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Practical Issues of Action-conditioned Next Image PredictionFeb 08 2018The problem of action-conditioned image prediction is to predict the expected next frame given the current camera frame the robot observes and an action selected by the robot. We provide the first comparison of two recent popular models, especially for ... More

Knot undulator to generate linearly polarized photons with low on-axis power densityFeb 02 2008Heat load on beamline optics is a serious problem to generate pure linearly polarized photons in the third generation synchrotron radiation facilities. For permanent magnet undulators, this problem can be overcome by a figure-8 operating mode. But there ... More

Physical properties of noncentrosymmetric tungsten and molybdenum aluminidesJul 10 2018Sep 27 2018A lack of spatial inversion symmetry gives rise to a variety of unconventional physics, from noncollinear order and Skyrmion lattice phases in magnetic materials to topologically-protected surface states in certain band insulators, to mixed-parity pairing ... More

Evidence of nematic order and nodal superconducting gap along [110] direction in RbFe2As2Mar 20 2018Dec 17 2018Unconventional superconductivity often intertwines with various forms of order, such as the "nematic" order which breaks the rotational symmetry of the lattice. Investigation of these ordered phases sheds crucial light on the superconductivity itself. ... 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

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

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

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

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

Understanding Intra-Class Knowledge Inside CNNJul 09 2015Jul 21 2015Convolutional Neural Network (CNN) has been successful in image recognition tasks, and recent works shed lights on how CNN separates different classes with the learned inter-class knowledge through visualization. In this work, we instead visualize the ... More

Size dependent thermoelectric properties of silicon nanowiresAug 12 2009Aug 13 2009By using first-principles tight-binding electronic structure calculation and Boltzmann transport equation, we investigate the size dependence of thermoelectric properties of silicon nanowires (SiNWs). With cross section area increasing, the electrical ... More

Robust linear magnetoresistance in WTe2May 29 2015Unsaturated magnetoresistance (MR) has been reported in WTe2, and remains irrepressible up to very high field. Intense optimization of the crystalline quality causes a squarely-increasing MR, as interpreted by perfect compensation of opposite carriers. ... More

Frenkel-Gross' irregular connection and Heinloth-Ngô-Yun's are the sameMar 18 2016Apr 04 2016We show that the irregular connection on G_m constructed by Frenkel-Gross (2009) and the one constructed by Heinloth-Ng\^o-Yun (2013) are the same, which confirms a conjecture of the latter author's.

Simulation Study of Laser Plasma Accelerator Via VorpalJan 03 2015In this paper, we use PIC code Vorpal to do the extensive simulation about the laser plasma accelerator in the linear, quasilinear and nonlinear regime respectively. We design the ~100 MeV or so laser plasma accelerator ( LPA ) via Vorpal simulation. ... More

Structure of Clifford Semigroups of MatricesJun 22 2010In this paper, we characterize completely the structure of Clifford semigroups of matrices over an arbitrary field. It is shown that a semigroups of matrices of finite order is a Clifford semigroup if and only if it is isomorphic to a subdirect product ... More

Projective dimension and the regularity of the path ideal of the line graphOct 10 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 Cohen-Macaulay and also provide some exact formulas for ... More

$\mathbb{A}^1$-equivalence of zero cycles on surfacesOct 06 2015Oct 18 2015In this paper, we study $\mathbb{A}^1$-equivalence classes of zero cycles on open complex algebraic surfaces. We prove the logarithmic version of Mumford's theorem on zero cycles and prove that log Bloch's conjecture holds for quasiprojective surfaces ... More

An upper bound for the probability of visiting a distant point by critical branching random walk in $\mathbb{Z}^4$Mar 01 2015In this paper, we solve an open question raised by Le Gall and Lin. 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 ... More

The higher sharp IIApr 19 2016Aug 02 2016We establish the descriptive set theoretic representation of the mouse $M_n^{#}$, which is called $0^{(n+1)#}$. This part deals with the case $n>3$.

Stability on Kähler-Ricci flow, IAug 11 2009In this paper, we prove that K\"ahler-Ricci flow converges to a K\"ahler-Einstein metric (or a K\"ahler-Ricci soliton) in the sense of Cheeger-Gromov as long as an initial K\"ahler metric is very closed to $g_{KE}$ (or $g_{KS}$) if a compact K\"ahler ... More

Modular equations for Lubin-Tate formal groups at chromatic level 2Aug 13 2015We give an integral lift of the Kronecker congruence for moduli of finite subgroups of elliptic curves. This leads to a uniform presentation for the power operation structure on Morava E-theories of height 2.

Elliptic genera of Berglund-Hübsch modelsDec 25 2010We match the elliptic genus of a Berglund-H\"ubsch model with the supertrace of $y^{J[0]}q^{L[0]}$ on a vertex algebra $V_{{\bf 1}, {\bf 1}}$. We show that it is a weak Jacobi form and the elliptic genus of one theory is equal to (up to a sign) the elliptic ... More

Backward stochastic viability property with jumps and applications to the comparison theorem for multidimensional BSDEs with jumpsJun 08 2010In this paper, we study conditions under which the solutions of a backward stochastic differential equation with jump remains in a given set of constrains. This property is the so-called "viability property". As an application, we study the comparison ... More

On the 1-density of Unit Ball CoveringNov 13 2007Dec 20 2007Motivated by modern applications like image processing and wireless sensor networks, we consider a variation of the famous Kepler Conjecture. Given any infinite set of unit balls covering the whole space, we want to know the optimal (lim sup) density ... More

Integer Matrix Exact Covering Systems and Product Identities for Theta FunctionsMay 27 2010In this paper, we prove that there is a natural correspondence between product identities for theta functions and integer matrix exact covering systems. We show that since $\mathbb{Z}^n$ can be taken as the disjoint union of a lattice generated by $n$ ... More

The Physics and End-Products of Merging CO WD BinariesOct 16 2014The merger of two carbon-oxygen white dwarfs has long been theorized to lead to a massive carbon-oxygen or oxygen-neon white dwarf, accretion-induced collapse to a neutron star, or a type Ia supernova. Determining which mergers lead to a particular outcome ... More

Poisson Subsampling Algorithms for Large Sample Linear Regression in Massive DataSep 07 2015Nov 23 2015Large sample size brings the computation bottleneck for modern data analysis. Subsampling is one of efficient strategies to handle this problem. In previous studies, researchers make more fo- cus on subsampling with replacement (SSR) than on subsampling ... More

Factorization for radiative heavy quarkonium decays into scalar GlueballAug 06 2015Sep 22 2015We establish the factorization formula for scalar Glueball production through radiative decays of vector states of heavy quarkonia, e.g. $J/\psi$, $\psi(2S)$ and $\Upsilon(nS)$, where the Glueball mass is much less than the parent heavy quarkonium mass. ... More

The Exclusive Decay of Upsilon into $h_c$, the $X(3940)$ and $X(4160)$Jul 08 2015Oct 13 2015In this paper, we study double charmonia production in Upsilon peaks, especially, a S-wave charmonium $\eta_c$ and a P-wave charmonium $h_c(^1P_1)$, or a S-wave charmonium $J/\psi$ and the $X(3940)$ and $X(4160)$ within the nonrelativistic QCD (NRQCD) ... More

Hidden charm octet tetraquarks from a diquark-antidiquark modelJul 11 2016Aug 10 2016Four exotic charmonium-like states, i.e. $X(4140)$, $X(4274)$, $X(4500)$, and $X(4700)$, have been observed very recently by LHCb Collaboration in the decay process $B^+\to J/\psi \phi K^+$ using the 3${\rm fb}^{-1}$ data of $p\bar p$ collision at $\sqrt ... More

Grace: a Cross-platform Micromagnetic Simulator On Graphics Processing UnitsNov 10 2014A micromagnetic simulator running on graphics processing unit (GPU) is presented. It achieves significant performance boost as compared to previous central processing unit (CPU) simulators, up to two orders of magnitude for large input problems. Different ... More

Molecular Model Checking a Temporal LogicAug 05 2016Aug 09 2016The 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

Fitting a Model to Data in Loss TomographyJul 20 2011Loss tomography has received considerable attention in recent years and a number of estimators have been proposed. Although most of the estimators claim to be the maximum likelihood estimators, the claim is only partially true since the maximum likelihood ... More

Bd \to π^- K^{(*)+} and Bs \to π^+(ρ^+) K^- decays with QCD factorization and flavor symmetryFeb 24 2010May 06 2010The QCD factorization (QCDF) method usually contains infrared divergences which introduce large model dependence to its predictions on charmless B decays. The amplitudes of charmless B decays can be decomposed into "tree" and "penguin" parts which are ... More

BEC-BCS Crossover with Feshbach Resonance for Three-Hyperfine-Species ModelDec 30 2012In a Feshbach resonance, the effective s-wave scattering length grows when one moves toward the resonance point, and eventually diverges at this point. There is one characteristic energy scale, $\delta_c$, defined as, in the negative side of the resonance ... More

Comments on "Anomalous Hydrodynamic Drafting of Interacting Flapping Flags"May 08 2009We make remarks on Ristroph and Zhang's [{\it Phys. Rev. Lett.} {\bf 101}, 194502 (2008)] paper. We argue especially that due to the interferences the calibration procedures in [1] were not complete and this will induce some measurements' error.

Exotic in Leptonic MachinesAug 07 2014Selected topics of exotics in leptonic machines are presented, including recent discovery of abnormal structures around the ppbar threshold and new information of the XYZ (charmonium-like) states.

Sharply covariant mutually unbiased basesFeb 27 2015Mutually unbiased bases (MUB) are an elusive discrete structure in Hilbert spaces. Many (complete sets of) MUB are group covariant, but little is known whether they can be sharply covariant in the sense that the generating groups can have order equal ... More

A solution for the differences in the continuity of continuum among mathematiciansFeb 03 2013There are the longstanding differences in the continuity of continuum among mathematicians. Starting from studies on a mathematical model of contact, we construct a set that is in contact everywhere by using the original idea of Dedekind's cut and weakening ... More

Stabilisation of Damped Waves on Spheres and on Zoll's Surfaces of RevolutionApr 18 2016We are interested in the strong stabilisation of damped waves when the geometric control condition is not satisfied. We begin with an unpublished result due to Gilles Lebeau, of the strong stabilisation of damped waves on $\mathbb{S}^d$, with the damping ... More

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

The effect of minijet on hadron spectra and azimuthal anisotropy in heavy-ion collisionsJun 30 2016Here I review the transverse momentum distributions of identified hadrons produced in Au-Au collisions at RHIC and Pb-Pb collisions at LHC in the framework of recombination model. Minijets play an important role in generating shower partons in the intermediate ... More

A State-Dependent Dual Risk ModelOct 13 2015In a dual risk model, the premiums are considered as the costs and the claims are regarded as the profits. The surplus can be interpreted as the wealth of a venture capital, whose profits depend on research and development. In most of the existing literature ... More

Asymptotic Structure of Constrained Exponential Random Graph ModelsAug 07 2014Oct 25 2015In this paper, we study exponential random graph models subject to certain constraints. We obtain some general results about the asymptotic structure of the model. We show that there exists non-trivial regions in the phase plane where the asymptotic structure ... More

Nonlinear Hawkes ProcessesApr 28 2013Jun 23 2013The Hawkes process is a simple point process that has long memory, clustering effect, self-exciting property and is in general non-Markovian. The future evolution of a self-exciting point process is influenced by the timing of the past events. There are ... More

Hole probabilities of SU(m+1) Gaussian random polynomialsMar 31 2014In this paper, we study hole probabilities $P_{0,m}(r,N)$ of SU(m+1) Gaussian random polynomials of degree $N$ over a polydisc $(D(0,r))^m$. When $r\geq1$, we find asymptotic formulas and decay rate of $\log{P_{0,m}(r,N)}$. In dimension one, we also consider ... More

Quantitative uniqueness of elliptic equationsDec 02 2013Dec 22 2014Based on a variant of frequency function, we improve the vanishing order of solutions for Schr\"{o}dinger equations which describes quantitative behavior of strong uniqueness continuation property. For the first time, we investigate the quantitative uniqueness ... More

Gluing formula of real analytic torsion forms and adiabatic limitMay 22 2014In this article we use the adiabatic method to prove the gluing formula of real analytic torsion forms for a flat vector bundle on a smooth fibration under the assumption that the fiberwise twisted cohomology groups associated to the fibration of the ... More

Recent Electroweak Results from the TevatronJul 18 2009I present the recent electroweak measurements related to single W, Z boson and diboson productions from the CDF and D0 experiments at the Fermilab Tevatron collider.

Electroweak and QCD Results from the TevatronSep 02 2011We report the latest electroweak and QCD results from two Tevatron experiments.

Log canonical thresholds in positive characteristicAug 25 2013In this paper, we study the singularities of a pair (X,Y) in arbitrary characteristic via jet schemes. For a smooth variety X in characteristic 0, Ein, Lazarsfeld and Mustata showed that there is a correspondence between irreducible closed cylinders and ... More

Viscosity solutions to second order parabolic PDEs on Riemannian manifoldsJun 08 2010In this work we consider viscosity solutions to second order parabolic PDEs $u_{t}+F(t,x,u,du,d^{2}u)=0$ defined on compact Riemannian manifolds with boundary conditions. We prove comparison, uniqueness and existence results for the solutions. Under the ... More

Two Boundary Centralizer Algebras for $\mathfrak{q}(n)$Jan 29 2019We define the degenerate two boundary affine Hecke-Clifford algebra $\mathcal{H}_d$, and show it admits a well-defined $\mathfrak{q}(n)$-linear action on the tensor space $M\otimes N\otimes V^{\otimes d}$, where $V$ is the natural module for $\mathfrak{q}(n)$, ... More

Derived equivalence between Shioda's fourfold and CM Mumford fourfoldOct 23 2018Shioda 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

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

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

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.

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

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

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

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

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

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

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

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.