total 10473took 0.10s

Categorization Problem on Controllability of Boolean Control NetworksApr 12 2019A Boolean control network (BCN) is a discrete-time dynamical system whose variables take values from a binary set $\{0,1\}$. At each time step, each variable of the BCN updates its value simultaneously according to a Boolean function which takes the state ... 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

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

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

An introduction to affine Grassmannians and the geometric Satake equivalenceMar 17 2016Apr 04 2016We introduce various affine Grassmannians, study their geometric properties, and give some applications. We also discuss the geometric Satake equivalence. These are the expanded lecture notes for a mini-course in 2015 PCMI summer school. References updated ... More

Study of an Equivalent Proposition of Riemann HypothesisSep 24 2016Let $H_n = \sum_{k = 1}^{n}\frac{1}{k}$. Using Chebyshev function and prime number theorem, this paper proves that, there exists a positive constant A, such that for all natural numbers $n = q_1 * q_2 *... * q_m$ or $n = q_1^{\alpha_1} * q_2^{\alpha_1} ... More

Low-intensity light switching of cavity-atom polaritonsFeb 03 2010Mar 22 2010I analyze an all-optical switching scheme in a cavity QED system consisting of multiple three-level atoms confined in a cavity mode. A control laser coupled to the atoms from free space induces quantum interference in the coupled cavity-atom system and ... More

The order of the group of self-homotopy equivalence of wedge spacesAug 01 2015In this paper $Aut(\Sigma X\vee \Sigma Y)^\#$ the order of the group of self-homotopy equivalence of wedge spaces is studied. Under the condition of reducibility, we decompose $ Aut(\bigvee\limits_{t=1}^{k}X_{t})$ to the product of subgroups which generalizes ... More

Rigidity of a family of spherical conical metricsFeb 06 2019We study the deformation of spherical conical metrics with at least some of the cone angles larger than $2\pi$. We show in this note via synthetic geometry that for one family of such metrics, there is local rigidity in the choice of cone positions if ... More

Maximal zero sequences for Fock spacesOct 11 2011A sequence $Z$ in the complex plane $\C$ is called a zero sequence for the Fock space $F^p_\alpha$ if there exists a function $f\in F^p_\alpha$, not identically zero, such that $Z$ is the zero set of $f$, counting multiplicities. We show that there exist ... More

Multiqubit Clifford groups are unitary 3-designsOct 09 2015We show that the multiqubit (including qubit) Clifford group in any even prime power dimension is not only a unitary 2-design, but also a unitary 3-design. Moreover, it is a minimal unitary 3-design except for dimension 4. As an immediate consequence, ... More

Projective dimension and regularity of the path ideal of the line graphOct 10 2016Oct 26 2016By generalizing the notion of the path ideal of a graph, we study some algebraic properties of some path ideals associated to a line graph. We show that the quotient ring of these ideals are always sequentially Cohen-Macaulay and also provide some exact ... More

Implications of the recent measurement of pure annihilation $B_s \to π^+ π^-$ decays in QCD factorizationJun 23 2011Jul 20 2011The CDF 3.7 sigma evidence of pure annihilation $B_s \to \pi^+ \pi^-$ decays, if confirmed, would imply a large annihilation scenario in the QCD factorization approach. This is somewhat unexpected as the large annihilation scenario was disfavored in previous ... More

B physics constraints on a flavor symmetric scalar model to account for the ttbar asymmetry and Wjj excess at CDFApr 16 2011Jul 22 2011Recently Nelson et al. proposed an interesting flavor symmetric model to account for the top quark forward-backward asymmetry and the dijet anomaly at CDF simultaneously with just three parameters: a coupling constant of order one, and two scalar masses ... More

The Complexity of HCP in Digraps with Degree Bound TwoApr 03 2007Jul 13 2007The Hamiltonian cycle problem (HCP) in digraphs D with degree bound two is solved by two mappings in this paper. The first bijection is between an incidence matrix C_{nm} of simple digraph and an incidence matrix F of balanced bipartite undirected graph ... More

K3 surfaces associated to Abelian Fourfolds of Mumford's TypeDec 17 2018Mumford constructed a family of abelian fourfolds with special stucture not characterized by endomorphism ring. Galluzzi showed that the weight 2 Hodge structure of such a variety decomposes into Hodge substructures via the action of Mumford-Tate group, ... More

On the Complexity of Protein Local Structure Alignment Under the Discrete Fréchet DistanceSep 05 2007We show that given $m$ proteins (or protein backbones, which are modeled as 3D polygonal chains each of length O(n)) the problem of protein local structure alignment under the discrete Fr\'{e}chet distance is as hard as Independent Set. So the problem ... More

Quantitative unique continuation of solutions to higher order elliptic equations with singular coefficientsApr 05 2017Mar 25 2018We investigate the quantitative unique continuation of solutions to higher order elliptic equations with singular coefficients. Quantitative unique continuation described by the vanishing order is a quantitative form of strong unique continuation property. ... More

Area bounds for minimal surfaces in geodesic ball of hyperbolic spaceDec 08 2016In hyperbolic space $H^n$ we set a geodesic ball of radius $\rho$. Consider a $k$ dimensional minimal submanifold passing through the origin of the geodesic ball with boundary lies on the boundary of that geodesic ball. We prove that its area is no less ... More

The Lp Minkowski problem for polytopes for 0 < p < 1Jun 29 2014Aug 02 2014Necessary and sufficient conditions are given for the existence of solutions to the discrete Lp Minkowski problem for the critical case where 0 < p < 1.

Preprojective cluster variables of acyclic cluster algebrasNov 29 2005Aug 30 2006For any valued quiver, by using BGP-reflection functors, an injection from the set of preprojective objects in the cluster category to the set of cluster variables of the corresponding cluster algebra is given, the images are called preprojective cluster ... More

Prescribing integral curvature equationJul 10 2014Feb 07 2015In this paper we formulate new curvature functions on $\mathbb{S}^n$ via integral operators. For certain even orders, these curvature functions are equivalent to the classic curvature functions defined via differential operators, but not for all even ... More

Game Theory for Cyber Deception: A TutorialMar 03 2019Deceptive and anti-deceptive technologies have been developed for various specific applications. But there is a significant need for a general, holistic, and quantitative framework of deception. Game theory provides an ideal set of tools to develop such ... More

On the critical branching random walk II: Branching capacity and branching recurrenceDec 01 2016Jan 31 2017We 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.

On the critical branching random walk I: Branching capacity and visiting probabilityNov 30 2016Jan 31 2017We 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

Large deviations for Markovian nonlinear Hawkes processesAug 11 2011Mar 17 2015Hawkes process is a class of simple point processes that is self-exciting and has clustering effect. The intensity of this point process depends on its entire past history. It has wide applications in finance, neuroscience and many other fields. In this ... More

The sharp lower bound for the volume of 3-folds of general type with χ(\Co{X})=1Oct 24 2007Let $V$ be a smooth projective 3-fold of general type. Denote by $K^{3}$, a rational number, the self-intersection of the canonical sheaf of any minimal model of $V$. One defines $K^{3}$ as a canonical volume of $V$. The paper is devoted to proving the ... More

The higher sharp IV: the higher levelsMay 30 2017We establish the descriptive set theoretic representation of the mouse $M_n^{\#}$, which is called $0^{(n+1)\#}$. This part deals with the case $n>3$.

Regular representations of the quantum groups at roots of unityNov 20 2007Dec 03 2007We study the bimodule structure of the quantum function algebra at roots of 1 and prove that it admits an increasing filtration with factors isomorphic to the tensor products of the dual of Weyl modules $V_\lambda^* \otimes V_{- \omega_0 \lambda}^*$. ... More

Multiple list colouring of planar graphsMay 16 2016This paper proves that for each positive integer $m$, there is a planar graph $G$ which is not $(4m+\lfloor \frac{2m-1}{9}\rfloor,m)$-choosable. Then we pose some conjectures concerning multiple list colouring of planar graphs.

Lie II theorem for Lie algebroids via higher groupoidsDec 31 2006May 20 2010Following Sullivan's spacial realization of a differential algebra, we construct a universal integrating Lie 2-groupoid for every Lie algebroid. Then We show that unlike Lie algebras which one-to-one correspond to simply connected Lie groups, Lie algebroids ... More

A generalized Morse index theoremApr 07 2005In this paper, we prove a Morse index theorem for the index form of even order linear Hamiltonian systems on the closed interval with reasonable self-adjoint boundary conditions. The highest order term is assumed to be nondegenerate.

Two Boundary Centralizer Algebras for $\mathfrak{gl}(n|m)$Sep 21 2018We define an action of the degenerate two boundary braid algebra $\mathcal{G}_d$ on the $\mathbb{C}$-vector space $M\otimes N\otimes V^{\otimes d}$, where $M$ and $N$ are arbitrary modules for the general linear Lie superalgebra $\mathfrak{gl}(n|m)$, ... More

Speedup of Micromagnetic Simulations with C++ AMP On Graphics Processing UnitsJun 29 2014A finite-difference Micromagnetic solver is presented utilizing the C++ Accelerated Massive Parallelism (C++ AMP). The high speed performance of a single Graphics Processing Unit (GPU) is demonstrated compared to a typical CPU-based solver. The speed-up ... More

BSDE and generalized Dirichlet forms: the infinite dimensional caseJan 16 2012We consider the following quasi-linear parabolic system of backward partial differential equations on a Banach space $E$: $(\partial_t+L)u+f(\cdot,\cdot,u, A^{1/2}\nabla u)=0$ on $[0,T]\times E,\qquad u_T=\phi$, where $L$ is a possibly degenerate second ... More

Gradient-based Sampling: An Adaptive Importance Sampling for Least-squaresMar 02 2018In modern data analysis, random sampling is an efficient and widely-used strategy to overcome the computational difficulties brought by large sample size. In previous studies, researchers conducted random sampling which is according to the input data ... More

Accelerate micromagnetic simulations with GPU programming in MATLABJan 25 2015A finite-difference Micromagnetic simulation code written in MATLAB is presented with Graphics Processing Unit (GPU) acceleration. The high performance of Graphics Processing Unit (GPU) is demonstrated compared to a typical Central Processing Unit (CPU) ... More

Diffraction induced Spin Pumping in Normal-Metal/Multiferroic-Helimagnet/Ferromagnet HeterostructuresMay 30 2014Generally the adiabatic quantum pumping phenomenon can be interpreted by the surface integral of the Berry curvature inside the cyclic loop. Spin angular momentum flow without charge current can be pumped out by magnetization precession in ferromagnet-based ... More

A note on the quantization error for in-homogeneous self-similar measuresAug 31 2016We further study the asymptotics of quantization errors for two classes of in-homogeneous self-similar measures $\mu$. We give a new sufficient condition for the upper quantization coefficient for $\mu$ to be finite. This, together with our previous work, ... More

Convergence order of the geometric mean errors for Markov-type measuresOct 26 2014We study the quantization problem with respect to the geometric mean error for Markov-type measures $\mu$ on a class of fractal sets. Assuming the irreducibility of the corresponding transition matrix $P$, we determine the exact convergence order of the ... More

Asymptotic order of the quantization errors for self-affine measures on Bedford-McMullen carpetsApr 19 2016Let $E$ be a Bedford-McMullen carpet determined by a set of affine mappings $(f_{ij})_{(i,j)\in G}$ and $\mu$ a self-affine measure on $E$ associated with a probability vector $(p_{ij})_{(i,j)\in G}$. We prove that, for every $r\in(0,\infty)$, the upper ... More

Asymptotic local uniformity of the quantization error for Ahlfors-David probability measuresAug 25 2017Feb 26 2018Let $\mu$ be an Ahlfors-David probability measure on $\mathbb{R}^q$, namely, there exist some constants $s_0>0$ and $\epsilon_0,C_1,C_2>0$ such that \[ C_1\epsilon^{s_0}\leq\mu(B(x,\epsilon))\leq C_2\epsilon^{s_0},\;\epsilon\in(0,\epsilon_0),\;x\in{\rm ... More

Regularity for harmonic maps into certain Pseudo-Riemannian manifoldsJan 10 2011Mar 20 2012In this article, we investigate the regularity for certain elliptic systems without a $L^2$-antisymmetric structure. As applications, we prove some $\epsilon$-regularity theorems for weakly harmonic maps from the unit ball $B= B(m) \subset \mathbb{R}^m ... More

Depth and Stanley depth of the path ideal associated to an $n$-cyclic graphDec 24 2016We compute the depth and Stanley depth for the quotient ring of the path ideal of length $3$ associated to a $n$-cyclic graph, given some precise formulas for depth when $n\not\equiv 1\,(\mbox{mod}\ 4)$, tight bounds when $n\equiv 1\,(\mbox{mod}\ 4)$ ... More

Analyzing DNA Hybridization via machine learningMar 27 2018Jul 02 2018In DNA computing, it is impossible to decide whether a specific hybridization among complex DNA molecules is effective or not within acceptable time. In order to address this common problem, we introduce a new method based on the machine learning technique. ... More

Molecular Model Checking a Temporal LogicAug 05 2016Feb 20 2017The molecular computing has been successfully employed to solve more and more complex computation problems. However, as an important complex problem, the model checking are still far from fully resolved under the circumstance of molecular computing, since ... More

Loss Tomography in General TopologyMar 25 2016Although there are a few works reported in the literature considering loss tomography in the general topology, there is few well established result since all of them rely either on simulations or on experiments that have many random factors affecting ... More

Evidence of Different Formation Mechanisms for Hot versus Warm Super-EarthsMar 05 2015Using the Kepler planet sample from Buchhave et al. and the statistical method clarified by Schlaufman, I show that the shorter-period super-Earths have a different dependence on the host star metallicity from the longer-period super-Earths, with the ... More

Experimental Study on CTL model checking using Machine LearningFeb 23 2019The existing core methods, which are employed by the popular CTL model checking tools, are facing the famous state explode problem. In our previous study, a method based on the Machine Learning (ML) algorithms was proposed to address this problem. However, ... More

Influence of Stellar Metallicity on Occurrence Rates of Planets and Planetary SystemsAug 28 2018Jan 24 2019We study the influence of stellar metallicity on the fraction of stars with planets (i.e., the occurrence rate of planetary systems) and the average number of planets per star (i.e., the occurrence rate of planets). The former directly reveals the planet ... More

Are valence quarks rotating?Oct 27 2012We suggest to compare the deep inelastic scattering structure functions measured in the unpolarized charged-lepton scattering off a transversely polarized proton and off a longitudinally polarized proton at larger Bjorken variable $x$, one may get a direct ... More

Application of Jet Trimming in Boosted Higgs SearchJul 09 2011We present the study of the $WH$ and $ZH$ search with the Higgs Boson decayed to $b\bar{b}$ at the Large Hadron Collider. The Higgs Boson and the Vector Boson are required to be boosted, and the Higgs Boson is reconstructed with Jet Trimming Technique. ... More

A Closed Form Maximum Likelihood Estimator to End-to-End Loss Rate EstimationApr 30 2011Oct 01 2012Loss tomography has been studied for more than 10 years and a number of estimators have been proposed. The estimators can be divided into two classes: maximum likelihood and non-maximum likelihood. The maximum likelihood estimators rely on the maximum ... More

Loss Rate Inference in Multi-Sources and Multicast-Based General TopologySep 14 2010Jul 20 2011Loss tomography has received considerable attention in recent years and a number of estimators have been proposed. Unfortunately, almost all of them are devoted to the tree topology despite the general topology is more common in practice. In addition, ... More

Several Conclusions on another site setting problemJun 02 2018Let $S = \{ {A_1},{A_2}, \cdots ,{A_n}\} $ be a finite point set in m-dimensional Euclidean space ${E^m}$, and$\left\| {{A_i}{A_j}} \right\|$ be the distance between $A_i$ and $A_j$. Define $\sigma (S) = \sum\limits_{1 \le i < j \le n} {\left\| {{A_i}{A_j}} ... More

Stabilization of Damped Waves on Spheres and Zoll Surfaces of RevolutionApr 18 2016Dec 17 2017We study the strong stabilization of wave equations on some sphere-like manifolds, with rough damping terms which do not satisfy the geometric control condition posed by Rauch-Taylor and Bardos-Lebeau-Rauch. We begin with an unpublished result of G. Lebeau, ... More

Quasiprobability representations of quantum mechanics with minimal negativityApr 24 2016Aug 25 2016Quasiprobability representations, such as the Wigner function, play an important role in various research areas. The inevitable appearance of negativity in such representations is often regarded as a signature of nonclassicality, which has profound implications ... More

On general (alpha,beta)-metrics with vanishing Douglas curvatureMay 29 2015In this paper, we study a class of Finsler metrics called general $(\alpha,\beta)$-metrics, which are defined by a Riemannian metric $\alpha$ and a $1$-form $\beta$. We find an equation which is necessary and sufficient condition for such Finsler metric ... More

Permutation Symmetry Determines the Discrete Wigner FunctionApr 15 2015Jan 10 2016The Wigner function provides a useful quasiprobability representation of quantum mechanics, with applications in various branches of physics. Many nice properties of the Wigner function are intimately connected with the high symmetry of the underlying ... More

On general $(α,β)$-metrics with isotropic Berwald curvatureJun 05 2015In this paper, we study a class of Finsler metrics called general $(\alpha,\beta)$-metrics, which are defined by a Riemannian metric $\alpha$ and a $1$-form $\beta$. We classify this class of Finsler metrics with isotropic Berwald curvature under certain ... More

Rigidity of Area-Minimizing $2$-Spheres in $n$-Manifolds with Positive Scalar CurvatureMar 14 2019Mar 28 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

Magnetic field induced quantum phase transitions in the two-impurity Anderson modelNov 30 2010In the two-impurity Anderson model, the inter-impurity spin exchange interaction favors a spin singlet state between two impurities leading to the breakdown of the Kondo effect. We show that a local uniform magnetic field can delocalize the quasiparticles ... More

Local Quantum Criticality of a One-Dimensional Kondo Insulator ModelMar 17 2018The continuous quantum phase transition and the nature of quantum critical point (QCP) in a modified Kondo lattice model with Ising anisotropic exchange interactions is studied within the density-matrix renormalization group algorithm. We investigate ... 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

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

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.

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.

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

A quantitative approach to choose among multiple mutually exclusive decisions: comparative expected utility theoryJan 08 2018Mutually exclusive decisions have been studied for decades. Many well-known decision theories have been defined to help people either to make rational decisions or to interpret people's behaviors, such as expected utility theory, regret theory, prospect ... More

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

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

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

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

Rigidity of Area-Minimizing $2$-Spheres in $n$-Manifolds with Positive Scalar CurvatureMar 14 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

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

Statistical inference for autoregressive models under heteroscedasticity of unknown formApr 06 2018Aug 09 2018This paper provides an entire inference procedure for the autoregressive model under (conditional) heteroscedasticity of unknown form with a finite variance. We first establish the asymptotic normality of the weighted least absolute deviations estimator ... 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

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

On Theorem 6 in "Relative Entropy and the Multivariable Multidimensional Moment Problem" [Mar 2006 1052-1066]May 30 2018Jun 06 2018Matrix-valued covariance extension and multivariate spectral estimation are formulated as generalized moment problems in the "THREE" approach and its extensions. Under this context, we discuss Theorem 6 in \cite{Georgiou-06} concerning the bijectivity ... More

Hyperspectral Unmixing: Ground Truth Labeling, Datasets, Benchmark Performances and SurveyAug 17 2017Oct 11 2017Hyperspectral unmixing (HU) is a very useful and increasingly popular preprocessing step for a wide range of hyperspectral applications. However, the HU research has been constrained a lot by three factors: (a) the number of hyperspectral images (especially ... More