With Convolutional Neural NetworksApr 24 2018Modern video codecs including the newly developed AOM/AV1 utilize hybrid coding techniques to remove spatial and temporal redundancy. However, efficient exploitation of statistical dependencies measured by a mean squared error (MSE) does not always produce ... More

Multi-Reference Video Coding Using Stillness DetectionMar 11 2018Encoders of AOM/AV1 codec consider an input video sequence as succession of frames grouped in Golden-Frame (GF) groups. The coding structure of a GF group is fixed with a given GF group size. In the current AOM/AV1 encoder, video frames are coded using ... More

Satellite Image Forgery Detection and Localization Using GAN and One-Class ClassifierFeb 13 2018Current satellite imaging technology enables shooting high-resolution pictures of the ground. As any other kind of digital images, overhead pictures can also be easily forged. However, common image forensic techniques are often developed for consumer ... More

Texture Segmentation Based Video Compression Using Convolutional Neural NetworksFeb 08 2018There has been a growing interest in using different approaches to improve the coding efficiency of modern video codec in recent years as demand for web-based video consumption increases. In this paper, we propose a model-based approach that uses texture ... More

Reliability Map Estimation For CNN-Based Camera Model AttributionMay 04 2018Among the image forensic issues investigated in the last few years, great attention has been devoted to blind camera model attribution. This refers to the problem of detecting which camera model has been used to acquire an image by only exploiting pixel ... More

Single-View Food Portion Estimation: Learning Image-to-Energy Mappings Using Generative Adversarial NetworksFeb 27 2018May 23 2018Due to the growing concern of chronic diseases and other health problems related to diet, there is a need to develop accurate methods to estimate an individual's food and energy intake. Measuring accurate dietary intake is an open research problem. In ... 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

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

Piecewise linear approximation for the dynamical $Φ^4_3$ modelApr 16 2015Oct 22 2017We construct a piecewise linear approximation for the dynamical $\Phi_3^4$ model on $\mathbb{T}^3$ by the theory of regularity structures in [Hai14]. For the dynamical $\Phi^4_3$ model it is proved in [Hai14] that a renormalisation has to be performed ... More

Weak universality of the dynamical $Φ_3^4$ model on the whole spaceNov 04 2018Nov 06 2018We prove the large scale convergence of a class of stochastic weakly nonlinear reaction-diffusion models on $\mathbb{R}^3$ to the dynamical $\Phi^4_3$ model by paracontrolled distributions on weighted Besov space. Our approach depends on the delicate ... More

Dirichlet form associated with the $Φ_3^4$ modelMar 29 2017Jun 25 2017We construct the Dirichlet form associated with the dynamical $\Phi^4_3$ model obtained in [Hai14, CC13] and [MW16]. This Dirichlet form on cylinder functions is identified as a classical gradient bilinear form. As a consequence, this classical gradient ... 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

Strong-Feller property for Navier-Stokes equations driven by space-time white noiseSep 27 2017Sep 29 2017In this paper we prove strong Feller property for the Markov semigroups associated to the two or three dimensional Navier-Stokes (N-S) equations driven by space-time white noise using the theory of regularity structures introduced by Martin Hairer in ... More

Three-dimensional Navier-Stokes equations driven by space-time white noiseMay 31 2014Jan 04 2017In 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

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

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

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 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.

Exotic Charmonium-like States at BESIIIMay 18 2015The recent measurement results of exotic charmonium-like states, the so called XYZ particles, at BESIII have been presented. I mainly discussed the charged Zc(3900) state, its neutral partner, and possible excited states.

Charmonium and Light Meson SpectroscopyDec 10 2012This talk reviews recent experimental results on selected topics in the spectroscopy of charmonia, charmonium-like states and light mesons.

On the gluing formula of real analytic torsion formsMay 13 2014In this paper we extend first the Bismut-Lott's analytic torsion form for flat vector bundles to the boundary case, then we establish its gluing formula on a smooth fibration under the assumption that a fiberwise Morse function exists. We assume that ... More

The RPC-based proposal for the ATLAS forward muon trigger upgrade in view of super-LHCOct 25 2012The innermost station of the present ATLAS forward muon detector needs to be upgraded for the super-LHC. We present a proposal to replace it with a sandwiched detector composed of several layers of small-radius Monitored Drift Tube chambers (sMDT) for ... More

Inclined Massive Planets in a Protoplanetary Disc: Gap Opening, Disc Breaking, and Observational SignaturesDec 04 2018We carry out three-dimensional hydrodynamical simulations to study planet-disc interactions for inclined high mass planets, focusing on the disc's secular evolution induced by the planet. We find that, when the planet is massive enough and the induced ... More

Rigidity of Area-Minimizing $2$-Spheres in $n$-Manifolds with Positive Scalar CurvatureMar 14 2019Mar 15 2019We prove that the least area of the non-contractible immersed spheres is no more than $4\pi$ in any oriented compact manifold with dimension $n+2\leq 7$ which satisfies $R\geq 2$ and admits a map to $\mathbf S^2\times T^n$ with nonzero degree. We also ... More

Global classical solutions of 3D compressible viscoelastic system near equilibriumSep 12 2018In this paper, we prove the global existence of general small solutions to compressible viscoelastic system. We remove the "initial state" assumption ($\tilde \rho_0 \det F_0 =1$) and the "div-curl" structure assumption compared with previous works. It ... More

Statistical Physics and Information Theory Perspectives on Linear Inverse ProblemsMay 15 2017Jul 12 2017Many real-world problems in machine learning, signal processing, and communications assume that an unknown vector $x$ is measured by a matrix A, resulting in a vector $y=Ax+z$, where $z$ denotes the noise; we call this a single measurement vector (SMV) ... More

Strongly Unitary Equivalence and Approximately Unitary Equivalence of Normal Compact Operators over Topological SpacesSep 01 2017Let $A$ and $B$ be compact operators over a topological space $X$ and suppose that these operators are normal and have same distinct eigenvalues at each point. By obstruction theory, we establish a necessary and sufficient condition for $A$ and $B$ to ... More

Optimal Strategies for a Long-Term Static InvestorNov 24 2013Oct 14 2014The optimal strategies for a long-term static investor are studied. Given a portfolio of a stock and a bond, we derive the optimal allocation of the capitols to maximize the expected long-term growth rate of a utility function of the wealth. When the ... More

Kernels and Ensembles: Perspectives on Statistical LearningDec 06 2007Since their emergence in the 1990's, the support vector machine and the AdaBoost algorithm have spawned a wave of research in statistical machine learning. Much of this new research falls into one of two broad categories: kernel methods and ensemble methods. ... 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

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.

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

Branching interlacements and tree-indexed random walks in torusDec 28 2018Jan 15 2019In this article, we introduce a model of branching interlacements made of a countable collection of tree-indexed random walk trajectories on $\mathbb{Z}^d,d\geq 5$ for general critical offspring distributions. We show that this model turns out to be the ... More

Generalized PMC model for the hybrid diagnosis of multiprocessor systemsSep 17 2017Sep 19 2017Fault diagnosis is important to the design and maintenance of large multiprocessor systems. PMC model is the most famous diagnosis model in the system level diagnosis of multiprocessor systems. Under the PMC model, only node faults are allowed. But in ... More

Spin-dependent electron grating effect from helical magnetization in multiferroic tunnel junctionsApr 27 2012In multiferroic oxides with a transverse helical magnetic order, the magnetization exchange coupling is sinusoidally space-dependent. We theoretically investigate the spin-dependent electron grating effect in normal-metal/helical-multiferroic/ferromagnettic ... More

Conductance in the Helimagnet- and Skyrmion-Lattice-Embedded Electron WaveguideNov 22 2013The helimagnet (HM) and skyrmion lattice (SL) are topologically nontrivial magnetic states. Their spin texture gives rise to finite topological magnetic field and Lorentz force. As a demonstration of the emergent electrodynamics besides the Hall effect, ... More

A scattering matrix approach to quantum pumping: Beyond the small-ac-driving-amplitude limitNov 06 2009In the adiabatic and weak-modulation quantum pump, net electron flow is driven from one reservoir to the other by absorbing or emitting an energy quantum $\hbar \omega $ from or to the reservoirs. In our approach, high-order dependence of the scattering ... More

A few results on the infimum of regular polygons equal-size split lineMay 15 2018If an n-side unit regular polygon is divided into m equal sized parts, then what is the minimum length of the split line ${l_{m,n}}$? This problem has its practical application in real world. This paper proved that ${l_{2,3}} = \sqrt {\frac{{\sqrt 3 \pi ... More

Explicit Maximum Likelihood Loss Estimator in Multicast TomographyApr 27 2010For the tree topology, previous studies show the maximum likelihood estimate (MLE) of a link/path takes a polynomial form with a degree that is one less than the number of descendants connected to the link/path. Since then, the main concern is focused ... More

A geometrizing higher twist effect on nuclear targetAug 30 2004Feb 13 2005The higher twist effects in deep inelastic scattering on the nuclear target are studied using time ordered perturbation theory. We showed that the collinear rescattering of the outgoing quark on the extra nucleons via the contacting gluon-pair is dominant ... More

Integral Solutions to Linear Indeterminate EquationMar 08 2011In this paper, using Euler's function, we give a formula of all integral solutions to linear indeterminate equation with $s$-variables $a_1x_1+a_2x_2+...+a_sx_s=n$. It is a explicit formula of the coefficients $a_1$, $a_2$,..., $a_s$ and the free term ... More

n-Groupoids and Stacky GroupoidsJan 14 2008Jun 29 2009We discuss two generalizations of Lie groupoids. One consists of Lie $n$-groupoids defined as simplicial manifolds with trivial $\pi_{k\geq n+1}$. The other consists of stacky Lie groupoids $\cG\rra M$ with $\cG$ a differentiable stack. We build a 1-1 ... More

Lie n-groupoids and stacky Lie groupoidsSep 14 2006Nov 13 2006We discuss two sorts of generalization of Lie groupoids. One is Lie $n$-groupoids defined as simplicial manifolds with trivial $\pi_{k\geq n+1}$. The other is the stacky Lie groupoid $\cG\rra M$ with $\cG$ a differentiable stack. We build 1-1 correspondence ... More

Integrating Lie algebroids via stacks and applications to Jacobi manifoldsMay 09 2005Lie algebroids can not always be integrated into Lie groupoids. We introduce a new object--``Weinstein groupoid'', which is a differentiable stack with groupoid-like axioms. With it, we have solved the integration problem of Lie algebroids. It turns out ... More

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

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

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

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

Functors and morphisms determined by subcategoriesOct 24 2017We study the existence and uniqueness of minimal right determiners in various categories. Particularly in a Hom-finite hereditary abelian category with enough projectives, we prove that the Auslander-Reiten-Smal{\o}-Ringel formula of the minimal right ... 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.

Vertex operator algebras associated to modified regular representations of affine Lie algebrasNov 17 2006Nov 20 2007Let $G$ be a simple complex Lie group with Lie algebra $\mf g$ and let $\af$ be the affine Lie algebra. We use intertwining operators and Knizhnik-Zamolodchikov equations to construct a family of $\N$-graded vertex operator algebras associated to $\mf ... More

On the comparison theorem for multidimensional SDEs with jumpsJun 08 2010In this note, we give a necessary and sufficient condition under which the comparison theorem holds for multidimensional stochastic differential equations (SDEs) with jumps and for matrix-valued SDEs with jumps.

Towards a dictionary for the Bargmann transformJun 21 2015There is a canonical unitary transformation from $L^2(\R)$ onto the Fock space $F^2$, called the Bargmann transform. The purpose of this article is to translate some important results and operators from the context of $L^2(\R)$ to that of $F^2$. Examples ... More

Uncertainty principles for the Fock spaceJan 12 2015Several uncertainty principles are proved for the Fock space.

Natural compactification of the moduli of toric pairs from the perspective of mirror symmetryOct 20 2014Sep 13 2016We construct a compactification of the moduli of toric pairs by using ideas from mirror symmetry. The secondary fan $\Sigma(Q)$ is used in [Ale02] to parametrize degenerations of toric pairs. It is also used in [CLS11] to control the variation of GIT. ... More

The Morse index theorem for regular Lagrangian systemsSep 18 2001In this paper, we prove a Morse index theorem for the index form of regular Lagrangian system with selfadjoint boundary condition.

The higher order terms in asymptotic expansion of color Jones polynomialsApr 03 2011Color Jones polynomial is one of the most important quantum invariants in knot theory. Finding the geometric information from the color Jones polynomial is an interesting topic. In this paper, we study the general expansion of color Jones polynomial which ... More

Information complementarity: A new paradigm for decoding quantum incompatibilityJun 26 2014Sep 14 2015The existence of observables that are incompatible or not jointly measurable is a characteristic feature of quantum mechanics, which lies at the root of a number of nonclassical phenomena, such as uncertainty relations, wave--particle dual behavior, Bell-inequality ... More

Nonexistence of sharply covariant mutually unbiased bases in odd prime dimensionsJun 18 2015Aug 23 2015Mutually unbiased bases (MUB) are useful in a number of research areas. The symmetry of MUB is an elusive and interesting subject. A (complete set of) MUB in dimension $d$ is sharply covariant if it can be generated by a group of order $d(d+1)$ from a ... More

Riesz transform characterization of weighted Hardy spaces associated to Schrödinger operatorsMay 21 2014In this paper, we characterize the weighted local Hardy spaces $h^p_\rho(\omega)$ related to the critical radius function $\rho$ and weights $\omega\in A_{1}^{\rho,\,\infty}(\mathbb{R}^{n})$ by localized Riesz transforms $\widehat{R}_j$, in addition, ... More

Nonuniform Dichotomy Spectrum Intervals: Theorem and ComputationFeb 12 2019Under the condition of nonuniformly bounded growth, %nonuniform exponential dichotomy spectrum for nonautonomous linear system is proposed the relationship of the nonuniform exponential dichotomy spectrum and the other two classical spectrums (the Lyapunov ... More

A note on eigenvalues of a class of singular continuous and discrete linear Hamiltonian systemsAug 01 2018In this paper, we show that the analytic and geometric multiplicities of an eigenvalue of a class of singular linear Hamiltonian systems are equal, where both endpoints are in the limit circle cases. The proof is fundamental and is given for both continuous ... More

Nonlinear Model Reduction Based On The Finite Element Method With Interpolated Coefficients: Semilinear Parabolic EquationsApr 01 2013Apr 28 2013For nonlinear reduced-order models, especially for those with non-polynomial nonlinearities, the computational complexity still depends on the dimension of the original dynamical system. As a result, the reduced-order model loses its computational efficiency, ... More

WIMPless dark matter and the excess gamma rays from the Galactic centerJan 23 2011Apr 05 2011In this paper we discuss the excess gamma rays from the Galactic center, the WMAP haze and the CoGeNT and DAMA results in WIMPless models. At the same time we also investigate the low energy constraints from the anomalous magnetic moment of leptons and ... More

Some sufficient conditions on Hamiltonian digraphDec 23 2008Z-mapping graph is a balanced bipartite graph $G$ of a digraph $D$ by split each vertex of $D$ into a pair of vertices of $G$. Based on the property of the $G$, it is proved that if $D$ is strong connected and $G$ is Hamiltonian, then $D$ is Hamiltonian. ... More

The Complexity of Determining Existence a Hamiltonian Cycle is $O(n^3)$Jun 19 2007The Hamiltonian cycle problem in digraph is mapped into a matching cover bipartite graph. Based on this mapping, it is proved that determining existence a Hamiltonian cycle in graph is $O(n^3)$.

A New View of Classification in Astronomy with the Archetype Technique: An Astronomical Case of the NP-complete Set Cover ProblemJun 23 2016We introduce a new generic Archetype technique for source classification and identification, based on the NP-complete set cover problem (SCP) in computer science and operations research (OR). We have developed a new heuristic SCP solver, by combining ... More

The Lp Minkowski problem for polytopes for negative pFeb 25 2016May 07 2016Existence of solutions to the Lp Minkowski problem is proved for all p less than 0. For the cirtical case of p=-n, which is known as the centro-affine Minkowski problem, this paper contains the main result in [71] as a special case.

Deformations of glassy polymers in very low temperature regime within cylindrical microporesAug 28 2008Apr 09 2009The deformation kinetics for glassy polymers confined in microscopic domain at very low temperature regime was investigated using a transition-rate-state dependent model considering the shear thinning behavior which means, once material being subjected ... More

Jet schemes and singularities of W^r_d(C) lociDec 05 2012Kempf proved that the theta divisor of a smooth projective curve C has rational singularities. In this paper we estimate the dimensions of the jet schemes of the theta divisor and show that all these schemes are irreducible. In particular, we recover ... More

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

The quantization for in-homogeneous self-similar measures with in-homogeneous open set conditionJul 05 2014Let $(g_i)_{i=1}^M$ be a family of contractive similitudes satisfying the open set condition. Let $\nu$ be a self-similar measure associated with $(g_i)_{i=1}^M$. We study the quantization problem for the in-homogeneous self-similar measure $\mu$ associated ... More

Constructing a CM Mumford fourfold from Shioda's fourfoldOct 23 2018Apr 15 2019Shioda proved that the Jacobian $A_S$ of the curve $y^2 = x^9 -1$ is a 4-dimensional CM abelian variety with codimension 2 Hodge cycles not generated by divisors. It was noted by Shioda that this behavior resembles the abelian varieties constructed by ... More

On a proof of the Bouchard-Sulkowski conjectureAug 14 2011In this short note, we give a proof of the free energy part of the BKMP conjecture of C^3 proposed by Bouchard and Sulkowski [4]. Hence the proof of the full BKMP conjecture for the case of C^3 has been finished.

The Laplace transform of the cut-and-join equation of Mariño-Vafa formula and its applicationsJan 05 2010By the same method introduced in [9], we calculate the Laplace transform of the celebrated cut-and-join equation of Mari\~no-Vafa formula discovered by C. Liu, K. Liu and J. Zhou [17]. Then, we study the applications of the polynomial identity (1) obtained ... More

A regularity theory for multiple-valued Dirichlet minimizing mapsAug 07 2006This paper discusses the regularity of multiple-valued Dirichlet minimizing maps into the sphere. It shows that even at branched point, as long as the normalized energy is small enough, we have the energy decay estimate. Combined with the previous work ... More

The internal structure of $\mathrm{HOD}^{L[x]}$ up to its WoodinNov 06 2017Nov 08 2017Assume $\boldsymbol{\Delta}^1_3$-determinacy. It is shown that for any $x \geq_T M_1^{\#}$, $\mathrm{HOD}^{L[x]}$ is a model of GCH, and in fact, it is a Jensen-Steel core model up to $\omega_2^{L[x]}$.

Auxiliary space preconditioners for virtual element methods on polytopal meshesNov 28 2018In this paper, we develop the auxiliary space preconditioners for solving the linear system arising from the virtual element methods discretization on polytopal meshes for the second order elliptic equations. The preconditioners are constructed based ... More

The optimal control related to Riemannian manifolds and the viscosity solutions to H-J-B equationsJan 16 2010This paper is concerned with the Dynamic Programming Principle (DPP in short) with SDEs on Riemannian manifolds. Moreover, through the DPP, we conclude that the cost function is the unique viscosity solution to the related PDEs on manifolds.

An axiomatic approach to the roughness measure of rough setsNov 28 2009May 25 2010In Pawlak's rough set theory, a set is approximated by a pair of lower and upper approximations. To measure numerically the roughness of an approximation, Pawlak introduced a quantitative measure of roughness by using the ratio of the cardinalities of ... More

Covering rough sets based on neighborhoods: An approach without using neighborhoodsNov 28 2009Dec 10 2010Rough set theory, a mathematical tool to deal with inexact or uncertain knowledge in information systems, has originally described the indiscernibility of elements by equivalence relations. Covering rough sets are a natural extension of classical rough ... More

Dirac-harmonic maps from degenerating spin surfaces I: the Neveu-Schwarz caseMar 26 2008We study Dirac-harmonic maps from degenerating spin surfaces with uniformly bounded energy and show the so-called generalized energy identity in the case that the domain converges to a spin surface with only Neveu-Schwarz type nodes. We find condition ... More

Ruin Probabilities for Risk Processes with Non-Stationary Arrivals and Subexponential ClaimsApr 06 2013Oct 14 2014In this paper, we obtain the finite-horizon and infinite-horizon ruin probability asymptotics for risk processes with claims of subexponential tails for non-stationary arrival processes that satisfy a large deviation principle. As a result, the arrival ... 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

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.

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.

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

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

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

On Vector ARMA Models Consistent with a Finite Matrix Covariance SequenceAug 15 2017Aug 28 2017We formulate the so called "VARMA covariance matching problem" and demonstrate the existence of a solution using the degree theory from differential topology.

Bredon Cohomology of Polyhedral ProductsNov 17 2018A polyhedral product is a natural subspace of a Cartesian product, which is specified by a simplicial complex K. The automorphism group Aut(K) of K induces a group action on the polyhedral product. In this paper we study this group action and give a formula ... More

Cyber InsuranceSep 30 2018This chapter will first present a principal-agent game-theoretic model to capture the interactions between one insurer and one user. The insurer is deemed as the principal who does not have incomplete information about user's security policies. The user, ... More

A momentum conserving $N$-body scheme with individual timestepsDec 29 2017$N$-body simulations study the dynamics of $N$ particles under the influence of mutual long-distant forces such as gravity. In practice, $N$-body codes will violate Newton's third law if they use either an approximate Poisson solver or individual timesteps. ... More

On the critical branching random walk III: the critical dimensionJan 31 2017In this paper, we study the critical branching random walk in the critical dimension, $Z^4$. We provide the asymptotics of the probability of visiting a fixed finite subset and the range of the critical branching random walk conditioned on the total number ... More

Higher Codimensional Alpha Invariants and Characterization of Projective SpacesMay 18 2018We generalize the definition of alpha invariant to arbitrary codimension. We also give a lower bound of these alpha invariants for K-semistable Q-Fano varieties and show that we can characterize projective spaces among all K-semistable Fano manifolds ... More